A Calculation Method for the Reachable Region of the Relative Motion of a Spacecraft in Monopulse

Abstract

The present invention provides a method for calculating the reachable domain of the relative motion of a spacecraft in monopulse. Relevant parameters for calculating the reachable domain of the relative motion of the monopulse are collected; according to the reference orbital altitude, the state transfer matrix of the relative motion of the spacecraft corresponding to any moment is obtained; and the natural evolution position of the relative motion of the spacecraft is obtained; a three-layer calculation loop is constructed to obtain the relative reachable position increment and the relative reachable position at different moments, different pitch angles, and different yaw angles; for any moment, taking the relative reachable position as discrete points and traversing all the values of the middle loop and the inner loop, a convex polyhedron is constructed to obtain the reachable domain at that arbitrary moment, and a spatial region with the natural evolution position of the relative motion of the spacecraft as the center and the convex polyhedron as the envelope boundary is obtained, and a set composed of the total relative reachable domains is obtained; the present application uses the relative state transfer matrix to realize the calculation of the natural evolution of the relative motion and the calculation of the reachable airspace under a given pulse, and has the advantages of high calculation efficiency and good accuracy.

Description

Technical Field

[0001] The design of the present invention belongs to the field of aerospace technology, and particularly relates to a method for calculating the reachable domain of the relative motion of a spacecraft with a single pulse. Background Art

[0002] In the spacecraft orbital game mission, there is often a need to calculate the reachable range of motion under a given control action. On the one hand, this can provide a basis for each spacecraft participating in the orbital game mission to evaluate its own maneuverability. On the other hand, it also provides a prerequisite for the selection and optimization of the game strategies of all parties. For example, for a pair of spacecraft in a pursuit-evasion process, the escaping spacecraft hopes to reach a place that the pursuing spacecraft cannot reach, so as to avoid danger. At this time, if there is a method that can calculate the reachable domain of motion under a given control, the escaping spacecraft can move towards the space outside the reachable domain of the pursuing spacecraft. Similarly, the pursuing spacecraft should move towards the range of the intersection of the reachable domains of the two as much as possible. Since the orbital game mission has characteristics such as fast response speed, drastic state transformation, short mission decision-making time, and significant mission decision-making consequences, this requires that the reachable domain calculation should meet the dual requirements of rapidity and accuracy.

[0003] In traditional space mission fields such as spacecraft mission planning and design, and space target tracking, some reachable domain calculation methods have emerged, such as Patent [1] (CN201710447097.4), Patent [2] (CN201810837425.6), etc. However, the limitations of these methods are relatively obvious and they are not applicable to the orbital game field with fierce confrontation scenarios. Among them, Patent [1] aims at the absolute reachable domain of a spacecraft in space, which does not meet the requirements of the relative reachable domain widely needed in the orbital game process, and its reachable domain calculation method involves high-time-consuming processes such as nonlinear calculation, and the rapidity of calculation is poor. While Patent [2] aims at the relative reachable domain calculation problem, but it solves the reachable domain solution under continuous control force, rather than the reachable domain calculation under the impulse velocity increment control required by the orbital game mission and its constraints. In addition to the above patents, other patents or papers have also widely reported reachable domain calculation methods applicable to various space missions. However, the existing methods cannot take into account the dual constraints of relative motion and impulse control at the same time, or the given calculation methods are too complex to meet the real-time requirements. Summary of the Invention

[0004] Aiming at the problems existing in the prior art, the present invention provides a method for calculating the reachable domain of the relative motion of a spacecraft with a single pulse, which can support the real-time and accuracy requirements of the relative reachable domain for the orbital game mission.

[0005] The present invention is realized through the following technical solutions:

[0006] A method for calculating the reachable domain of the relative motion of a spacecraft monopulse, characterized by including the following steps:

[0007] S1: Collect the reference orbit altitude, initial time, terminal time, initial relative position, initial relative velocity, maximum value of the single-pulse velocity increment, number of time discretizations, number of pulse pitch angle discretizations, and number of pulse yaw angle discretizations;

[0008] S2: Calculate the reference orbit angular velocity according to the reference orbit altitude, and then calculate the "position-position" transfer matrix and "velocity-position" transfer matrix of the relative motion of the spacecraft corresponding to any time;

