A trajectory planning method for target window rendezvous

Abstract

The application provides a trajectory planning method for target window rendezvous, comprising the following steps: step one, calculating the latitude amplitude angle range that can be reached; step two, preliminarily calculating the time of strategy orbit transfer; step three, correcting the time of orbit transfer through the way of orbit recursion; step four, calculating the strategy of orbit transfer; and step five, long-term drift correction strategy. The application provides a trajectory planning scheme for reaching a fixed target orbit (circular orbit) at a specified phase within a given time, and proposes a scheme for correcting the strategy of orbit transfer based on orbit recursion.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of space orbit rendezvous control, in particular to a self-generalized trajectory planning method for target window rendezvous. BACKGROUND

[0002] Spacecraft development is not limited to earth observation and communication satellites. After the formation of a network of space vehicles, space vehicles have stronger functions. The development of space stations provides a docking point for space vehicles in orbit. In-orbit refueling of spacecraft extends the life of the spacecraft. The development of the above technologies requires high-precision orbit rendezvous technology.

[0003] Orbit rendezvous technology is divided into long-distance rendezvous technology and close-range rendezvous docking technology. Long-distance rendezvous is mainly based on ground measurement and guidance technology. Close-range rendezvous technology requires inter-satellite communication and relative measurement technology.

[0004] Current long-distance rendezvous is usually completed by long-term drifting after orbit semi-major axis adjustment. High-precision rapid long-distance rendezvous control is usually completed by Lambert guidance. Although Lambert guidance control has high precision, the variable orbit strategy requires high selection of variable orbit points and variable orbit pulse number. The multi-pulse optimal Lambert guidance scheme needs to be optimized based on genetic algorithm and other optimization algorithms. SUMMARY

[0005] The self-generalized trajectory planning method for target window rendezvous of the present application provides a trajectory planning scheme for reaching a specified phase of a fixed target orbit (circular orbit) within a given time. A scheme based on orbit recursive correction variable orbit strategy is proposed.

[0006] To achieve the above purpose, the present application realizes the following technical solutions:

[0007] A trajectory planning method for target window rendezvous, comprising the following steps:

[0008] Step one, calculate the latitude amplitude angle range that can be reached;

[0009] Step two, preliminarily calculate the variable orbit time of the strategy;

[0010] Step three, correct the variable orbit time by orbit recursion;

[0011] Step four, calculate the variable orbit strategy;

[0012] Step five, long-term drifting correction strategy.

[0013] Optionally, the latitude amplitude angle range calculation of step one further comprises:

[0014] The time T during the journey in the intermediate orbit mid For half an orbital period, the semi-major axis of the orbit is a. mid =0.5(a) s +a t Then we have:

[0015]

[0016] Among them, a s Let a be the semi-major axis of the initial orbit. t For the semi-major axis of the window track, The angular velocity of the intermediate orbit is μ = 3.986004415e14, and the gravitational constant is 3.986004415e14.

[0017] The intermediate orbit running time T is calculated using a recursive orbital method. mid The correction process is as follows:

[0018] 1) The semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and true anomaly of the intermediate orbit are respectively: a mid , i mid =i s Ω mid =Ω s ω mid =0,f mid =0; where i s Ω represents the current orbital inclination. s The right ascension of the ascending node of the current orbit;

[0019] 2) The orbit determined by the above orbital elements is used as the initial value for recursion, and the recursion time is T. mid The latitude argument u of the recursive orbit is obtained. dt ;

[0020] 3) Calculate the time correction amount Update T mid =T mid -Δt, if Δt≤0.001, then exit the iteration; otherwise, go to step 2);

[0021] T mid The rendezvous time is the corrected fixed time, and the rendezvous time is T. a Then time T needs to be... a -T mid Assigned to T cs and T ed If the latitudinal argument reaches its two extreme values ​​when all time is allocated to the initial orbit or the final orbit, then the latitudinal argument limit achievable by this strategy is:

[0022] u1=u0+nt • (T a -T mid )+π

[0023] u2 = u0 + n s • (T a -T mid )+π

[0024] where u0 is the initial latitude amplitude; is the initial orbit angular velocity; is the final orbit angular velocity.

