Method for Planning Collision Avoidance Maneuver of Multiple Orbit-approaching Spacecraft

Abstract

The present invention provides a method for spacecraft collision avoidance maneuver planning considering multi-loop approach. First, based on the precise ephemeris of the on-orbit spacecraft and the space target, the rendezvous approach conditions are analyzed to determine whether avoidance is needed, which can ensure good avoidance effects and avoid the situation of collision risks reappearing shortly after avoidance. Secondly, the range of feasible avoidance strategies and the optimal avoidance maneuver strategy are given simultaneously. While providing reference and operable recommended strategies for satellite management and control personnel, it ensures high flexibility. Finally, the avoidance effect review results of the proposed maneuver strategy are given, which can be applied to the avoidance effect review of any given maneuver strategy, expanding the applicable scope of the method and improving the reliability of the method.

Description

Technical Field

[0001] The present invention belongs to the field of on-orbit spacecraft measurement and control management, and is applicable to the calculation of spacecraft collision avoidance maneuver strategies. Background Art

[0002] With the continuous development of human space activities, a large number of satellites and space debris have been operating in the Earth's orbit for a long time, and the risks of natural rendezvous and mutual collisions between space targets have become increasingly prominent. For a spacecraft operating normally in orbit, when encountering a serious collision threat from other space targets, it is necessary to implement avoidance maneuver control to reduce the collision risk and ensure the safety of the satellite.

[0003] Traditional collision avoidance maneuver planning methods only consider avoiding the approach conditions at a single rendezvous moment. However, due to the periodicity of spacecraft orbital motion, there are two approach opportunities between the spacecraft and the target within one orbital period. In the several orbital periods before and after the rendezvous moment, there may be a relatively large collision risk for each approach opportunity. Although the avoidance strategy of the traditional method can reduce the collision risk at the original rendezvous moment, it cannot guarantee the collision risks of multiple approaches in the several orbital periods before and after the rendezvous moment, and may even increase the risk. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art, the present invention provides a spacecraft collision avoidance maneuver planning method considering multiple-circle approaches. Aiming at the collision avoidance problem of multiple approaches occurring in consecutive multiple orbital periods, the collision avoidance maneuver planning is carried out with the closest distance of multiple-circle and multiple approaches as the planning goal to improve the maneuver avoidance effect.

[0005] The technical solutions adopted by the present invention to solve its technical problems include the following steps:

[0006] Step 1, determine the analysis start time t 0 and the end time t f , and according to the precise ephemeris of the on-orbit spacecraft and the space target, obtain the position vector r 1 (t) and velocity vector v 1 (t) of the space target at any time t, as well as the position vector r 2 (t) and velocity vector v 2 (t) of the spacecraft;

[0007] Find the approach times t 0 of the spacecraft and the space target during the time from the start time t f to the end time t k , the corresponding closest approach distances d k , radial distances R k , approach angles θ k and approach velocities Δvk ;

[0008] Define the equivalent distance index Analyze the equivalent distance s of previous approaches k , and determine the minimum equivalent distance s * The corresponding approach time t * , approach distance d * , radial distance R * , approach angle θ * , and approach speed Δv * ;

[0009] Given the avoidance implementation threshold s of the rendezvous equivalent distance col , if s * ≤s col Then the rendezvous needs to implement avoidance and enter Step 2 and Step 3;

[0010] Step 2: Determine the avoidance maneuver control time window according to the spacecraft tracking and control plan and the spacecraft control logic. The earliest controllable time is t c0 , and the latest control time is t cf ;

[0011] Determine the control quantity threshold according to the spacecraft platform maneuverability limit and orbit maintenance constraint. The upper and lower limits of the control quantity are Δa up and Δa low ;

[0012] Establish a post-control orbit prediction model of the spacecraft based on precise ephemeris and relative dynamics equations;

