A natural evolution-based analysis method for optimal pursuit-starting azimuth of track pursuit and escape

Abstract

The application discloses a natural evolution-based analysis method for optimal pursuit-starting direction of orbit pursuit and escape, and comprises the following steps: setting that pursuit and escape are performed on the same orbit plane, establishing an orbit coordinate system with the initial position of the escape spacecraft as the origin based on the orbit height and the initial relative distance between the escape spacecraft and the pursuit spacecraft, and determining the initial state of the escape spacecraft and the pursuit spacecraft; bringing the initial state of the escape spacecraft and the pursuit spacecraft into a spacecraft orbit transfer equation to deduce the relative distance between the pursuit and escape spacecrafts after orbit transfer, and deducing the optimal pursuit-starting direction; solving the optimal pursuit-starting direction by using a numerical solution method, and changing the transfer time to obtain the optimal pursuit-starting direction under different transfer times. Through the deduction of the orbit transfer equation, the optimal pursuit-starting direction on the same orbit plane is obtained, which is helpful to the research on the selection of the initial position in subsequent orbit pursuit and escape.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology and relates to a method for analyzing the optimal pursuit initiation orientation based on natural evolution of orbital pursuit. Background Technology

[0002] During a spacecraft chase, the pursuing spacecraft needs to catch up with the fleeing spacecraft as quickly as possible. However, spacecraft have limited fuel, so relying solely on their own maneuverability to catch up is extremely costly. Utilizing the characteristics of the space environment and selecting a suitable initial pursuit position is essential, as it allows the pursuing spacecraft to catch up with the fleeing spacecraft faster and more fuel-efficiently.

[0003] Currently, spacecraft have a limited detection range; outside this range, they cannot detect enemy information. If a pursuing spacecraft remains outside the detection range of an escaping spacecraft, the escaping spacecraft will not maneuver. Only when the pursuing spacecraft enters its detection range will the escaping spacecraft maneuver. Existing research lacks analysis of the optimal initial pursuit position for the pursuing spacecraft. Summary of the Invention

[0004] The purpose of this invention is to solve the problems in the prior art and provide a method for analyzing the optimal pursuit initiation position based on natural evolution in orbital pursuit, thereby solving the problem of selecting the optimal pursuit initiation position for the pursuing spacecraft in orbital pursuit.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit includes the following steps:

[0007] The pursuit and escape are set to take place on the same orbital plane. Based on the orbital altitude and the initial relative distance between the escaping spacecraft and the pursuing spacecraft, an orbital coordinate system is established with the initial position of the escaping spacecraft as the origin to determine the initial state of the escaping spacecraft and the pursuing spacecraft.

[0008] The initial states of the escaping and pursuing spacecraft are substituted into the spacecraft orbital transfer equations for derivation. The relative distance between the two parties after the orbital transfer time is obtained, and the optimal pursuit initiation position is derived.

[0009] The optimal pursuit initiation position was determined using a numerical solution method, and the optimal pursuit initiation position was obtained under different transfer times by changing the transfer time.

[0010] Furthermore, the X-axis of the orbital coordinate system points from the Earth's center towards the direction of the escaping spacecraft, and the Y-axis is the velocity direction within the orbital plane where the escaping spacecraft is located.

[0011] Furthermore, the initial state of the escape spacecraft is as follows:

[0012]

[0013] Furthermore, the initial state of the pursuing spacecraft is as follows:

[0014] X P0 =[sinθ·r,cosθ·r,0,0,0,0] T

[0015] Where r represents the initial relative distance between the escaping spacecraft and the pursuing spacecraft, and θ represents the angle between the line connecting the pursuing and escaping spacecraft and the Y-axis.

