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

Abstract

The invention discloses a rapid rendezvous window planning method for low-orbit spacecraft, which belongs to the field of aerospace. The implementation method of the present invention is as follows: after a rocket used for ground launch reaches the edge of the atmosphere, the rocket performs a maneuver and then rendezvous with the target spacecraft during its ascent. Obtain the rendezvous window for the spacecraft rendezvous target mission. The rapid planning of the rendezvous window is mainly divided into three steps. The first step is to obtain the ascending reachable range based on the envelope of the rocket shutdown point and the pulse size. The second step is to use the height, range reachable range and target fixation of the ascender on the ground. The system position is used to judge the coarse window; the third step is to obtain the coarse window, turn the rocket direction to the target direction, obtain the shutdown point position in the inertial system, and use the Lambert method to calculate the velocity increment based on this point, if the constraints are met , then it is determined that the rocket and the target can rendezvous, that is, rapid planning of the rendezvous window for low-orbit spacecraft is achieved. The invention has the advantages of fast planning speed and strong applicability.

Description

A rapid planning method for rendezvous windows for low-orbit spacecraft

Technical field

The invention relates to a method for rapid planning of rendezvous windows for low-orbit spacecraft, and in particular to a method for quickly planning rendezvous windows for rendezvous problems of low-orbit non-cooperative spacecrafts, and belongs to the field of aerospace.

Background technique

Near-Earth space is the main area of many aerospace activities, including satellite launches, space exploration, and the International Space Station. In addition, there are also many hidden dangers in near-Earth space, such as space debris, abandoned satellite debris, etc. The rendezvous of low-orbit spacecraft is an effective means to ensure the safety of near-Earth space missions. There are a large number of aircraft in the near-Earth space at all times. When an abandoned spacecraft or a spacecraft that poses a threat to its own safety is found, it needs to be rendezvous in a timely manner. The rendezvous technology for low-orbit spacecraft is a key technology in this field, and the determination of the rendezvous window for low-orbit spacecraft is a prerequisite for achieving rendezvous.

In the research on the developed spacecraft rendezvous window calculation, the prior technology [1] (see [1] Jia Feida, Han Hongwei, Wen Changxuan. Target interception and launch window calculation based on the reachable range of the ascending trajectory [J]. Aerospace Acta Sinica Sinica, 2022, 43(04):403-412.), for the low-orbit target interception mission, a launch window planning method using ascending trajectory reachable range analysis is proposed. The ascending reachable range of the interceptor is determined based on the ascending trajectory optimization model, and the launch window is initially screened based on the crossing relationship between the target sub-satellite point and the outer envelope of the ascending trajectory reachable range. Finally, for the selected quasi-launch window, the precise launch window is obtained by accurately determining the positional relationship between the target subsatellite point and the reachable range sub-ring of each ascent time. Since it is necessary to continuously optimize the trajectory and compare the reachable range, it takes a long time and cannot solve the problem of rapid planning of rendezvous windows for non-cooperative spacecraft. At the same time, this technology does not consider conditions such as fuel consumption constraints and illumination constraints, and cannot solve the intersection window problem that considers multiple constraints.

Prior technology [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.), based on the two-dimensional rendezvous windows of the spacecraft reach the domain, first consider the waiting time constraint to calculate the reachable phase range on the target orbit, then based on the interceptor fuel constraint, further determine the reachable phase range of the target orbit within the interceptor reachable domain, and finally obtain the final result based on the total mission duration constraint. rendezvous window. However, this method is only applicable to space-based interception problems and cannot solve ground-based launch interception problems facing spacecraft targets.

Contents of the invention

The rendezvous described in the present invention means that the positions of the spacecraft coincide with each other, and there is no restriction on the relative speed. The characteristic of the spacecraft low-orbit target rendezvous problem is that the target's actions are unknown in advance, so it is necessary to obtain a rendezvous window that satisfies constraints such as speed increment and illumination in a short time to achieve rendezvous with the target spacecraft. The technical problem to be solved by a rapid rendezvous window planning method for low-orbit spacecraft disclosed by the present invention is: for non-cooperative spacecraft in low-orbit space, under conditions such as fuel consumption constraints and illumination constraints, based on the spacecraft capability boundary, Solve the problem of a rendezvous window that meets the constraints, and then plan the spacecraft rendezvous trajectory based on the obtained rendezvous window. The invention has the advantages of fast planning speed and strong applicability.

