CN117485604A - Intersection window rapid planning method for low-orbit spacecraft - Google Patents

Intersection window rapid planning method for low-orbit spacecraft Download PDF

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Publication number
CN117485604A
CN117485604A CN202311440730.9A CN202311440730A CN117485604A CN 117485604 A CN117485604 A CN 117485604A CN 202311440730 A CN202311440730 A CN 202311440730A CN 117485604 A CN117485604 A CN 117485604A
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rocket
window
range
target
intersection
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乔栋
庞博
温昶煊
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/64—Systems for coupling or separating cosmonautic vehicles or parts thereof, e.g. docking arrangements
    • B64G1/646—Docking or rendezvous systems
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • Automation & Control Theory (AREA)
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Abstract

The invention discloses a low-orbit spacecraft-oriented intersection window rapid planning method, and belongs to the field of aerospace. The implementation method of the invention comprises the following steps: after the rocket applied to ground launching reaches the atmospheric edge, the rocket meets a target spacecraft in the ascending process after one maneuver. And obtaining an intersection window for the spacecraft intersection target task. The rapid planning of the intersection window mainly comprises three steps, wherein in the first step, the ascending reachable range is obtained according to the envelope of the rocket shutdown point and the pulse size; secondly, judging a coarse window by utilizing the height, the range reaching range and the target in the ground system position of the lifter; and thirdly, after the rough window is obtained, shooting the rocket to a target direction, obtaining a shutdown point position under an inertia system, calculating a speed increment by adopting a Lambert method based on the shutdown point position, and judging that the rocket can meet the target if the constraint is met, namely, realizing the rapid planning of the meeting window facing the low-orbit spacecraft. The method has the advantages of high planning speed and strong applicability.

Description

Intersection window rapid planning method for low-orbit spacecraft
Technical Field
The invention relates to a method for rapidly planning a meeting window for a low-orbit spacecraft, in particular to a method for rapidly planning and obtaining the meeting window aiming at the meeting problem of a low-orbit non-cooperative spacecraft, and belongs to the field of aerospace.
Background
Near-earth space is a major area of many aerospace activities, including satellite launching, space exploration, and international space stations, among others, and there are many hidden hazards to near-earth space, such as space debris, waste satellite fragments, and the like. The meeting of the low-orbit spacecraft is an effective means for ensuring the safety of the task in the near-earth space. There are a large number of aircrafts in the near-earth space at any time, and when the existence of the abandoned or the safety-threatening aircrafts is found, the abandoned or the safety-threatening aircrafts need to be intersected in time. The intersection technology for the low-orbit spacecraft is a key technology in the field, and the determination of the intersection window for the low-orbit spacecraft is a precondition for realizing the intersection.
In the research of the developed spacecraft intersection window calculation, in the prior art [1] (see [1] Gu Fei reach, han Hongwei, wen. Target interception emission window calculation based on the ascending track reachable range [ J ]. Astronomy report 2022,43 (04): 403-412.), an emission window planning method utilizing ascending track reachable range analysis is proposed for the low-orbit target interception task. And determining the ascending reachable range of the interceptor based on the ascending track optimization model, and performing primary screening on the emission window according to the crossing relation of the target understar point and the outer envelope of the ascending track reachable range. Finally, aiming at the screened quasi-emission window, the position relation between the target understar point and each rising duration reachable range subring is accurately judged, so that the accurate emission window is obtained. Because the optimization solution and the reachable range comparison of the track are required to be continuously carried out, the time consumption is long, and the problem of rapid planning of the intersection window of the non-cooperative spacecraft cannot be solved. Meanwhile, the technology does not consider the conditions of burnup constraint, illumination constraint and the like, and can not solve the problem of meeting windows considering various constraints.
In the prior art [2] (see Duan J H.Rapid onboard generation of two-dimensional rendezvous windows for autonomous rendezvous mission [ J ]. The Journal of the Astronautical Sciences,2020, 67:1320-1343.) the reachable phase range on the target orbit is calculated based on the spacecraft two-dimensional reachable domain, firstly taking into account the waiting time constraint, then the reachable phase range of the target orbit in the interceptor reachable domain is further determined based on the interceptor fuel constraint, and finally the final intersection window is obtained according to the constraint of the total mission time. However, the method is only suitable for the space-based interception problem, and cannot solve the ground-based emission interception problem facing the spacecraft target.