[0025] Optionally, the step two of preliminary calculation of the transfer time further comprises:

[0026] determining the fixed-point phase u t +k·2π (k is an integer) within the interval range composed of u1 and u2;

[0027] From the result of step one, if the time is all allocated on the final orbit, the phase obtained is u1, then the time needed to be allocated to the initial orbit can be calculated by the following way:

[0028] Δu = u t -u1

[0029] Convert Δu to [0, 2π], if n s -n t < 0, then Δu = Δu - 2π, the transfer time T bg is calculated by the following formula:

[0030]

[0031] then the running time T ed on the final orbit is:

[0032] T ed = T a -T mid -T bg .

[0033] Optionally, the step three of transfer time correction further comprises:

[0034] The orbit at the transfer strategy calculation time is described by the orbit elements: a s , e s , i s , Ω s , ω s , f s ; the final orbit at the window constraint under the rendezvous time is described by the orbit elements: a t , e t = 0, i t=i s Ω t =Ω s ω t =0,f t =u t ;

[0035] The strategy calculated in steps one and two yields an initial orbital travel time of T. bg The travel time in the intermediate orbit is T. mid During the end orbit travel time T ed The following section corrects T using a trajectory recursion algorithm. bg During the correction process, keep T mid Keep it unchanged, keep T bg With T ed The sum remains unchanged, and T is iteratively corrected. bg The steps are as follows:

[0036] 1) The time T is calculated from the orbital time using the strategy. bg The latitude argument u of the spacecraft during the first orbital change was obtained. bg1 Time T is calculated by reversing the orbital time from the rendezvous point. ed The latitude argument u of the spacecraft during the second orbital change was obtained. bg2 ;

[0037] 2) Calculate the time correction amount Before calculation, (u) bg2 -u bg1 -π) redirects to [-π,π]; after correction, T bg =T bg -Δt,T ed =T ed +Δt; if Δt≤0.001, exit the iteration; otherwise, go to step 1).

[0038] Optionally, step four, calculating the trajectory change strategy, further includes:

[0039] The recursive time T is derived from the orbital time calculated by the strategy. bg The position of the orbit change point during the first orbit change was obtained as follows: Therefore, the speed increments for the two orbital changes are:

[0040]

[0041]

[0042] Therefore, the orbital change strategy is: 1) The first orbital change occurs at time T. bg Afterwards, the velocity increment in the orbital system is [Δv1 00]; 2) The time of the second orbital change is T. bg +T mid, the velocity increment in the orbital system is [Δv200].

[0043] Optionally, the step five long-term drift correction strategy further comprises:

[0044] If T bg >T s , T s is the current orbit period, then when T bg ≤T s , the strategy is recalculated from step one;

[0045] If T ed >T T , T T is the terminal orbit period, then after the orbit transfer strategy in step four is completed, the following phase control is performed:

[0046] The orbit after the orbit transfer is described by the orbital elements a ed , e ed , i ed , Ω ed , ω ed , f ed ; the remaining mission time is T last , and the remaining phase is u last =u t -u ed , where u ed =ω ed +f ed , and u last is converted to [0, 2π];

[0047] The time required at the current orbit running phase u last is calculated:

[0048]

[0049] where ω is the orbital angular velocity;

[0050] The time t ed is iteratively corrected using the orbit recursion method, and the steps are as follows:

[0051] 1) The orbit phase is obtained from the orbit recursion time t ed after the orbit transfer is completed.

[0052] 2) The time correction amount Δt is calculated. Before calculation, u is converted to [-π, π], the corrected time t ed =t ed +Δt; if Δt≤0.001, the iteration is exited, otherwise step 1) is converted.