[0013] Given the control time change step δt and the control quantity change step δa, within the avoidance maneuver control time window [t c0 , t cf and the control quantity threshold [Δa low , Δa up , select multiple avoidance maneuver control times t ci ∈[t c0 , t cf and multiple control quantities Δa i ∈[Δa low , Δa up at equal steps;

[0014] Traverse all combinations of the maneuver strategy control time t ci and the control quantity Δa i . Analyze the minimum equivalent distance of multiple approaches of the post-avoidance maneuver orbit within multiple orbital periods before and after the original natural rendezvous approach time t * as well as the corresponding approach times approach distance​ Radial distance Approach angle and approach speed

[0015] Set the threshold s for the minimum equivalent distance after avoidance, th , and filter out the maneuver strategies that satisfy to obtain the feasible avoidance control strategy interval;

[0016] Step 3: Select optimization variables, including the avoidance maneuver control time t c and the semi-major axis control quantity Δa, and give the upper and lower limits of the optimization variables t c ∈[t c0 , t cf , Δa ∈ [Δa low , Δa up ;

[0017] Set the optimization goal to minimize the absolute value |Δa| of the semi-major axis control quantity;

[0018] Given the constraint condition as the threshold s for the minimum equivalent distance after avoidance th , for a set of maneuver control times t c and semi-major axis control quantities Δa, calculate the corresponding multiple minimum equivalent distances of approach to satisfy s * (t c , Δa) ≥ s th ;

[0019] Solve the optimal avoidance maneuver strategy planning problem described in this step to obtain the optimal control time and semi-major axis control quantity;

[0020] Step 4: Based on the optimal control time and semi-major axis control quantity obtained in Step 3, or make a preference selection within the feasible avoidance control strategy interval obtained in Step 2, or arbitrarily give other control times t c and semi-major axis control quantities Δa of the avoidance maneuvers to be implemented;

[0021] According to the spacecraft post-control orbit prediction model established in Step 2, obtain the precise ephemeris of the spacecraft after implementing the avoidance maneuver, and then through the method in Step 1, analyze the rendezvous and approach conditions between the spacecraft and the space target after implementing the avoidance maneuver, and determine the minimum equivalent distance s * , the corresponding approach time t * , the approach distance d * , the radial distance R * , the approach angle θ * and the approach speed Δv * ;

[0022] Set the threshold s for the minimum equivalent distance after avoidance thVerify whether the maneuver strategy meets the avoidance effect constraint s * ≥s th If this condition is met, it is confirmed that the avoidance maneuver strategy is feasible, and the spacecraft is allowed to implement the avoidance according to this strategy; if any given maneuver strategy does not meet the avoidance effect constraint, repeat this step and adjust the avoidance strategy based on the feasible strategy range and optimal result in Step 2 and Step 3.

[0023] The time span from the analysis start time to the terminal time is not less than 1 day.

[0024] The rendezvous avoidance implementation threshold s col takes values from 30 to 300 m.

[0025] Based on the maneuverability limit of the spacecraft platform and the orbit maintenance constraint, determine that the upper and lower limits of the control quantity threshold are within the range of ±1000 m.

[0026] The described spacecraft post-control orbit prediction model uses the input precise ephemeris of the spacecraft to describe the natural motion, and uses the relative orbit dynamics model to describe the relative orbit motion after applying control compared to without applying control.

[0027] The minimum equivalent distance threshold s after avoidance th is not less than 30 m and s th >s col .

[0028] Step 3 described above calls a gradient-free optimization algorithm to solve the optimal avoidance maneuver strategy planning problem; the called gradient-free optimization algorithm uses a multi-layer single connection algorithm, a genetic algorithm or a differential evolution algorithm.