Disclosure of Invention
The intersection described in the present invention refers to the position coincidence of the spacecraft, without constraint on the relative speed. The method aims at the problem of the low-orbit target intersection of the spacecraft, and is characterized in that the action of the target is unknown in advance, so that an intersection window meeting the constraints of speed increment, illumination and the like needs to be obtained in a short time, and the intersection of the target spacecraft is realized. The invention discloses a low-orbit spacecraft-oriented intersection window rapid planning method which aims to solve the technical problems that: aiming at a low-orbit space non-cooperative spacecraft, solving the problem of meeting windows conforming to constraints based on spacecraft capability boundaries under the conditions of burnup constraint, illumination constraint and the like, and planning the meeting track of the spacecraft according to the obtained meeting windows. The method has the advantages of high planning speed and strong applicability.
The aim of the invention is achieved by the following technical scheme.
The invention discloses a low-orbit spacecraft-oriented intersection window rapid planning method which is applied to a rocket launched on the ground to reach the atmosphere edge, and the rocket is intersected with a target spacecraft in the ascending process after one maneuver is carried out on the rocket. And obtaining an intersection window for the spacecraft intersection target task. The rapid planning of the intersection window mainly comprises three steps, wherein in the first step, the ascending reachable range is obtained according to the envelope of the rocket shutdown point and the pulse size; secondly, judging a coarse window by utilizing the height, the range reaching range and the target in the ground system position of the lifter; and thirdly, after the rough window is obtained, shooting the rocket to a target direction, obtaining a shutdown point position under an inertia system, calculating a speed increment by adopting a Lambert method based on the shutdown point position, and judging that the rocket can meet the target if the constraint is met, namely, realizing the rapid planning of the meeting window facing the low-orbit spacecraft.
The invention discloses a low-orbit spacecraft-oriented intersection window rapid planning method, which comprises the following steps:
step one: taking the rocket into consideration, powering off after exiting the earth atmosphere, applying a pulse at a shutdown point, then continuing to ascend and stopping at the highest point, thus realizing the reachable range prediction.
The reachable range refers to a set of positions that can be reached in the process of reaching the highest point after the rocket is pulsed.
Neglecting the earth rotation effect, all directions can be obtained by adjusting rocket shooting direction, and the maximum reachable range of any direction is simplified to be an in-plane reachable range. Define the state of rocket as x when the rocket is shut down 0 ＝[r 0 ,θ 0 ,v r0 ,v t0 ] T Wherein r is 0 For the geocentric sagittal diameter theta at shutdown 0 In order to move the internal geocentric angle of the plane when the machine is turned off, v r0 For radial velocity magnitude, v t0 For the speed of the vertical direction of the sagittal direction of the earth in the motion plane, the speed increment corresponding to the pulse is deltav, and the maneuvering direction is alpha, the rocket state x after the pulse 1 Is that
x 1 ＝[r 0 ,θ 0 ,v r ,v t ] T ＝[r 0 ,θ 0 ,v r0 +Δvcosα,v t0 +Δvsinα] T (1)
Wherein v is r To the radial velocity after maneuver, v t Is the speed of the vertical direction of the sagittal direction of the ground in the plane of the movement after maneuver.
From this state, the eccentricity e and true near point angle f of the rocket after the pulse are obtained 0
Wherein mu is the gravitational constant of the central celestial body,is the post-pulse velocity. The position p= [ r, θ where the rocket can reach] T From the direction of velocity increment alpha and instantaneousThe true near point angle f is completely determined, wherein r is the instantaneous geocentric vector diameter, θ is the geocentric angle in the instantaneous motion plane, and the reachable range of the rocket is +.>Represented as
The altitude h is easily obtained from the rocket position p r ＝r-R e And range s=θ - θ 0 +s 0 ＝f-f 0 +s 0 Wherein R is e Is the radius of the earth, s 0 Is the ascending course in rocket atmosphere.
And (5) solving the reachable range of the rocket according to formulas (5) - (14). At the terminal sagittal radius r f In a fixed condition, its course s is expressed as
Where h is the angular momentum after maneuver, r f Is the terminal geocentric sagittal diameter.
Intermediate function g (r f ,α)
The corresponding pulse direction is satisfied when the range gets the extreme value
In the above
Obtaining an equation by shifting, squaring and arranging the term (7)
Wherein a, b, d are intermediate variables:
equation (9) is a trigonometric higher-order equation of α, and is difficult to solve directly. But when alpha is determined it is r f And thus can be solved inversely. Fixing alpha and solving r corresponding to the requirement (9) f Then at r f When the speed increment is alpha, the range takes the extreme value.