[0053] By R is rounded to get the number of orbits R in the end orbit n , the target orbit period of the phase change is calculated as:

[0054]

[0055] The semi-major axis of the phase change target orbit is obtained as:

[0056]

[0057] The semi-major axis of the target orbit is corrected by the method of orbit recursion, the steps are as follows:

[0058] 1) The phase change orbit is described by the orbit elements as: tx , i tx =i ed , Ω tx = Ω ed , ω tx = ω ed , f tx = f ed ;

[0059] 2) The orbit determined by the above orbit elements is used as the initial value for orbit recursion, and the recursion time is T tx , the latitude amplitude after recursion is obtained as

[0060] 3) The correction time is calculated as Before calculation, u is converted to [-π, π], where u tx = ω tx + f tx , The corrected semi-major axis of the orbit is If Δt≤0.001, exit the iteration, otherwise go to step 1);

[0061] The velocity increment of the phase change orbit is:

[0062]

[0063] The orbit is changed in the orbit system, and the velocity increment of the orbit change is [Δv tx 00];

[0064] After the strategy calculation is completed, the orbit change can be performed, and after the orbit change is completed, after running R n orbits, the orbit change [-Δv tx 00] can return to the end orbit, and finally glide to the mission window.

[0065] Compared with the prior art, the present application has the following advantages:

[0066] (1) The strategy calculation process of the present application is simple;

[0067] (2) The present application adopts Hohmann transfer in the transfer process, and realizes optimal fuel consumption;

[0068] (3) The present application realizes transfer from a circular orbit to a circular orbit, and can be repeatedly used to realize multiple rendezvous control. BRIEF DESCRIPTION OF DRAWINGS

[0069] In order to more clearly illustrate the technical solutions of the present application, the drawings required to be used in the description will be briefly introduced as follows. Obviously, the drawings in the following description are one embodiment of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings:

[0070] Figure 1 A flow chart of a trajectory planning method for target window rendezvous provided by the present application;

[0071] Figure 2 A schematic diagram of transfer process;

[0072] Figure 3 A schematic diagram of terminal correction. DETAILED DESCRIPTION

[0073] The scheme proposed by the present application will be further described in detail in combination with the drawings and specific embodiments. The advantages and features of the present application will be more clear according to the following description. It should be noted that the drawings are very simplified and all use non-precise proportions, only to facilitate, clear and assist the purpose of explaining the embodiments of the present application. In order to make the purpose, features and advantages of the present application more obvious and easy to understand, please refer to the drawings. It should be noted that the structure, proportion, size and the like shown in the drawings attached to the present specification are only used to cooperate with the content disclosed in the specification, so as to be understood and read by those skilled in the art, and do not have technical significance to limit the conditions of the present application implementation, so any modification of structure, change of proportion relationship or adjustment of size, without affecting the effect and purpose that can be produced by the present application, should still fall within the scope of the technical content disclosed by the present application.

[0074] The application provides an autonomous universal trajectory planning technology for target window rendezvous, which can be applied to a coplanar rendezvous task of a space vehicle in a near-circular orbit.

[0075] The application plans a rendezvous trajectory by time distribution based on the rendezvous window, corrects the distributed time by orbit recursion, and finally completes the window rendezvous of the target by Hohmann transfer.

[0076] As shown in the figure, the autonomous universal trajectory planning method for target window rendezvous provided by the application comprises the following steps: Figure 1

[0077] Step one, calculate the range of the latitude amplitude angle that can be reached;

[0078] Step two, preliminarily calculate the transfer time of the strategy;

[0079] Step three, correct the transfer time by orbit recursion;

[0080] Step four, calculate the transfer strategy;

[0081] Step five, long-term drift correction strategy.

[0082] Specifically, the range of the latitude amplitude angle that can be reached by the autonomous universal trajectory planning technology for target window rendezvous in step one further comprises the following steps:

[0083] The time T mid in the middle orbit is half of the orbit period, the orbit semi-major axis is a mid = 0.5(a s +a t ), and the following equation is obtained:

[0084]

[0085] Wherein, a s is the initial orbit semi-major axis, a t is the window orbit semi-major axis, ​is the intermediate orbit angular velocity, μ = 3.986004415e14 is the earth gravitational constant;

[0086] The formula is a two-body formula, and the orbit recursion method is used to correct the intermediate orbit running time T mid , and the specific iterative correction process is as follows.