[0029] The beneficial effects of the present invention are as follows: A spacecraft collision avoidance maneuver evaluation model based on precise ephemeris and relative orbit dynamics model is established, and an avoidance maneuver planning method is proposed. First, based on the precise ephemeris of the on-orbit spacecraft and the space target, this method analyzes the rendezvous approaching conditions and judges whether avoidance is needed. The judgment method based on precise ephemeris avoids the influence of the orbit prediction model error, has high credibility, and reduces missed alarms and false alarms; when analyzing, the approaching conditions in the entire time period are considered, and for complex situations such as multi-loop periodic approaches, good avoidance effects can be guaranteed, and the situation of collision risk reappearing shortly after avoidance can be avoided. Second, this method simultaneously gives the feasible avoidance strategy range and the optimal avoidance maneuver strategy, providing reference and operable recommended strategies for satellite management and control personnel, while ensuring high flexibility. Finally, this method gives the avoidance effect review result of the proposed maneuver strategy, which can be applied to the avoidance effect review of any given maneuver strategy, expanding the application range of the method and improving the reliability of the method. Brief Description of the Drawings

[0030] Figure 1 is the flow chart of the present invention. Detailed implementation manners

[0031] The present invention will be further described below in conjunction with the accompanying drawings and embodiments, and the present invention includes but is not limited to the following embodiments.

[0032] The technical solutions adopted by the present invention to solve its technical problems include the following steps:

[0033] Step 1: Analyze the rendezvous approach conditions based on the precise ephemeris of the on-orbit spacecraft and the space target

[0034] (1) Determine the start time t 0 and the end time t f , and based on the precise ephemeris of the on-orbit spacecraft and the space target, use the interpolation method to obtain the position vector r 1 (t) and velocity vector v 1 (t) of the space target at any time t, as well as the position vector r 2 (t) and velocity vector v 2 (t) of the spacecraft. Preferably, the time span from the start time to the end time should be no less than 1 day, generally 2 to 10 days.

[0035] (2) Use the one-dimensional search algorithm to find the successive approach times t 0 from the start time t f to the end time t k of the spacecraft and the space target during the time, the corresponding successive approach minimum distances are d k , the radial distances are R k , the approach angles are θ k , and the approach velocities are Δv k , where k = 1, 2, 3,....

[0036] (3) Generally, the orbit prediction error is larger in the tangential direction and smaller in the radial direction. Therefore, the assessment of the collision risk and the avoidance effect needs to comprehensively consider the successive approach minimum distance d k and the radial distance R k , and define the equivalent distance index as shown in Equation (1):

[0037]

[0038] s k The smaller s k , the higher the collision risk, and the larger s

[0039] (4) Analyze the equivalent distance s k of each approach and determine the minimum equivalent distance s *, namely

[0040] s * = min(s k ), k = 1, 2, 3, ... (2)

[0041] corresponding to the approaching moment t * , approaching distance d * , radial distance R * , approaching angle θ * , approaching speed Δv * .

[0042] (5) Given the avoidance implementation threshold s of the rendezvous equivalent distance col , then the judgment condition for the rendezvous to require avoidance implementation is

[0043] s * ≤ s col (3)

[0044] Preferably, the value range of the rendezvous avoidance implementation threshold is generally between 30 and 300 m.

[0045] Step 2: Given the avoidance maneuver control time window and control quantity threshold, analyze the feasible avoidance range

[0046] (1) According to the spacecraft tracking and control plan and spacecraft control logic, determine the avoidance maneuver control time window, and the earliest controllable moment is t c0 , and the latest control moment is t cf .

[0047] (2) According to the spacecraft platform maneuverability limit and orbit maintenance constraint, determine the control quantity threshold. The long-term orbit maintenance of the spacecraft generally only implements tangential control to raise or lower the semi-major axis of the orbit. Therefore, the semi-major axis change amount can be used to characterize the magnitude and direction of the control quantity, and the upper and lower limits of the control quantity are Δa up and Δa low . Preferably, according to the orbit maneuverability of the current on-orbit satellite, the upper and lower limits of the semi-major axis control quantity should be within the range of ±1000 m.