The object of the present invention is achieved through the following technical solutions.

The invention discloses a rapid rendezvous window planning method for low-orbit spacecraft. It is applied to a ground-launched rocket that reaches the edge of the atmosphere. After the rocket performs a maneuver, it rendezvous with the target spacecraft during its ascent. Obtain the rendezvous window for the spacecraft rendezvous target mission. The rapid planning of the rendezvous window is mainly divided into three steps. The first step is to obtain the ascending reachable range based on the envelope of the rocket shutdown point and the pulse size. The second step is to use the height, range reachable range and target fixation of the ascender on the ground. The system position is used to judge the coarse window; the third step is to obtain the coarse window, turn the rocket direction to the target direction, obtain the shutdown point position in the inertial system, and use the Lambert method to calculate the velocity increment based on this point, if the constraints are met , then it is determined that the rocket and the target can rendezvous, that is, rapid planning of the rendezvous window for low-orbit spacecraft is achieved.

The invention discloses a quick rendezvous window planning method for low-orbit spacecraft, which includes the following steps:

Step 1: Consider that the rocket shuts down after leaving the earth's atmosphere, and applies a pulse at the shutdown point. Then the rocket continues to rise and stops when it reaches the highest point, that is, the reachable range prediction is achieved.

The reachable range refers to the set of positions that can be reached after the rocket applies a pulse and reaches the highest point.

Ignoring the influence of the earth's rotation, all directions can be obtained by adjusting the rocket direction, and the maximum reachable range in any direction is simplified to the in-plane reachable range. Define _{the state of the rocket} when _{it is} shut _down ^as direction velocity, v _t0 is the velocity in the direction perpendicular to the geocentric radial direction in the motion plane, the velocity increment corresponding to the pulse is Δv, assuming the maneuvering direction is α, then the rocket state x ₁ after the pulse is

x ₁ =[r ₀ ,θ ₀ ,v _r ,v _t ] ^T =[r ₀ ,θ ₀ ,v _r0 +Δvcosα,v _t0 +Δvsinα] ^T (1)

Among them, v _r is the radial velocity after maneuvering, and v _t is the velocity in the direction perpendicular to the geocentric sagittal direction in the motion plane after maneuvering.

From this state, the eccentricity e and true near-point angle f ₀ of the rocket after the pulse are obtained

where μ is the gravitational constant of the central celestial body, is the post-pulse velocity. Then the position p = [r, θ] ^T that the rocket can reach is completely determined by the speed increment direction α and the instantaneous true periapsis angle f, where r is the instantaneous geocentric vector diameter, θ is the geocentric angle in the instantaneous motion plane, and the rocket Reachable range/> Expressed as

From the rocket position p, it is easy to obtain the height h _r = rR _e and the range s = θ - θ ₀ + s ₀ = ff ₀ + s ₀ , where Re _is the radius of the earth and s ₀ is the ascending range of the rocket in the atmosphere.

Solve the rocket reachable range according to formulas (5)-(14). When the terminal vector diameter r _f is fixed, its voyage s is expressed as

where h is the angular momentum after maneuvering, and r _f is the terminal geocentric vector diameter.

Intermediate function g(r _f ,α)

Then the corresponding pulse direction when the voyage reaches the extreme value satisfies

In the above formula

Move the terms of equation (7), square it, and sort it out to get the equation

Where a, b, d are intermediate variables:

Equation (9) is a high-order trigonometric equation of α, which is difficult to solve directly. But when α is determined, it is a quadratic equation of r _f , so it can be solved inversely. Fix α and solve for r _f that satisfies (9). Then at r _f , when the speed increment takes α, the voyage reaches the extreme value.

Since only r _f ≠r ₀ needs to be considered, equation (9) continues to be simplified to obtain a linear equation about r _f . Then the analytical formula of r _f is

Among them, a _j and b _j are intermediate variables:

Traverse α∈[0,2π), and use equation (11) to calculate the corresponding extreme end height. During the derivation process, the rocket's ascent conditions are relaxed, so judgment conditions need to be added. If the obtained altitude satisfies Equation (13), then it meets the conditions of the rocket's ascent period, and can be put into Equation (5) to obtain the range corresponding to this altitude.