[0009] S3: Calculate the natural evolution position of the relative motion of the spacecraft corresponding to any time according to the "position-position" transfer matrix, "velocity-position" transfer matrix, initial relative position, and relative velocity;

[0010] S4: Construct a three-layer calculation loop, including an outer loop, a middle loop, and an inner loop, and then calculate the relative reachable position increment and relative reachable position at different times, different pitch angles, and different yaw angles;

[0011] S5: For any time, construct a convex polyhedron with the relative reachable position as the discrete point and traversing all the values of the middle loop and the inner loop, obtain the reachable domain at this arbitrary time, and obtain the set composed of the total relative reachable domain, which is a spatial region centered on the natural evolution position of the relative motion of the spacecraft and bounded by the convex polyhedron.

[0012] Further, the initial relative position r(t0) is:

[0013] r(t0) = [x0, y0, z0] T ,

[0014] where x is the coordinate of the maneuvering spacecraft on the x-axis of the orbital coordinate system, y is the coordinate of the maneuvering spacecraft on the y-axis of the orbital coordinate system; z is the coordinate of the maneuvering spacecraft on the z-axis of the orbital coordinate system; v x is the velocity component of the maneuvering spacecraft on the x-axis of the orbital coordinate system; v y is the velocity component of the maneuvering spacecraft on the y-axis of the orbital coordinate system; v z is the velocity component of the maneuvering spacecraft on the z-axis of the orbital coordinate system.

[0015] Further, the initial relative velocity v(t0) is:

[0016] v(t0) = fv x0 , v y0 , v z0 T ;

[0017] ​Among them, x is the coordinate of the maneuvering spacecraft on the x-axis of the orbital coordinate system, y is the coordinate of the maneuvering spacecraft on the y-axis of the orbital coordinate system; z is the coordinate of the maneuvering spacecraft on the z-axis of the orbital coordinate system; v x is the velocity component of the maneuvering spacecraft on the x-axis of the orbital coordinate system; v y is the velocity component of the maneuvering spacecraft on the y-axis of the orbital coordinate system; v z is the velocity component of the maneuvering spacecraft on the z-axis of the orbital coordinate system.

[0018] Furthermore, the orbital angular velocity is:

[0019]

[0020] Among them, μ = 3.986×10 14 is the Earth's gravitational constant, with the unit of rad 2 ·s -2 ·m 3 ; a E = 6378137 is the average radius of the Earth, with the unit of meters.

[0021] Furthermore, the "position-position" transfer matrix is:

[0022]

[0023] Among them, φ 11 = 4 - 3cosθ, φ 21 = 6(sinθ - θ), φ 33 = cosθ; and θ = ω·(t i - t).

[0024] Furthermore, the "velocity-position" transfer matrix is:

[0025]

[0026] Among them, φ 24 = -φ 15 , φ 36 = φ 14 ; and θ = ω·(t i - t).

[0027] Furthermore, the natural evolution position is:

[0028] r p (t i ) = Φ rr (t i , t0)·r(t0) + Φ rv (ti , t0)·v(t0);

[0029] Among them,

[0030] Furthermore, the outer loop (i = 1, 2, …, n t ), the middle loop (j = 1, 2, …, n α ), the inner loop (k = 1, 2, …, n β );

[0031] The relative reachable position increment is Δr(t i , α j , β k ):

[0032] Δr(t i , α j , β k ) = Φ rv (t i , t0)·Δv j,k ;

[0033] Among them, Δv j,k = [cosα j cosβ k , cosα j sinβ k , sinα j T ·Δv max ,

[0034] Furthermore, the relative reachable position is r(t i , α j , β k ):

[0035] r(t i , α j , β k ) = r p (t i ) + Δr(t i , α j , β k );

[0036] Among them,

[0037] Furthermore, the specific method for constructing the convex polyhedron S i is:

[0038] Using the Delaunay triangulation algorithm, with all discrete points r(t i , α j , β​k )Construct a triangulation matrix \(T\) based on the foundation i ;

[0039] Using the Graham scan method, starting from the triangulation matrix \(T\) i to obtain a convex polyhedron \(S\) i ;

[0040] where \(j = 1, 2, \cdots, n\) α , \(k = 1, 2, \cdots, n\) β .