[0016] Furthermore, the relative distance between the pursuing and fleeing parties after the orbital transfer time is:

[0017] J(t) = ||M·(X) P (t)-X E (t))||2

[0018] Where J(t) represents the relative distance between the pursuing and fleeing parties after the orbital transfer time t, and X P (t) represents the final state of the pursuing spacecraft, X E (t) represents the final state of the escaping spacecraft, and M represents the matrix that transforms the state difference between the pursuer and the pursuer into a relative position difference:

[0019]

[0020] Furthermore, the final state X of the pursuing spacecraft P (t) and the final state X of the escaped spacecraft E (t) is:

[0021] X P (t)=Φ(t,t0)·X P (t0)

[0022] X E (t)=Φ(t,t0)·X E (t0)

[0023] Where Φ(t,t0) represents the CW equation transition matrix from time t0 to time t:

[0024]

[0025] Furthermore, the process of deriving the orbital transfer equations by substituting the initial states of the escaping and pursuing spacecraft into the equations is as follows:

[0026] The initial state X of the escaped spacecraft E(t0) = [0; 0; 0; 0; 0; 0], the initial state X of the pursuing spacecraft P Substituting (t0)=[sinθ·r;cosθ·r;0;0;0;0] into J(t), we get:

[0027]

[0028] Simplify to get

[0029]

[0030] Furthermore, the derivation process of the optimal pursuit initiation position is as follows:

[0031] Establish a function f, where f is the value under the square root of J(t), and the function f is defined as follows:

[0032] f = A·sin2θ + B·cos2θ + C

[0033] Where A = 6(sinnΔt - nΔt),

[0034] Based on the trigonometric function formulas, we introduce angle β and let... get:

[0035]

[0036] When sin(2θ-β)=-1, that is When the function f reaches its minimum value θ * This is the optimal starting point for pursuit.

[0037] Furthermore, the method for determining the optimal pursuit initiation position is as follows:

[0038] Using the initial position of the escaping spacecraft as the center, draw a planar circle with radius r. The pursuing spacecraft starts its attack from this circle. Then, both the pursuing and escaping spacecraft undergo orbital evolution. After time t, calculate the relative distance between them and take the minimum value J. b (t) = minJ(t), corresponding to the azimuth θ b This is the optimal azimuth angle for pursuit.

[0039] Furthermore, the calculation process for the relative distance between the two parties is as follows:

[0040] Divide the entire circle into N equal parts, gradually increasing θ1 = 0° to obtain the angle of each part, θ = [θ1, θ2, ..., θ]. N ], calculate the final relative distance, and obtain the final relative distance J(t) = [J1(t), J2(t), ..., J N(t)].

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

[0042] This invention provides a method for analyzing the optimal pursuit initiation azimuth based on natural evolution in orbital pursuit. Considering the influence of spacecraft natural evolution, it analyzes the pursuit of an escaping spacecraft from different azimuths outside the perception range. Both spacecraft rely solely on the constraints of space dynamics, and after a certain transfer time, their relative distances are obtained. The method analyzes the final relative distances obtained from different initiation azimuths of the pursuing spacecraft, and the azimuth represented by the minimum value is the optimal pursuit azimuth. Through the derivation of the orbital transfer equations, an analytical solution for the optimal pursuit initiation azimuth under the same orbital plane is obtained, and the correctness of the analytical solution is verified through numerical analysis. This method is helpful for subsequent research on the selection of initial positions in orbital pursuit. Attached Figure Description

[0043] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 The flowchart shows the optimal pursuit initiation location analysis method based on natural evolution for trajectory pursuit and escape according to the present invention.

[0045] Figure 2 This is a diagram of the orbital coordinate system established by the initial position of the escaped spacecraft according to the present invention.

[0046] Figure 3 This is a schematic diagram illustrating the natural evolution of the pursuit and escape trajectories in this invention.

[0047] Figure 4 This is a diagram showing the final relative distances from different orientations in this invention.

[0048] Figure 5 This is a graph showing the relationship between the transfer time of the present invention, the optimal pursuit start position, and the f-function. Detailed Implementation

[0049] The following description, in conjunction with the accompanying drawings, illustrates exemplary embodiments of this application, including various details to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0050] Obviously, the described embodiments are only some, not all, of the embodiments in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0051] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0052] The present invention will now be described in further detail with reference to the accompanying drawings:

[0053] See Figure 1 This invention provides a method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit, comprising the following steps:

[0054] S1, assuming both the pursuer and the fleeing spacecraft are on the same orbital plane, an orbital coordinate system is established based on the orbital altitude 'a', with the initial position of the fleeing spacecraft as the origin. The X-axis points from the Earth's center towards the fleeing spacecraft, and the Y-axis represents the velocity direction within the orbital plane of the fleeing spacecraft. Figure 2 As shown. The initial state of the escaped spacecraft is determined to be...