In addition, since only the reachable range during the ascent is considered, the above envelope is not complete, and it is also necessary to consider the situation where the voyage reaches the boundary rather than the extreme value. When the voyage reaches the boundary, the true periapsis angle is 180°. Then the extreme range and altitude corresponding to the speed increment direction α are

At this point, the reachable range envelope of a single shutdown point has been obtained. The shutdown point states are traversed and the union is obtained to obtain the reachable range of the rocket during the ascent period.

Step 2: The calculation of the entire coarse window is divided into three steps. In the first step, for time t _c , first calculate the ground-fixed position of the target, then calculate its position vector relative to the launch point, and obtain the range. Compare it with the reachable range obtained in step 1. If it is less than the maximum range, it is determined that the rocket and the target can rendezvous. Traverse the time period to obtain a coarse window 1 that satisfies the intersection condition. In the second step, based on the coarse window 1, calculate the target height at time t _c and determine whether the range at this height is satisfied. If so, it is determined that the rocket and the target can intersect. The third step is to calculate the illumination situation on the basis of coarse window 2. If the intersection moment is in the shadow area of the earth, remove the window and obtain the final coarse window 3.

Step 3: Based on the obtained coarse window 3, first calculate the direction of the target relative to the launch point at time t _c within the window, convert the shutdown point envelope to the direction, and obtain the state of the shutdown point in the inertial frame. Based on this point, the Lambert algorithm is used for calculation. If the minimum speed increment is less than the allowed speed increment Δv, it is determined that the rocket and the target can intersect, that is, the acquisition of the precise window is achieved.

Step 4: For the low-orbit spacecraft at a predetermined height, plan the rendezvous trajectory of the spacecraft according to the precise rendezvous window obtained in step 3, and then realize the rendezvous between the rocket and the low-orbit spacecraft.

Beneficial effects:

1. The invention discloses a fast rendezvous window planning method for low-orbit spacecraft. It predicts the reachable range for each shutdown point and does not limit the number of shutdown points. Therefore, it is suitable for given multiple atmospheric edges. Intersection window calculation for states.

2. The invention discloses a rapid rendezvous window planning method for low-orbit spacecraft. The reachable range of the rocket during the ascent stage is calculated analytically, and the geometric relationship between the reachable range and the target is used for judgment. Therefore, rendezvous window planning high speed. The planning speed is fast compared with the prior art [1].

3. The invention discloses a quick rendezvous window planning method for low-orbit spacecraft. It performs precise calculation of the window by taking into account restrictions such as illumination and the earth's shadow area on the basis of a rough window. Therefore, it is suitable for rendezvous that considers multiple constraints. Window planning: Plan the spacecraft rendezvous trajectory according to the obtained rendezvous window, and then realize the rendezvous between the rocket and the low-orbit spacecraft.

Description of the drawings

Figure 1 is a flow chart of a rapid rendezvous window planning method for low-orbit spacecraft disclosed in the present invention.

Figure 2 is an envelope diagram of the reachable range of the shutdown point of a fast rendezvous window planning method for low-orbit spacecraft disclosed in the present invention.

Detailed ways

In order to better illustrate the purpose and advantages of the present invention, the content of the invention will be further described below in conjunction with the accompanying drawings and examples.

Example 1:

After the ground-launched rocket reaches the edge of the atmosphere, it performs a maneuver and then rendezvous with the target spacecraft during its ascent. Obtaining the rendezvous window is the first step in the spacecraft rendezvous target mission and is the basic condition for the successful implementation of the mission. The calculation of the rendezvous window is mainly divided into three steps. The first step is to obtain the ascent reachable range based on the envelope of the rocket shutdown point and the pulse size. The second step is to use the altitude of the ascender, the range reachable range and the target on the ground. The position of the fixed system is judged as a coarse window; in the third step, after obtaining the coarse window, turn the rocket direction to the target direction to obtain the shutdown point position in the inertial system, and use the Lambert method to calculate the velocity increment based on this point. If If it is constrained, it is considered to be intersectionable. The atmospheric edge status is shown in Table 1.

Table 1 Atmospheric edge states

Step 1: Consider that the rocket shuts down after exiting the earth's atmosphere, applies a pulse at the shutdown point, and then the rocket continues to rise and stops at the highest point, that is, the prediction of the rocket's reachable range is achieved. The reachable range in the present invention refers to the set of positions that can be reached after the rocket applies a pulse and reaches the highest point.