[0048] (3) The post-control orbit motion of the spacecraft can be decomposed into natural motion without applying control and relative orbit motion after applying control relative to the non-control case. The natural motion can be described by the input precise ephemeris of the spacecraft, and the relative orbit motion after applying control relative to the non-control case can be described by the relative orbit dynamics model. Thus, a post-control orbit prediction model based on the precise ephemeris and relative dynamics equation can be established to evaluate the avoidance effect of the spacecraft and the space target after the maneuver is implemented.

[0049] (4) Given the control time change step δt and control quantity change step δa, within the avoidance maneuver control time window [tc0 ,t cf , and the control quantity threshold [Δa low , Δa up , multiple avoidance maneuver control times t are selected at equal step lengths within the range ci ∈[t c0 , t cf , and multiple control quantities Δa i ∈[Δa low , Δa up , i = 1, 2, 3,....

[0050] (5) Traverse and select all combinations of the maneuver strategy control time t ci and the control quantity Δa i . In multiple orbital periods before and after the original natural rendezvous approaching moment t * , analyze the multiple closest minimum equivalent distances of the orbit after the avoidance maneuver corresponding to the approaching moment approach distance radial distance approach angle approach speed i = 1, 2, 3,....

[0051] (6) Set the threshold s of the minimum equivalent distance after avoidance th , and screen out the maneuver strategies that satisfy . These are the feasible avoidance control strategy intervals. Preferably, the threshold s of the minimum equivalent distance after avoidance th should not be less than 30 m. Generally, for conservatism, the set value of this threshold can be between 50 - 500 m. In addition, it should be ensured that the equivalent distance threshold after avoidance is greater than the avoidance implementation threshold of the rendezvous condition, that is, s th > s col , otherwise the avoidance cannot be effectively implemented.

[0052] Step three, call the optimization algorithm to plan the optimal avoidance maneuver strategy

[0053] (1) Select the optimization variables, which are the avoidance maneuver control moment t c and the semi-major axis control quantity Δa, and give the upper and lower limits of the optimization variables t c ∈[t c0 , t cf , Δa ∈ [Δa low , Δa up .

[0054] (2) Set the optimization objective, which is to minimize the absolute value |Δa| of the semi-major axis control quantity, that is, the spacecraft achieves avoidance with the least fuel consumption.

[0055] (3) Given the constraint conditions, the threshold s of the minimum equivalent distance after avoidance th , that is, for a set of maneuver control times t c and the semi-major axis control quantity Δa, calculate the corresponding multiple minimum equivalent distances s * , satisfying

[0056] s * (t c , Δa) ≥ s th (4)

[0057] (4) Call well-known gradient-free optimization algorithms such as the Multi-level Single-linkage algorithm, genetic algorithm, differential evolution algorithm, etc. to solve the optimal avoidance maneuver strategy planning problem jointly described in steps (1), (2), and (3) of this step, and obtain the optimal control time and semi-major axis control quantity.

[0058] Step Four: Recheck the avoidance effect of the planned maneuver strategy

[0059] (1) According to the optimal control time and semi-major axis control quantity obtained in step three, or make a tendency selection within the feasible avoidance control strategy interval obtained in step two, or arbitrarily specify other control times t of the planned avoidance maneuver c and the semi-major axis control quantity Δa.

[0060] (2) According to the spacecraft post-control orbit prediction model established in step two (3), obtain the precise ephemeris of the spacecraft after implementing the avoidance maneuver, and then through the method of step one, analyze the rendezvous and approach conditions between the spacecraft and the space target after implementing the avoidance maneuver, and determine the minimum equivalent distance s * , the corresponding approach time t * , the approach distance d * , the radial distance R * , the approach angle θ * , the approach speed Δv * .

[0061] (3) Set the threshold s of the minimum equivalent distance after avoidance th , and verify whether this maneuver strategy meets the avoidance effect constraint s * ≥ s th , and if the condition is met, it is a confirmed feasible avoidance maneuver strategy, allowing the spacecraft to implement the avoidance according to this strategy; if the arbitrarily specified maneuver strategy does not meet the avoidance effect constraint, it should return to step four (1) and adjust the avoidance strategy according to the feasible strategy interval and optimal results of steps two and three.