Since only r is considered f ≠r 0 In this case, equation (9) continues to be simplified, giving a representation of r f Is r f The analytical formula of (2) is
Wherein a is j ,b j As an intermediate variable:
traversing alpha epsilon [0,2 pi ], and calculating the corresponding extreme value tail end height by using a formula (11). In the deduction process, the rising condition of the rocket is relaxed, so that the judgment condition is added. If the obtained altitude satisfies the formula (13), the altitude satisfies the rocket ascending period condition, and the altitude can be brought into the formula (5) to obtain the range corresponding to the altitude.
In addition, since only the reachable range during the ascent is considered, the envelope is not complete, and the case where the voyage takes a boundary other than an extremum is considered. When the range gets the boundary, the true near point angle is 180 degrees. The extreme range and altitude corresponding to the speed increment direction alpha is
The reachable range envelope of a single shutdown point is obtained, the state of the shutdown point is traversed, and the reachable range of the rising period of the rocket is obtained by combining.
Step two: the calculation of the entire coarse window is divided into three steps. First, for t c And (3) calculating the ground system position of the target, calculating the position vector of the target relative to the launching point, obtaining the range, comparing the range with the range obtained in the step (A), and judging that the rocket and the target can meet if the range is smaller than the maximum range. Traversing the time period to obtain a coarse window 1 meeting the intersection condition. Second, on the basis of the coarse window 1, t is calculated c And (5) determining whether the range at the moment is satisfied or not according to the target height, and if so, determining that the rocket and the target can meet. Thirdly, calculating the illumination condition on the basis of the rough window 2, and eliminating the window if the intersection time is in the earth shadow area to obtain a final rough window 3.
Step three: based on the obtained coarse window 3, first the intra-window t is calculated c And the moment target is shot relative to the emission point, and the shutdown point envelope is converted into the shot to obtain the state of the shutdown point under the inertia system. And calculating by adopting a Lambert algorithm based on the point, and if the minimum speed increment is smaller than the allowable speed increment Deltav, judging that the rocket and the target can meet, namely realizing the acquisition of the fine window.
Step four: aiming at the low-orbit spacecraft with the preset height, planning the intersecting track of the spacecraft according to the intersecting precision window obtained in the step three, so as to realize the intersection of the rocket and the low-orbit spacecraft.
The beneficial effects are that:
1. the invention discloses a low-orbit spacecraft-oriented intersection window rapid planning method, which predicts the reachable range aiming at each shutdown point, and does not limit the number of the shutdown points, so that the method is suitable for calculating the intersection window given a plurality of atmospheric edge states.
2. According to the low-orbit spacecraft-oriented intersection window rapid planning method disclosed by the invention, the reachable range of the rocket in the ascending stage is calculated in an analytic mode, and the geometric relationship between the reachable range and a target is utilized for judgment, so that the intersection window planning speed is high. The programming speed is fast compared with the prior art [1 ].
3. The invention discloses a low-orbit spacecraft-oriented intersection window rapid planning method, which is used for carrying out fine calculation on windows by considering limitations such as illumination, earth shadow areas and the like on the basis of a coarse window, so that the method is suitable for intersection window planning by considering various constraints; planning the intersecting track of the spacecraft according to the obtained intersecting window, and further realizing the intersection of the rocket and the low-orbit spacecraft.
Drawings
Fig. 1 is a flowchart of a low orbit spacecraft-oriented intersection window rapid planning method disclosed by the invention.
Fig. 2 is a shutdown point reachable range envelope diagram of the low-orbit spacecraft-oriented intersection window rapid planning method disclosed by the invention.
Detailed Description
For a better description of the objects and advantages of the present invention, the following description will be given with reference to the accompanying drawings and examples.
Example 1:
after the rocket launched on the ground reaches the atmosphere edge, the rocket is maneuvered once and then meets the target spacecraft in the ascending process. The meeting window is obtained as the first step of the spacecraft meeting target task, and is the basic condition for successful implementation of the task. The calculation of the intersection window mainly comprises three steps, namely, a first step, obtaining an ascending reachable range according to the envelope of the rocket shutdown point and the pulse size; secondly, judging a coarse window by utilizing the height, the range reaching range and the target in the ground system position of the lifter; and thirdly, after a coarse window is obtained, shooting the rocket to a target direction, obtaining a shutdown point position under an inertia system, calculating a speed increment by adopting a Lambert method based on the shutdown point position, and if the speed increment meets the constraint, considering that the speed increment can meet. The atmospheric edge conditions are shown in table 1.