[0041] Compared with the prior art, the present invention has the following beneficial technical effects:

[0042] The present invention provides a method for calculating the reachable domain of the relative motion of a spacecraft single pulse, which collects the reference orbit altitude, initial time, terminal time, initial relative position, initial relative velocity, maximum value of the single pulse velocity increment, number of time discretizations, number of pulse pitch angle discretizations, and number of pulse yaw angle discretizations; according to the reference orbit altitude, calculates the reference orbit angular velocity, and further calculates the "position-position" transfer matrix and "velocity-position" transfer matrix of the relative motion of the spacecraft at any corresponding time; calculates the natural evolution position of the relative motion of the spacecraft at any corresponding time according to the "position-position" transfer matrix, "velocity-position" transfer matrix, initial relative position and relative velocity; constructs a three-layer calculation loop, including an outer loop, a middle loop and an inner loop, and then calculates the relative reachable position increment and relative reachable position at different times, different pitch angles and different yaw angles; for any time, taking the relative reachable position as discrete points and traversing all the values of the middle loop and the inner loop, constructs a convex polyhedron, obtains the reachable domain at this arbitrary time, and takes the natural evolution position of the relative motion of the spacecraft as the center and the convex polyhedron as the envelope boundary of the space region, obtains the set composed of the total relative reachable domain; the present application uses the relative state transfer matrix to realize the calculation of the natural evolution of the relative motion and the calculation of the reachable airspace under a given pulse, and can calculate the space range that can be reached after any discrete time within a given time range starting from any initial relative state and applying a pulse velocity increment with a given upper limit constraint near any given reference orbit; it has the advantages of high calculation efficiency and good accuracy, provides conditions for the optimal selection of game strategies for orbital game tasks, and the present application can also be extended to fields such as space orbit rendezvous, orbital maneuver and on-orbit service. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flow chart of a method for calculating the reachable domain of the relative motion of a spacecraft single pulse according to the present invention;

[0044] Figure 2 is a schematic diagram of the convex polyhedron obtained at time \(t1\) in a specific embodiment of the present invention;

[0045] Figure 3 It is a schematic diagram of the convex polyhedron obtained at time t2 in a specific embodiment of the present invention;

[0046] Figure 4 It is a schematic diagram of the convex polyhedron obtained at time t3 in a specific embodiment of the present invention;

[0047] Figure 5 It is a schematic diagram of the convex polyhedron obtained at time t4 in a specific embodiment of the present invention. Specific embodiments

[0048] The following further elaborates on the present invention in conjunction with specific embodiments, which is an explanation rather than a limitation of the present invention.

[0049] To enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

[0050] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units does not necessarily need to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products, or devices.

[0051] The present invention provides a method for calculating the reachable domain of the relative motion of a spacecraft single pulse, as Figure 1 shown, including the following steps:

[0052] S1: Collect the reference orbit altitude, initial time, terminal time, initial relative position, initial relative velocity, maximum value of the single-pulse velocity increment, number of time discretizations, number of pulse pitch angle discretizations, and number of pulse yaw angle discretizations;

[0053] S2: According to the reference orbit altitude, calculate the reference orbit angular velocity, and then calculate the "position-position" transfer matrix and "velocity-position" transfer matrix of the relative motion of the spacecraft corresponding to any time;

[0054] S3: Calculate the natural evolution position of the relative motion of the spacecraft corresponding to any moment based on the "position - position" transfer matrix, the "velocity - position" transfer matrix, the initial relative position, and the relative velocity;

[0055] S4: Construct a three - layer calculation loop, including an outer loop, a middle loop, and an inner loop, and then calculate the relative reachable position increment and the relative reachable position at different moments, different pitch angles, and different yaw angles;

[0056] S5: For any moment, construct a convex polyhedron with the relative reachable position as discrete points and traversing all values of the middle loop and the inner loop, obtain the reachable domain at this arbitrary moment, and obtain the set composed of the total relative reachable domains, which is a spatial region centered on the natural evolution position of the spacecraft relative motion and with the convex polyhedron as the envelope boundary.

[0057] Preferably, the initial relative position r(t0) is:

[0058] r(t0) = [x0, y0, z0] T ,

[0059] The initial relative velocity v(t0) is:

[0060] v(t0) = [v x0 , v y0 , v z0 T ;

[0061] where x is the coordinate of the maneuvering spacecraft on the x - axis of the orbital coordinate system, y is the coordinate of the maneuvering spacecraft on the y - axis of the orbital coordinate system; z is the coordinate of the maneuvering spacecraft on the z - axis of the orbital coordinate system; v x is the velocity component of the maneuvering spacecraft on the x - axis of the orbital coordinate system; v y is the velocity component of the maneuvering spacecraft on the y - axis of the orbital coordinate system; v z is the velocity component of the maneuvering spacecraft on the z - axis of the orbital coordinate system.