[0062] The embodiments of the present invention include the following steps:

[0063] Step 1: Analyze the rendezvous and approach conditions based on the precise ephemerides of the on-orbit spacecraft and the space target

[0064] Based on the precise ephemerides of satellite A and space target B from the k-th day to the (k + 4)-th day in 2021, it is found through analysis that there are multiple approach events between the two, as shown in Table 1.

[0065] Table 1 List of approach events between satellite A and space target B

[0066] Serial Number Time Approach Distance (m) Radial Distance (m) Approach Angle (°) Equivalent Distance (m) 1 09:42:58 on the (k + 1)th day 4478.4 102.2 160.8 447.8 2 11:20:27 on the (k + 1)th day 207.2 -16.3 160.6 20.7 3 12:57:55 on the (k + 1)th day 5008.5 35.2 160.4 500.8

[0067] The equivalent distance of the second approach is the closest, and the time t * is 11:20:27 on the (k + 1)-th day. The approach distance d * = 207.2 m, the radial distance R * = -16.3 m, the approach angle θ * = 160.6°, and the equivalent distance s * = 20.7 m.

[0068] Given the avoidance implementation threshold s of the rendezvous equivalent distance col = 30 m, and it satisfies the avoidance implementation condition s * ≤ s col , so an avoidance maneuver needs to be implemented.

[0069] Step 2: Given the avoidance maneuver control time window and control quantity threshold, analyze the feasible avoidance range

[0070] (1) Based on the spacecraft tracking and control plan and the spacecraft control logic, determine the avoidance maneuver control time window. The earliest controllable time t c0 is 19:30:00 on the k-th day, and the latest control time t cf is 21:00:00 on the k-th day.

[0071] (2) Based on the limitations of the spacecraft platform maneuverability and the orbit maintenance constraints, a tangential control method needs to be adopted to reduce the semi-major axis of the orbit. The lower limit of the control quantity is Δa low = -200 m, and the upper limit is Δa up = -100 m.

[0072] (3) The C-W equation is a simple and effective relative orbit dynamics model of spacecraft, as shown in Equation (5)

[0073]

[0074] In the formula, n is the average orbital angular velocity of the spacecraft, and a is the thrust acceleration of the spacecraft.

[0075] There is an analytical solution to this equation. By using the precise ephemeris of the spacecraft and superimposing the C-W equation, the orbital motion of the spacecraft after implementing the avoidance maneuver can be described.

[0076] (4) Given the control time variation step size δt = 600 s and the control quantity variation step size δa = 10 m, within the avoidance maneuver control time window [t c0 , t cf and the control quantity threshold [Δa low , Δa up , select the avoidance maneuver control time t ci ∈ [t c0 , t cf and the control quantity Δa i ∈ [Δa low , Δa up at equal step lengths, where i = 1, 2, 3,....

[0077] (5) Traverse all combinations of the control time t ci and the control quantity Δa i . Within multiple orbital periods before and after the original natural rendezvous approach time t * , analyze the multiple closest minimum equivalent distances s i * of the orbit after the avoidance maneuver, where i = 1, 2, 3,.... The analysis results of the minimum equivalent distances of each maneuver strategy are shown in Table 2. Among them, the first row is the semi-major axis control quantity of the avoidance maneuver, the first column is the avoidance maneuver control time, and the middle numbers are the minimum equivalent distances in the multiple-circle approach for the corresponding maneuver strategies.