TABLE 1 atmospheric edge State
Step one: taking the rocket into consideration, powering off after exiting the earth atmosphere, applying a pulse at a shutdown point, then continuing to ascend and stopping at the highest point, thus realizing the prediction of the reachable range of the rocket. The reachable range in the invention refers to the set of positions that can be reached in the process of reaching the highest point after the rocket is pulsed.
Neglecting the earth rotation effect, all directions can be obtained by adjusting the rocket shooting direction, and the maximum reachable range of any direction can be simplified into an in-plane reachable range. Traversing given shutdown points, respectively obtaining the reachable range corresponding to each shutdown point, and then predicting the outer envelope. The outer envelope is formed by a curve formed by connecting a closest curve of the range of a first shutdown point, a farthest curve of the range of a last shutdown point and a farthest point of the reachable range of each shutdown point, and the shape of the outer envelope is approximate to a sector. The furthest distance is 3400km and the maximum height is 3379km. Converting it into altitude schedule with altitude interval of 50km, the result is shown in Table 2
TABLE 2 altitude range table
Step two: the calculation of the whole coarse window is divided into three steps: first, for t c At the moment of time of day,firstly, calculating the ground system position of the target, then calculating the position vector of the relative launching point of the target, obtaining the range, comparing the range with the range obtained in the step one, and judging that the rocket and the target can meet if the range is smaller than the maximum range. Traversing the time period to obtain a coarse window 1 meeting the intersection condition. Second, on the basis of the coarse window 1, t is calculated c And (5) determining whether the range at the moment is satisfied or not according to the target height, and if so, determining that the rocket and the target can meet. Thirdly, calculating the illumination condition on the basis of the rough window 2, and eliminating the window if the intersection time is in the earth shadow area to obtain a final rough window 3.
For t c At the moment, firstly, the ground system position of the target is calculated, then, the position vector of the target relative to the emission point is calculated, the range is compared with the reachable range calculated in the upper subsection, and if the range is smaller than the maximum range, the intersection is judged. Traversing the time period to obtain a coarse window 1 meeting the intersection condition. For target a (six numbers see table 3), the coarse window 1 within 1 day from day 0 of 2021, month 4, 21 is shown in table 4.
TABLE 3 six target counts
TABLE 4 coarse Window 1
On the basis of the coarse window 1, t is calculated c The target height at the moment is determined whether the range at the height is satisfied, and if so, the intersection is determined. And traversing the time of the coarse window 1 to obtain a coarse window 2. Target a is shown in table 5 for a coarse window 2 within 1 day from 2021, 4, 21, day 0.
TABLE 5 coarse Window 2
On the basis of the rough window 2, calculating the illumination condition, and if the intersection time is in the earth shadow area, removing the window to obtain a final rough window 3. Target a is shown in table 6 for a coarse window 3 within 1 day from 2021, 4, 21, day 0.
TABLE 6 coarse Window 3
Step three: based on the obtained coarse window 3, first the intra-window t is calculated c And the moment target is shot relative to the emission point, and the shutdown point envelope is converted into the shot to obtain the state of the shutdown point under the inertia system. And calculating by adopting a Lambert algorithm based on the point, and if the minimum speed increment is smaller than the allowable speed increment Deltav, judging that the rocket and the target can meet, namely realizing the acquisition of the fine window.
Target a is shown in table 7 for the fine window within 1 day from 2021, 4, 21, day 0.
TABLE 7 Fine Window
Step four: aiming at a low-orbit spacecraft with the height of 1100km, planning the intersecting track of the spacecraft according to the intersecting precision window obtained in the step three, so as to realize the intersection of the rocket and the low-orbit spacecraft.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.