[0062] Preferably, the orbital angular velocity is:

[0063]

[0064] where μ = 3.986×10 14 is the Earth's gravitational constant, with the unit of rad 2 ·s -2 ·m 3 ; a E = 6378137 is the average radius of the Earth, with the unit of meters.

[0065] Preferably, the "position - position" transfer matrix is:

[0066]

[0067] The "speed - position" transfer matrix is:

[0068]

[0069] Among them, φ 11 = 4 - 3cosθ, φ 21 = 6(sinθ - θ), φ 33 = cosθ, φ 24 = -φ 15 , φ 36 = φ 14 ; and θ = ω·(t i - t).

[0070] Preferably, the natural evolution position is:

[0071] r p (t i ) = Φ rr (t i , t0)·r(t0) + Φ rv (t i , t0)·v(t0);

[0072] Preferably, the outer loop (i = 1, 2,..., n t ), middle loop (j = 1, 2,..., n α ), inner loop (k = 1, 2,..., n β );

[0073] The relative reachable position increment is Δr(t i , α j , β k ):

[0074] Δr(t i , α j , β k ) = Φ rv (t i , t0)·Δv j,k ;

[0075] Among them, Δv j,k = [cosα j cosβ k , cosα j sinβ k , sinα j T ·Δv​max ;

[0076] The relative reachable position is r(t i , α j , β k ):

[0077] r(t i , α j , β k ) = r p (t i ) + Δr(t i , α j , β k );

[0078] Wherein

[0079] Preferably, the specific method for constructing the convex polyhedron S i is as follows: Using the Delaunay triangulation algorithm, taking all discrete points r(t i , α j , β k ) as the basis to construct a triangulation matrix T i ;

[0080] Using the Graham scan method, starting from the triangulation matrix T i to obtain the convex polyhedron S i ;

[0081] where j = 1, 2,..., n α , k = 1, 2,..., n β .

[0082] A preferred embodiment of the present invention is as follows:

[0083] Assume that near a circular reference orbit with an orbital altitude h = 500 km, there is a spacecraft. Its initial relative position and velocity are shown in Table 1, and the upper limit of the single-pulse velocity increment is Δv max = 1 m / s. Assume that the initial time t0 = 0 and the terminal time t f = 1000 s. The number of time discretizations n t = 10, the number of pulse pitch angle discretizations n α = 20, and the number of pulse yaw angle discretizations n β = 20. It is required to calculate the relative motion reachable domain at all discrete times.

[0084] Table 1 Initial relative position and velocity of the spacecraft

[0085] Component <![CDATA[x0(m)]]> <![CDATA[y0(m)]]> <![CDATA[z0(m)]]> <![CDATA[v x0 (m / s)]]> <![CDATA[v y0 (m / s)]]> <![CDATA[v z0 (m / s)]]> Value 1000 2000 3000 1 2 3

[0086] The following gives the specific implementation steps of using this invention patent.

[0087] S1, input the reference orbit altitude h, initial time t0, terminal time t f , initial relative position r(t0), initial relative velocity v(t0), maximum single-pulse velocity increment Δv max , number of time discretizations n t , number of pulse pitch angle discretizations n α , number of pulse yaw angle discretizations n β . See the relevant numerical values in the aforementioned problem background introduction and the data in Table 1.

[0088] S2, according to the reference orbit altitude h, calculate the reference orbit angular velocity ω, and then calculate the "position-position" transfer matrix Φ i of the relative motion of the spacecraft corresponding to any time t rr (t i , t0) and the "velocity-position" transfer matrix Φ rv (t i , t0); where

[0089] First, substitute h = 500×10 3 m into the formula where μ = 3.986×10 14 , a E = 6378137, and obtain: ω = 0.0011 rad / s.

[0090] Then, calculate the transfer matrices at each time t i as follows:

[0091]

[0092] where: φ 11 = 4 - 3cosθ, φ 21 = 6(sinθ - θ), φ 33 = cosθ, φ 24 = -φ 15 , φ 36 = φ 14 ; and θ = 0.0011·t i .