[0078] Table 2 Analysis of the minimum equivalent distances of the traversed maneuver strategies

[0079]

[0080] (6) Set the threshold of the minimum equivalent distance after avoidance s th = 200 m, and screen out the maneuver strategies that satisfy . These are the feasible avoidance control strategies. In Table 2, the data in the 1st, 2nd, 3rd, 8th, 9th, 10th, 11th columns of the first row, the 9th, 10th, 11th columns of the second row, the 9th, 10th, 11th columns of the fifth row, the 1st, 2nd, 6th, 7th, 8th, 9th, 10th, 11th columns of the sixth row, the 1st, 2nd, 6th, 7th, 8th, 9th, 10th, 11th columns of the seventh row, the 1st, 2nd, 6th, 7th, 8th, 9th, 10th, 11th columns of the eighth row, the 1st, 2nd, 6th, 7th, 8th, 9th, 10th, 11th columns of the ninth row, and the 1st, 2nd, 6th, 7th, 8th, 9th, 10th, 11th columns of the tenth row all correspond to the control strategies that do not reach the avoidance threshold, and the other data correspond to the feasible avoidance control strategies.

[0081] Step 3: Invoke the optimization algorithm to plan the optimal avoidance maneuver strategy

[0082] (1) Set the avoidance maneuver control time t c and the upper and lower limits of the semi-major axis control quantity Δa. The earliest controllable time t c0 is 19:30:00 on the k-th day, and the latest control time t cf is 21:00:00 on the k-th day. The lower limit of the semi-major axis control quantity is Δa low = -200m, and the upper limit is Δa up = -100m.

[0083] (2) Invoke the Multi-level Single-linkage algorithm to plan the optimal avoidance maneuver strategy and obtain the optimal control time t c is 19:51:51 on the k-th day, and the optimal semi-major axis control quantity is Δa = -100m. The corresponding minimum equivalent distance s * = 207.6m, approaching time t * is 11:20:26 on the (k + 1)-th day, approaching distance d * = 1333.9m, radial distance R * = -207.6m, approaching angle θ * = 160.6°.

[0084] Step 4: Recheck the avoidance effect of the planned maneuver strategy

[0085] (1) Assume that the first alternative avoidance strategy to be rechecked is the optimal maneuver strategy obtained in Step 3, with control time t c being 19:51:51 on the k-th day and semi-major axis control quantity Δa = -100m.

[0086] Recheck and calculate the approaching conditions at multiple times before and after the original natural encounter approaching time t * as shown in Table 3.

[0087] Table 3 Post-control avoidance effect of the first avoidance strategy

[0088] Serial Number Time Approach Distance (m) Radial Distance (m) Approach Angle (°) Equivalent Distance (m) 1 09:42:58 on the (k + 1)th day 5829.9 -91.2 160.8 583.0 2 11:20:26 on the (k + 1)th day 1333.9 -207.6 160.6 207.6 3 12:57:55 on the (k + 1)th day 3312.4 -153.6 160.4 331.2

[0089] The equivalent distance of the second approach is the smallest, and the time t * is 11:20:26 on the (k + 1)-th day, approaching distance d * = 1333.9m, radial distance R * = -207.6m, approaching angle θ * = 160.6°, equivalent distance s * = 207.6m, meeting the avoidance threshold s th = 200m requirement.

[0090] Recheck and confirm that the maneuver strategy meets the avoidance requirements.

[0091] (2) Assume that the second alternative avoidance strategy to be rechecked is another optional maneuver strategy, and the control time t c is 19:30:00 on the k-th day, and the semi-major axis control quantity Δa = -200 m.

[0092] According to Table 2 of the calculation results in Step 2, it can be seen that this optional maneuver strategy does not reach the effective avoidance threshold and is a maneuver strategy not recommended by the method of the present invention.

[0093] Recheck and calculate the multiple approaching conditions before and after the original natural rendezvous approaching time t * as shown in Table 4.