[0055] S2, based on the initial relative distance r between the escaping spacecraft and the pursuing spacecraft, the initial state of the pursuing spacecraft is obtained as X. P0 =[sinθ·r,cosθ·r,0,0,0,0] T , where θ is the angle between the line connecting the pursuing spacecraft and the escaping spacecraft and the Y-axis.

[0056] S3. Substitute the initial states of the escaping spacecraft and the pursuing spacecraft into the spacecraft orbital transfer equation for derivation. Set the transfer time as t, obtain the relative distance J(t) between the two parties after time t, and derive the optimal pursuit start position.

[0057] S3.1 analyzes the situation where, in the absence of a pulse, the pursuing spacecraft, under dynamic constraints, drifts naturally within different launch orientations and a fixed transfer time t. Finally, the relative distance to the escaping spacecraft is calculated, and the optimal launch orientation is the one with the smallest relative distance. The relative distance J(t) after time t is expressed as:

[0058] J(t) = ||M·(X) P (t)-X E (t))||2

[0059] Among them, the final state X of the pursuing spacecraft P (t) and the final state X of the escaped spacecraft E (t) is:

[0060] X P (t)=Φ(t,t0)·X P (t0)

[0061] X E (t)=Φ(t,t0)·X E (t0)

[0062] Φ(t,t0) represents the CW equation transition matrix from time t0 to time t:

[0063]

[0064] Δt=t-t0

[0065] M represents the matrix that transforms the state difference between the pursuer and the pursuer into a relative position difference:

[0066]

[0067] S3.2, change the initial state X of the escaped spacecraft. E (t0) = [0; 0; 0; 0; 0; 0] and the initial state X of the pursuing spacecraft P Substituting (t0)=[sinθ·r;cosθ·r;0;0;0;0] into J(t) for formula derivation, we get:

[0068]

[0069] Simplifying, we get

[0070]

[0071] S3.3 From the above equation, we can see that the minimum value of the final relative distance J(t) is independent of the initial relative distance r, but depends on the transition time and the initial orientation. We establish a function f, where f is the square root of J(t), which is equivalent to the behavior of the final relative distance at its minimum. The focus is on the relationship between the function f and the initial orientation. The function f is defined as follows:

[0072] f = A·sin2θ + B·cos2θ + C

[0073] Where A = 6(sinnΔt - nΔt),

[0074] Based on the trigonometric function formulas, we introduce angle β and let... get:

[0075]

[0076] When sin(2θ-β)=-1, that is When the function f reaches its minimum value, that is... θ * This is the optimal starting point for pursuit.

[0077] S4. The optimal pursuit start position is determined by numerical solution method, and the optimal pursuit start position is obtained under different transfer times by changing the transfer time.

[0078] S4.1 Since the pursuing and escaping spacecraft are pursuing each other in the same orbital plane, we only consider the pursuing spacecraft's pursuit from different azimuths within a 360° plane. Therefore, we draw a planar circle with radius r, centered on the initial position of the escaping spacecraft. The pursuing spacecraft's starting position is within this circle. Then, both spacecraft undergo orbital evolution, and after time t, the relative distance between them is calculated. Figure 3 As shown.

[0079] S4.2, divide the entire circle into N equal parts, gradually increasing θ1 = 0° to obtain the angle of each part, i.e., θ = [θ1, θ2, ..., θ]. N ], calculate the final relative distance, and obtain the final relative distance corresponding to N parts.

[0080] J(t) = [J1(t), J2(t), ..., J N (t)].

[0081] S4.3, then take the minimum value J among N parts. b (t) = minJ(t), corresponding to the azimuth θ b This is the optimal azimuth angle for pursuit.