[0093] S3, according to the transfer matrices Φ rr (t i , t0), Φ rv (t i , t0) and the initial relative position r(t0), relative velocity v(t0), calculate the relative position at any time t iThe natural evolution position \(r\) of the corresponding spacecraft's relative motion p (t i ), and the calculation formula is:

[0094] r p (t i ) = Φ rr (t i , t0)·r(t0) + Φ rv (t i , t0)·v(t0);

[0095] where \(t\) i = 100·i, i = 1, 2, …, 10. The specific results of \(r\) p (t i ) are shown in Table 2:

[0096] Table 2 Natural evolution positions of the spacecraft's relative motion at each discrete moment

[0097] <![CDATA[t i (s)]]> <![CDATA[x(t i )(m)]]> <![CDATA[y(t i )(m)]]> <![CDATA[z(t i )(m)]]> 100 1140.3 2186.0 3281.0 200 1359.8 2332.1 3521.9 300 1655.8 2421.0 3719.7 400 2024.7 2436.4 3872.0 500 2462.0 2362.3 3976.8 600 2962.4 2184.4 4033.1 700 3519.7 1889.4 4039.9 800 4127.1 1465.2 3997.4 900 4777.2 901.8 3905.9 1000 5462.0 190.4 3766.6

[0098] S4, construct a three - layer calculation loop, specifically:

[0099] For i = 1, 2, …, 10;

[0100] For j = 1, 2, …, 20;

[0101] For k = 1, 2, …, 20;

[0102] t i = 100·i, α j = 0.1π·j - π, β k = 0.1π·k;

[0103] Δv j,k = [cosα j cosβ k , cosα j sinβ k , sinα j T ·Δv max ;

[0104] Δr(t i , α j , β k ) = Φ rv (t i , t0)·Δv j,k ;

[0105] r(t i , α j , β k ) = r​p (t i ) + Δr(t i , α j , β k )。

[0106] End

[0107] End

[0108] End

[0109] Furthermore, the relative reachable position increment Δr(t i , different pitch angles α j , and different yaw angles β k ) and the relative reachable position r(t i , α j , β k ) are calculated at different times t i , α j , β k ); Due to the large amount of data (10×20×20×2 = 8000), no specific display is made here.

[0110] S5. For any time t i , taking r(t i , α j , β k ) as discrete points and traversing all values of j and k, a convex polyhedron S i is constructed. Specifically, first, the Delaunay triangulation algorithm is used to construct a triangulation matrix T i , α j , β k ) (where j = 1, 2,..., 20 and k = 1, 2,..., 20) as the basis; then the Graham scan method is used to obtain the convex polyhedron S i starting from the triangulation matrix T i . The convex polyhedra at four times t1 = 100s, t3 = 300s, t6 = 600s, and t i = 1000s are shown in 10 , Figure 2 , Figure 3 , Figure 4 and Figure 5 respectively. Then the reachable domain at time t i is: a spatial region Φ p (t i ) centered at r i with the convex polyhedron S i as the envelope boundary; the total relative reachable domain is the set composed of Φ i , that is, Φ = {Φ i i = 1, 2,..., nt}。