[0094] Table 4 Post-control avoidance effect of the second avoidance strategy

[0095] Serial Number Time Approach Distance (m) Radial Distance (m) Approach Angle (°) Equivalent Distance (m) 1 09:42:57 on the (k + 1)th day 7296.8 -67.6 160.8 729.7 2 11:20:26 on the (k + 1)th day 2962.2 -178.4 160.6 296.2 3 12:57:55 on the (k + 1)th day 1499.4 -117.9 160.4 149.9

[0096] At the moment closest to the original rendezvous condition, that is, the second approaching moment, the equivalent distance after the implementation of the avoidance maneuver reaches 296.2, meeting the effective avoidance threshold; however, the equivalent distance at the third approaching moment after the control implementation is the smallest, and the time t * is 12:57:55 on the (k + 1)-th day, the approaching distance d * = 1499.4 m, the radial distance R * = -117.9 m, the approaching angle θ * = 160.4°, and the equivalent distance s * = 149.9 m, which does not meet the avoidance threshold requirement of s th = 200 m.

[0097] Thus, it can be seen that if the analysis method considering multiple orbits of approach of the present invention is not used, since this maneuver strategy can increase the approaching distance at the original approaching time to be higher than the avoidance threshold, it may be regarded as an effective avoidance maneuver strategy; after using the method of the present invention, it can be judged during the analysis of the feasible avoidance strategy in Step 2 that this maneuver strategy does not meet the avoidance requirements, and the recheck calculation results in Step 4 also confirm that this strategy will reduce the distance of the third approach and cannot effectively avoid the space target. Using the optimal maneuver strategy (Strategy 1) obtained in Step 3, an avoidance effect better than the given strategy (Strategy 2, semi-major axis control quantity -200 m) can be achieved with a smaller semi-major axis control quantity (-100 m).

[0098] Therefore, this application example can prove that the collision avoidance maneuver planning method proposed by the present invention can avoid the problem of the collision risk reappearing in the short term after control for the collision avoidance problem with multiple close approaches occurring in multiple consecutive orbital periods, and effectively improve the maneuver avoidance effect.