Ignoring the influence of the earth's rotation, all directions can be obtained by adjusting the rocket direction, and the maximum reachable range in any direction can be simplified to the in-plane reachable range. The given shutdown points are traversed, and the reachable range corresponding to each shutdown point is obtained respectively, and then the outer envelope is predicted. The outer envelope is composed of a curve connected by the closest curve of the first shutdown point, the furthest curve of the last shutdown point, and the farthest point of the reachable range of each shutdown point. The shape is approximately a fan shape. The longest range is 3400km and the maximum altitude is 3379km. Convert it to an altitude range table with an altitude interval of 50km. The results are shown in Table 2.

Table 2 Altitude and range range table

Step 2: The calculation of the entire coarse window is divided into three steps: In the first step, for time t _c , first calculate the ground-fixed position of the target, then calculate its position vector relative to the launch point, and obtain the range, which is the same as in step 1. Comparing the obtained reachable range, if it is less than the maximum range, it is determined that the rocket and the target can rendezvous. Traverse the time period to obtain a coarse window 1 that satisfies the intersection condition. In the second step, based on the coarse window 1, calculate the target height at time t _c and determine whether the range at this height is satisfied. If so, it is determined that the rocket and the target can intersect. The third step is to calculate the illumination situation on the basis of coarse window 2. If the intersection moment is in the shadow area of the earth, remove the window and obtain the final coarse window 3.

For time t _c , first calculate the ground-fixed position of the target, then calculate its position vector relative to the launch point, and obtain the range. Compare it with the reachable range obtained in the previous section. If it is less than the maximum range, determine To be rendezvous. Traverse the time period to obtain a coarse window 1 that satisfies the intersection condition. For target A (see Table 3 for six numbers), its rough window 1 within 1 day from 0:00 on April 21, 2021 is shown in Table 4.

Table 3 Target six numbers

Table 4 Coarse Window 1

On the basis of coarse window 1, calculate the target height at time t _c and determine whether the range at this height is satisfied. If so, it is determined that intersection is possible. Traverse the time of coarse window 1 to obtain coarse window 2. The rough window 2 of target A within 1 day from 0:00 on April 21, 2021 is shown in Table 5.

Table 5 Coarse Window 2

On the basis of coarse window 2, the illumination situation is calculated. If the intersection moment is in the shadow area of the earth, the window is eliminated to obtain the final coarse window 3. The coarse window 3 of Target A within 1 day from 0:00 on April 21, 2021 is shown in Table 6.

Table 6 Coarse Window 3

Step 3: Based on the obtained coarse window 3, first calculate the direction of the target relative to the launch point at time t _c within the window, convert the shutdown point envelope to the direction, and obtain the state of the shutdown point in the inertial frame. Based on this point, the Lambert algorithm is used for calculation. If the minimum speed increment is less than the allowed speed increment Δv, it is determined that the rocket and the target can intersect, that is, the acquisition of the precise window is achieved.

The precise window for Target A within 1 day from 0:00 on April 21, 2021 is shown in Table 7.

Table 7 Fine Window

Step 4: For the low-orbit spacecraft at an altitude of 1100km, plan the rendezvous trajectory of the spacecraft according to the precise rendezvous window obtained in step 3, and then realize the rendezvous between the rocket and the low-orbit spacecraft.

The above-mentioned specific description further explains the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above-mentioned are only specific embodiments of the invention and are not intended to limit the protection of the invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims (2)