[0082] S4.4, change the size of the transfer time, repeat steps S3 and S4 to obtain the optimal pursuit start position under different transfer times, and obtain the pattern therein.

[0083] Example 1:

[0084] Assume that the escape satellite E is in a circular orbit with an altitude of 42,000 km. Establish a relative coordinate system with the initial position of the escape spacecraft as the origin. The initial state of the escape spacecraft is shown in Table 1.

[0085] Table 1. Initial relative position and velocity (km, km / s) of the escape spacecraft E

[0086] E 0 0 0 0 0 0

[0087] The specific implementation steps of this embodiment are given below:

[0088] S1, input the orbital altitude a = 4200km and establish an orbital coordinate system with the initial position of the escaped spacecraft as the origin. The X-axis points from the Earth's center to the direction of the escaped spacecraft, and the Y-axis is the velocity direction within the orbital plane of the escaped spacecraft. Figure 2 As shown. Let the initial state of the escape spacecraft be X. E0 =[0,0,0,0,0,0] T ;

[0089] S2, input the initial relative distance r = 10km between the escaping spacecraft and the pursuing spacecraft;

[0090] S3, assuming both the pursuing and escaping spacecraft are on the same orbital plane, let θ be the angle between the line connecting the pursuing and escaping spacecraft and the Y-axis, and obtain the initial state of the pursuing spacecraft as X. P0 =[sinθ·10000,cosθ·10000,0,0,0,0] T ;

[0091] S4. Analyze the situation where, in the absence of a pulse, the pursuing spacecraft is only subject to dynamic constraints and drifts naturally within different launch orientations and a fixed transfer time t = 14400 s. Finally, calculate the relative distance with the escaping spacecraft. The optimal launch orientation is the one with the smallest relative distance. The relative distance J(t) after time t is expressed as:

[0092] J(t) = ||M·(X) P (t)-X E (t))||2

[0093] Among them, the final state X of the pursuing spacecraft P (t) and the final state X of the escaped spacecraft E (t) is:

[0094] X P (t)=Φ(t,t0)·X P (t0)

[0095] X E (t)=Φ(t,t0)·X E (t0)

[0096] M represents the matrix that transforms the state difference between the pursuer and the pursuer into a relative position difference:

[0097]

[0098] Φ(t,t0) represents the CW equation transition matrix from time t0 to time t:

[0099]

[0100] Δt=t-t0

[0101] The initial state X of the escape spacecraft E (t0) = [0; 0; 0; 0; 0; 0], the initial state X of the pursuing spacecraft P Substituting (t0)=[sinθ·10000;cosθ·10000;0;0;0;0] into J(t) for formula derivation, we get:

[0102]

[0103] Simplifying, we get

[0104]

[0105] From the above formula, we can see that the minimum value of the final relative distance J(t) is independent of the initial relative distance r, but depends on the transition time and the initial orientation. We establish a function f, where f is the square root of J(t), which is equivalent to the expression of the minimum value of the final relative distance. The focus is on the relationship between the function f and the initial orientation. The function f is defined as follows:

[0106] f = A·sin2θ + B·cos2θ + C

[0107] in,

[0108] A=6(sin(n·14400)-n·14400),

[0109]

[0110]

[0111] Based on the trigonometric function formulas, we introduce angle β and let... get:

[0112]

[0113] When sin(2θ-β)=-1, that is When the function f reaches its minimum value, that is... θ * This is the optimal starting point for pursuit.

[0114] S5. Since the pursuing and escaping spacecraft are in the same orbital plane, we only consider the pursuing spacecraft's pursuit from different azimuths within a 360° plane. Therefore, we draw a plane circle with a radius of r = 10000m, using the initial position of the escaping spacecraft as the center. The pursuing spacecraft's starting position is within this circle. Then, both spacecraft evolve their orbits, and after time t, we calculate their relative distance. Figure 3 As shown.

[0115] Divide the entire circle into 36,000 equal parts, gradually increasing the angle from θ1 = 0° to obtain the angle of each part, i.e., θ = [θ1, θ2, ..., θ]. 36000 The final relative distance is calculated to obtain the final relative distance J(t) corresponding to 36,000 units = [J1(t), J2(t), ..., J...]. 36000 [t], create a relative distance map for each direction, such as Figure 4 As shown.