Claims

1. A method for spacecraft collision avoidance maneuver planning considering multi - loop approach, characterized in that, it includes the following steps: Step 1, determine the starting time \(t\) of the analysis 0 and the ending time \(t\) f , and based on the precise ephemeris of the on-orbit spacecraft and the space target, obtain the position vector \(\mathbf{r}(t)\) of the space target at any time \(t\) 1 and the velocity vector \(\mathbf{v}(t)\) 1 , as well as the position vector \(\mathbf{r}(t)\) of the spacecraft 2 and the velocity vector \(\mathbf{v}(t)\) 2 ; Find the starting time t 0 to the ending time t f The successive approaching times t of the spacecraft and the space target within the time k , the corresponding successive closest approach distances are d k , the radial distance is R k , the approach angle is θ k and the approach velocity is Δv k ; Define the equivalent distance index Analyze the equivalent distance s of each approach k , and determine the minimum equivalent distance s * The corresponding approach time t * , approach distance d * , radial distance R * , approach angle θ * and approach speed Δv * ; The avoidance implementation threshold s for a given rendezvous equivalent distance col , if s * ≤ s col then avoidance needs to be implemented for the rendezvous, and proceed to Step 2 and Step 3; Step 2: Determine the avoidance maneuver control time window according to the spacecraft tracking and control plan and the spacecraft control logic. The earliest controllable moment is t c0 , and the latest controllable moment is t cf ; Determine the control quantity threshold based on the limitations of the spacecraft platform's maneuvering ability and the constraints of orbit maintenance. The upper and lower limits of the control quantity are Δa up and Δa low ; Establish a post - control orbit prediction model of the spacecraft based on precise ephemeris and relative dynamics equations; Given a control time variation step size δt and a control quantity variation step size δa, within the avoidance maneuver control time window [t c0 , t cf and the control quantity threshold [Δa low , Δa up , multiple avoidance maneuver control times t ci ∈ [t c0 , t cf and multiple control quantities Δa i ∈ [Δa low , Δa up are selected at equal step sizes; Traverse and select each maneuver strategy control time t ci and all combinations of the control quantity Δa i within multiple orbital periods before and after the original natural rendezvous approach time t * Analyze the minimum equivalent distance of multiple approaches of the orbit after the avoidance maneuver control as well as the corresponding approach time approach distance radial distance approach angle and approach speed Set the threshold s for the minimum equivalent distance after avoidance th , and filter out the maneuvering strategies that satisfy to obtain the interval of feasible avoidance control strategies; Step 3: Select optimization variables, including the avoidance maneuver control moment \(t\) c and the semi-major axis control quantity \(\Delta a\), and give the upper and lower limits of the optimization variables \(t\) c \(\in[t\) c0 ,t\) cf , \(\Delta a\in[\Delta a\) low ,\Delta a\) up ; Set the optimization goal as the minimum absolute value |Δa| of the semi - major axis control quantity; The given constraint is the threshold s of the minimum equivalent distance after avoidance th , for a set of maneuver control times t c and the semi-major axis control quantity Δa, calculate the corresponding multiple times of the proximity to the minimum equivalent distance satisfying s * (t c , Δa) ≥ s th ; Solve the optimal avoidance maneuver strategy planning problem described in this step to obtain the optimal control time and the semi - major axis control quantity; Step 4: Based on the optimal control time and semi-major axis control quantity obtained in Step 3, or make a preferential selection within the feasible avoidance control strategy interval obtained in Step 2, or arbitrarily specify the control time t of other avoidance maneuvers to be implemented c and the semi-major axis control quantity Δa; Based on the post-control orbit prediction model of the spacecraft established in Step 2, obtain the precise ephemeris of the spacecraft after the avoidance maneuver is implemented. Then, through the method in Step 1, analyze the rendezvous and approach conditions between the spacecraft and the space target after the avoidance maneuver is implemented, and determine the minimum equivalent distance s after the avoidance * , the corresponding approach time t * , the approach distance d * , the radial distance R * , the approach angle θ * and the approach velocity Δv * ; Set the threshold \(s\) for the minimum equivalent distance after avoidance th , and verify whether the maneuver strategy satisfies the avoidance effect constraint \(s\) * \(\geq s\) th , and satisfying this condition means that the avoidance maneuver strategy is confirmed to be feasible, allowing the spacecraft to implement avoidance according to this strategy; if any given maneuver strategy does not satisfy the avoidance effect constraint, repeat this step and adjust the avoidance strategy according to the feasible strategy interval and the optimal result in Step 2 and Step 3.

2. The method for spacecraft collision avoidance maneuver planning considering multi - loop approach according to claim 1, characterized in that, the time span from the analysis start time to the end time is not less than 1 day.

3. The method for spacecraft collision avoidance maneuver planning considering multi - loop approach according to claim 1, characterized in that, The intersection avoidance implementation threshold s col takes a value of 30 to 300 m.

4. The method for spacecraft collision avoidance maneuver planning considering multi - loop approach according to claim 1, characterized in that, According to the spacecraft platform maneuverability limit and orbit maintenance constraint, determine that the upper and lower limits of the control quantity threshold are within the range of ±1000m.

5. The method for spacecraft collision avoidance maneuver planning considering multi - loop approach according to claim 1, characterized in that, the post - control orbit prediction model of the spacecraft uses the input spacecraft precise ephemeris to describe the natural motion, and uses the relative orbit dynamics model to describe the relative orbit motion after applying control compared to without applying control.

6. The method for spacecraft collision avoidance maneuver planning considering multi - loop approach according to claim 1, characterized in that, The minimum equivalent distance threshold s after avoidance th is not less than 30 m and s th > s col .

7. The method for spacecraft collision avoidance maneuver planning considering multi - loop approach according to claim 1, characterized in that, in step three, a gradient - free optimization algorithm is called to solve the optimal avoidance maneuver strategy planning problem; the called gradient - free optimization algorithm uses a multi - layer single - connection algorithm, a genetic algorithm or a differential evolution algorithm.

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