1. A rapid rendezvous window planning method for low-orbit spacecraft, which is characterized by: including the following steps: Step 1: Consider that the rocket shuts down after leaving the earth's atmosphere, applies a pulse at the shutdown point, and then the rocket continues to rise and stops at the highest point, that is, the reachable range prediction is achieved; The reachable range refers to the set of positions that can be reached after the rocket applies a pulse and reaches the highest point; Ignoring the influence of the earth's rotation, all directions can be obtained by adjusting the rocket direction, and the maximum reachable range in any direction is simplified to the in-plane reachable range; define the state when the rocket is shut down as x ₀ = [r ₀ ,θ ₀ ,v _r0 , v _t0 ] ^T , where r ₀ is the geocentric radial diameter when shutting down, θ ₀ is the geocentric angle in the motion plane when shutting down, v _r0 is the radial velocity, v _t0 is the velocity perpendicular to the geocentric radial direction in the motion plane size, the velocity increment corresponding to the pulse is Δv, assuming the maneuvering direction is α, then the rocket state x ₁ after the pulse is x ₁ =[r ₀ ,θ ₀ ,v _r ,v _t ] ^T =[r ₀ ,θ ₀ ,v _r0 +Δvcosα,v _t0 +Δvsinα] ^T (1) where v _r is the radial velocity after maneuvering, v _t is the velocity in the direction perpendicular to the geocentric sagittal direction in the motion plane after maneuvering; From this state, the eccentricity e and true near-point angle f ₀ of the rocket after the pulse are obtained where μ is the gravitational constant of the central celestial body, is the post-pulse velocity; then the position p=[r,θ] ^T that the rocket can reach is completely determined by the velocity increment direction α and the instantaneous true periapsis angle f, where r is the instantaneous geocentric vector diameter and θ is the instantaneous motion plane. Inland center angle, rocket reachable range/> Expressed as From the rocket position p, it is easy to obtain the height h _r = rR _e and the range s = θ - θ ₀ + s ₀ = ff ₀ + s ₀ , where Re _is the radius of the earth and s ₀ is the ascending range of the rocket in the atmosphere; Solve the rocket reachable range according to formulas (5)-(14); when the terminal vector radius r _f is fixed, its range s is expressed as where h is the angular momentum after maneuvering, r _f is the terminal geocentric vector diameter; Intermediate function g(r _f ,α) Then the corresponding pulse direction when the voyage reaches the extreme value satisfies In the above formula Move the terms of equation (7), square it, and sort it out to get the equation Where a, b, d are intermediate variables: Equation (9) is a high-order trigonometric equation of α, which is difficult to solve directly; but when α is determined, it is a quadratic equation of r _f , so it can be solved inversely; fix α, and solve the corresponding r that satisfies (9) _f , then at r _f , when the speed increment is α, the voyage reaches the extreme value; Since only r _f ≠r ₀ needs to be considered, equation (9) continues to be simplified to obtain a linear equation about r _f . Then the analytical formula of r _f is Among them, a _j and b _j are intermediate variables: Traverse α∈[0,2π) and use equation (11) to calculate the corresponding extreme end height; during the derivation process, the rocket’s ascent condition is relaxed, so a judgment condition needs to be added; if the obtained height satisfies equation (13), Then it meets the conditions of the rocket's ascent period, and it is put into equation (5) to obtain the range corresponding to this altitude; In addition, since only the reachable range during the ascent is considered, the above envelope is not complete. It is also necessary to consider the situation where the range reaches the boundary rather than the extreme value. When the range reaches the boundary, the true periapsis angle is 180°; then the speed increment The extreme range and altitude corresponding to direction α are At this point, the reachable range envelope of a single shutdown point has been obtained. The shutdown point status is traversed and the union is obtained to obtain the reachable range of the rocket during the ascent period; Step 2: The calculation of the entire coarse window is divided into three steps; in the first step, for time t _c , first calculate the ground-fixed position of the target, then calculate its position vector relative to the launch point, and obtain the range, which is the same as in step 1 Comparing the obtained reachable range, if it is less than the maximum range, it is determined that the rocket and the target can intersect; traverse the time period to obtain a coarse window 1 that meets the intersection conditions; the second step is based on the coarse window 1 , calculate the height of the target at time t _c , and determine whether the range at this height is satisfied. If so, it is determined that the rocket and the target can intersect; the third step is to calculate the illumination situation based on the coarse window 2. If the intersection is in the shadow of the earth at the time of intersection Within the area, the window is eliminated to obtain the final rough window 3; Step 3: Based on the obtained coarse window 3, first calculate the direction of the target relative to the launch point at time t _c in the window, convert the shutdown point envelope to the direction, and obtain the state of the shutdown point in the inertial frame; based on this point, use The Lambert algorithm performs calculations. If the minimum speed increment is less than the allowed speed increment Δv, it is determined that the rocket and the target can intersect, that is, the acquisition of the precise window is achieved. 2. A quick rendezvous window planning method for low-orbit spacecraft as claimed in claim 1, characterized in that: it also includes step 4: for the low-orbit spacecraft at a predetermined height, the precise rendezvous window obtained in step 3 is Plan the rendezvous trajectory of the spacecraft to achieve the rendezvous between the rocket and the low-orbit spacecraft.