Claims (2)

1. A low orbit spacecraft-oriented intersection window rapid planning method is characterized by comprising the following steps of: comprises the following steps of the method,
step one: taking the rocket into consideration, powering off after exiting the earth atmosphere, applying a pulse at a shutdown point, and then continuing to ascend and stopping at the highest point to realize the reachable range prediction;
the reachable range refers to a position set which can be reached in the process of reaching the highest point after the rocket is applied with a pulse;
neglecting the earth rotation influence, all directions can be obtained by adjusting rocket shooting, and the maximum reachable range of any direction is simplified into an in-plane reachable range; define the state of rocket as x when the rocket is shut down 0 ＝[r 0 ,θ 0 ,v r0 ,v t0 ] T Wherein r is 0 For the geocentric sagittal diameter theta at shutdown 0 In order to move the internal geocentric angle of the plane when the machine is turned off, v r0 For radial velocity magnitude, v t0 For the speed of the vertical direction of the sagittal direction of the earth in the motion plane, the speed increment corresponding to the pulse is deltav, and the maneuvering direction is alpha, the rocket state x after the pulse 1 Is that
x 1 ＝[r 0 ,θ 0 ,v r ,v t ] T ＝[r 0 ,θ 0 ,v r0 +Δvcosα,v t0 +Δvsinα] T (1)
Wherein v is r To the radial velocity after maneuver, v t The speed of the vertical direction of the sagittal direction of the earth in the plane of motion after maneuver;
from this state, the eccentricity e and true near point angle f of the rocket after the pulse are obtained 0
Wherein mu is the gravitational constant of the central celestial body,is the post-pulse velocity; the position p= [ r, θ where the rocket can reach] T Is completely determined by the speed increment direction alpha and the instantaneous true near point angle f, wherein r is the instantaneous geocentric vector diameter, theta is the geocentric angle in the instantaneous motion plane, and the reachable range of the rocket is +.>Represented as
The altitude h is easily obtained from the rocket position p r ＝r-R e And range s=θ - θ 0 +s 0 ＝f-f 0 +s 0 Wherein R is e Is the radius of the earth, s 0 Is the ascending course in rocket atmosphere;
solving the reachable range of the rocket according to formulas (5) - (14); at the terminal sagittal radius r f In a fixed condition, its course s is expressed as
Where h is the angular momentum after maneuver, r f Is the terminal geocentric sagittal diameter;
intermediate function g (r f ,α)
The corresponding pulse direction is satisfied when the range gets the extreme value
In the above
Obtaining an equation by shifting, squaring and arranging the term (7)
Wherein a, b, d are intermediate variables:
the formula (9) is a trigonometric function higher-order equation of alpha, and is difficult to solve directly; but when alpha is determined it is r f So that an inverse solution can be made; fixing alpha and solving r corresponding to the requirement (9) f Then at r f When the speed increment is alpha, the range obtains an extreme value;
since only r is considered f ≠r 0 In this case, equation (9) continues to be simplified, giving a representation of r f Is r f The analytical formula of (2) is
Wherein a is j ,b j As an intermediate variable:
traversing alpha epsilon [0,2 pi ], and calculating the corresponding extreme value terminal height by using a formula (11); in the deduction process, the rising condition of the rocket is relaxed, so that a judging condition is needed to be added; if the obtained altitude meets the formula (13), the altitude meets the condition of the rising period of the rocket, and the altitude is brought into the formula (5) to obtain the range corresponding to the altitude;
in addition, since only the reachable range during the rising period is considered, the envelope is not complete, and the situation that the voyage gets the boundary instead of the extremum is considered; when the range gets the boundary, the true near point angle is 180 degrees; the extreme range and altitude corresponding to the speed increment direction alpha is
The reachable range envelope of a single shutdown point is obtained, the state of the shutdown point is traversed, and the reachable range of the rising period of the rocket is obtained by combining;
step two: the calculation of the whole coarse window is divided into three steps; first, for t c Firstly, calculating the ground system position of the target, then calculating the position vector of the target relative to the launching point, obtaining the range, comparing the range with the reachable range obtained in the step one, and judging that the rocket and the target can meet if the range is smaller than the maximum range; traversing the time period to obtain a coarse window 1 meeting the intersection condition; second, on the basis of the coarse window 1, t is calculated c The target height at the moment is judged whether the range at the height is satisfied, and if so, the rocket and the target can meet; thirdly, calculating the illumination condition on the basis of the rough window 2, and eliminating the window if the intersection time is in the earth shadow area to obtain a final rough window 3;
step three: based on the obtained coarse window 3, first the intra-window t is calculated c The moment target is shot relative to the emission point, the envelope of the shutdown point is converted into the shot, and the state of the shutdown point under the inertia system is obtained; and calculating by adopting a Lambert algorithm based on the point, and if the minimum speed increment is smaller than the allowable speed increment Deltav, judging that the rocket and the target can meet, namely realizing the acquisition of the fine window.
2. The method for rapidly planning the meeting window of the low-orbit spacecraft according to claim 1, wherein the method comprises the following steps: the method also comprises the following steps: aiming at the low-orbit spacecraft with the preset height, planning the intersecting track of the spacecraft according to the intersecting precision window obtained in the step three, so as to realize the intersection of the rocket and the low-orbit spacecraft.
CN202311440730.9A 2023-11-01 2023-11-01 Intersection window rapid planning method for low-orbit spacecraft Pending CN117485604A (en)

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