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the reachable domain of the relative motion of a spacecraft monopulse, characterized in that Including the following steps: S1: Collect the reference orbit altitude, initial time, terminal time, initial relative position, initial relative velocity, maximum value of single-pulse velocity increment, number of time discretizations, number of pulse pitch angle discretizations, and number of pulse yaw angle discretizations; S2: Calculate the reference orbit angular velocity based on the reference orbit altitude, and then calculate the "position-position" transfer matrix and "velocity-position" transfer matrix of the relative motion of the spacecraft corresponding to any time; S3: Calculate the natural evolution position of the relative motion of the spacecraft corresponding to any time based on the "position-position" transfer matrix, "velocity-position" transfer matrix, initial relative position, and relative velocity; S4: Construct a three-layer calculation loop, including an outer loop, a middle loop, and an inner loop, and then calculate the relative reachable position increment and relative reachable position at different times, different pitch angles, and different yaw angles; The outer loop (i = 1, 2, …, n t ), the middle loop (j = 1, 2, …, n α ), and the inner loop (k = 1, 2, …, n β ); The relative reachable position increment is Δr(t i , α j , β k ): Δr(t i ,α j ,β k ) = Φ rv (t i ,t0)·Δv j,k ; where, Δv j,k = [cosα j cosβ k , cosα j sinβ k , sinα j T ·Δv max , Φ rv (t i , t0) represents the "velocity-position" transfer matrix; t0 represents the initial time, t f represents the terminal time;​ Δv max represents the maximum value of the single-pulse velocity increment, n t represents the number of time discretizations; n α represents the number of pulse pitch angle discretizations; n β represents the number of pulse yaw angle discretizations; The relative reachable position is r(t i , α j , β k ): r(t i ,α j ,β k ) = r p (t i ) + Δr(t i ,α j ,β k ); Among them, t i represents any moment, α j represents different pitch angles, β k represents different yaw angles; r p (t i ) represents the natural evolution position; S5: For any time, construct a convex polyhedron with the relative reachable position as the discrete points and traversing all the values of the middle loop and the inner loop, obtain the reachable domain at this arbitrary time, and obtain the set composed of the total relative reachable domains, which is a spatial region centered on the natural evolution position of the relative motion of the spacecraft and bounded by the convex polyhedron as the envelope boundary.

2. The method for calculating the reachable domain of the relative motion of a single pulse of a spacecraft according to claim 1, wherein The initial relative position r(t0) is: r(t0) = [x0, y0, z0] T , Among them, x is the coordinate of the maneuvering spacecraft on the x-axis of the orbital coordinate system, y is the coordinate of the maneuvering spacecraft on the y-axis of the orbital coordinate system; z is the coordinate of the maneuvering spacecraft on the z-axis of the orbital coordinate system; v x is the velocity component of the maneuvering spacecraft on the x-axis of the orbital coordinate system; v y is the velocity component of the maneuvering spacecraft on the y-axis of the orbital coordinate system; v z is the velocity component of the maneuvering spacecraft on the z-axis of the orbital coordinate system.

3. The method for calculating the reachable domain of the relative motion of a single pulse of a spacecraft according to claim 1, characterized in that The initial relative velocity v(t0) is: v(t0) = [v x0 , v y0 , v z0 T ;​ where x is the coordinate of the maneuvering spacecraft on the x-axis of the orbital coordinate system, y is the coordinate of the maneuvering spacecraft on the y-axis of the orbital coordinate system; z is the coordinate of the maneuvering spacecraft on the z-axis of the orbital coordinate system; v x is the velocity component of the maneuvering spacecraft on the x-axis of the orbital coordinate system; v y is the velocity component of the maneuvering spacecraft on the y-axis of the orbital coordinate system; v z is the velocity component of the maneuvering spacecraft on the z-axis of the orbital coordinate system.

4. The method for calculating the reachable domain of the relative motion of a single pulse of a spacecraft according to claim 1, wherein The orbit angular velocity is: where μ = 3.986×10 14 is the Earth's gravitational constant, with the unit of rad 2 ·s -2 ·m 3 ; a E = 6378137 is the average radius of the Earth, and h represents the reference orbit altitude.

5. The calculation method of the reachable domain of the relative motion of a single pulse of a spacecraft according to claim 1, characterized in that, The "position-position" transfer matrix is: Among them, φ 11 = 4 - 3cosθ, φ 21 = 6(sinθ - θ), φ 33 = cosθ; and there is θ = ω·(t i - t).

6. The method for calculating the reachable domain of the relative motion of a single pulse of a spacecraft according to claim 1, characterized in that, The "velocity-position" transfer matrix is: Among them, φ 24 = -φ 15 , φ 36 = φ 14 ; and there is θ = ω·(t i - t).

7. The method for calculating the reachable domain of the relative motion of a single pulse of a spacecraft according to claim 1, characterized in that, The natural evolution position is: r p (t i ) = Φ rr (t i , t0)·r(t0) + Φ rv (t i , t0)·v(t0); Among them, 8. The method for calculating the reachable domain of the relative motion of a single pulse of a spacecraft according to claim 1, characterized in that, The described convex polyhedron S i The specific method is as follows: Using the Delaunay triangulation algorithm, based on all discrete points r(t i , α j , β k ), construct the triangulation matrix T i ; Using the Graham scan method, starting from the triangulation matrix T i to obtain the convex polyhedron S i ; where j = 1, 2, …, n α , k = 1, 2, …, n β .

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