[0116] Then take the minimum value J from the 36,000 samples. 933 (t)=J 18933 J(t) = minJ(t) = 9039.9m, and the corresponding azimuth θ = 9.33° or 189.33° is the optimal pursuit azimuth angle.

[0117] The transfer time was varied, ranging from 0 to 24 hours, and experiments were conducted. Steps S4 and S5 were repeated to obtain the optimal pursuit initiation location for different transfer times, such as... Figure 5 As shown, when the initial direction of the pursuing spacecraft is close to the Y-axis, the final relative distance is smaller. The relationship between the function and the transmission time indicates that the longer the transmission time, the smaller the final relative distance.

[0118] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit, characterized in that, Includes the following steps: The pursuit and escape are set to take place on the same orbital plane. Based on the orbital altitude and the initial relative distance between the escaping spacecraft and the pursuing spacecraft, an orbital coordinate system is established with the initial position of the escaping spacecraft as the origin to determine the initial state of the escaping spacecraft and the pursuing spacecraft. The initial states of the escaping and pursuing spacecraft are substituted into the spacecraft orbital transfer equations for derivation. The relative distance between the two parties after the orbital transfer time is obtained, and the optimal pursuit initiation position is derived. The optimal pursuit initiation position was determined using a numerical solution method, and the optimal pursuit initiation position was obtained under different transfer times by changing the transfer time. The derivation process of the optimal pursuit initiation position is as follows: Establish function, The function is The value under the square root, where The function is defined as follows: in, , , ; Based on the trigonometric function formulas, we introduce... Angle, let , ,get: when At that time, that is hour, The function obtains its minimum value as , This is the optimal starting point for pursuit.

2. The method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit as described in claim 1, characterized in that, The X-axis of the orbital coordinate system points from the Earth's center toward the direction of the escaping spacecraft, and the Y-axis is the velocity direction within the orbital plane of the escaping spacecraft.

3. The method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit as described in claim 1, characterized in that, The initial state of the escape spacecraft is: 。 4. The method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit as described in claim 1, characterized in that, The initial state of the pursuing spacecraft was: Where r represents the initial relative distance between the escaping spacecraft and the pursuing spacecraft. This represents the angle between the line connecting the pursuing and escaping spacecraft and the Y-axis.

5. The method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit as described in claim 1, characterized in that, The relative distance between the pursuing and fleeing parties after the orbital transfer time is: in, Indicates orbital transfer time The relative distance between the two sides in the subsequent pursuit and escape This indicates the final state of the pursuing spacecraft. This indicates the final state of the escaped spacecraft. The matrix representing the transformation of the state difference between the pursuer and the pursuer into a relative position difference: 。 6. The method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit as described in claim 5, characterized in that, The final state of the pursuing spacecraft The final state of the escape spacecraft for: in, express Time's up The CW equation transition matrix at time t: 。 7. The method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit as described in claim 1, characterized in that, The process of deriving the orbital transfer equations by substituting the initial states of the escape and pursuit spacecraft into the spacecraft's initial states is as follows: The initial state of the escape spacecraft The initial state of the spacecraft being pursued Substitute ,get: Simplify to get 。 8. The method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit as described in claim 1, characterized in that, The method for determining the optimal pursuit initiation point is as follows: Using the initial position of the escaped spacecraft as the center, and a radius of... Imagine a planar circle. The launch point of the pursuing spacecraft is within this circle. Then, both the pursuing and fleeing spacecraft undergo orbital evolution. Calculate the relative distance between the two parties after a certain time, and take the minimum value. The corresponding direction This is the optimal azimuth angle for pursuit.

9. The method for analyzing the optimal pursuit initiation location based on natural evolution in orbital pursuit as described in claim 8, characterized in that, The calculation process for the relative distance between the two parties is as follows: Divide the entire circle into N equal parts, from Gradually increase the angle to obtain each individual angle. Then, calculate the final relative distance to obtain the final relative distance corresponding to N parts. .

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