[0087] 1) The intermediate orbit semi-major axis, orbit eccentricity, orbit inclination, orbit right ascension of ascending node, orbit argument of perigee, and true anomaly of perigee are respectively: mid , i mid =i s , Ω mid =Ω s , ω mid =0, f mid =0; wherein, i s is the current orbit inclination, Ω s is the current orbit right ascension of ascending node;

[0088] 2) The orbit determined by the above orbit elements is used as the initial value for recursion, and the recursion time is T mid , to obtain the latitude amplitude u dt of the orbit after recursion;

[0089] 3) Calculate the time correction amount , update T mid =T mid -Δt. If Δt≤0.001, exit the iteration, otherwise go to step 2);

[0090] T mid is the corrected fixed time, and the rendezvous time is T a , so the time T a -T mid needs to be allocated to T cs and T ed . When the time is allocated to the initial orbit or to the terminal orbit, the two extreme values of the latitude amplitude are reached, and the latitude amplitude limit that can be reached by the strategy is:

[0091] u1=u0+n t ·(T a -T mid )+π

[0092] u2=u0+n s ·(T a -T mid )+π

[0093] Wherein, u0 is the initial latitude amplitude; is the initial orbit angular velocity; is the terminal orbit angular velocity.

[0094] The step two of preliminary calculating the transfer time of strategy further comprises the following steps:

[0095] Determine the fixed point phase u t +k·2π(k is an integer) in the interval range composed of u1 and u2;

[0096] From the result of step one, if the time is all allocated to the terminal orbit, the phase obtained is u1, thus the time needed to be allocated to the initial orbit can be calculated by the following way:

[0097] Δu=u t -u1

[0098] Limit the range of Δu to [0, 2π], if n s -n t <0, then Δu=Δu-2π. The transfer time T bg is calculated by the following formula:

[0099]

[0100] Then the running time T ed of the terminal orbit is:

[0101] T ed =T a -T mid -T bg .

[0102] The step three of transfer time correction of strategy further comprises the following steps:

[0103] The orbit of the transfer strategy calculation time is described by the orbit elements as follows: a s , e s , i s , Ω s , ω s , f s . The terminal orbit under the window constraint is described by the orbit elements as follows at the conjunction time: a t , e t =0, i t =i s , Ω t =Ω s , ω t =0, f t =u t ;

[0104] The strategy obtained by the preliminary calculation of steps one and two is that the running time of the initial orbit is T bg , the running time of the intermediate orbit is T mid , and the running time of the terminal orbit is T edThe following uses a trajectory recursion algorithm to correct T. bg During the correction process, keep T mid Keep it unchanged, keep T bg With T ed The sum remains unchanged. Iteratively correct T bg The steps are as follows:

[0105] 1) The time T is calculated from the orbital time using the strategy. bg (T bg The meaning is how long after starting the orbital change begins, referring to the moment of the orbital change. Therefore, the initial orbital travel time is T. bg The recursion is used to obtain the latitudinal argument at the moment of orbital change; therefore, the recursion time is also T. bg ), to obtain the latitudinal argument u of the spacecraft during the first orbital change. bg1 The time T is calculated by working backwards from the rendezvous point. ed (The recursion here is to solve for the latitudinal argument at the moment of the second orbit change, which is to deduce backwards from the rendezvous time (the endpoint), hence the addition of the symbol - to indicate that it is a backward deduction. The backward deduction time is the time required to travel after reaching the terminal orbit.) This yields the latitudinal argument u of the spacecraft at the moment of the second orbit change. bg2 .

[0106] 2) Time correction amount Before calculation, (u) bg2 -u bg1 -π) to [-π,π]. Corrected T bg =T bg -Δt,T ed =T ed +Δt. If Δt≤0.001, exit the iteration; otherwise, go to step 1).

[0107] Step four, which calculates the trajectory change strategy, further includes the following steps:

[0108] The recursive time T is derived from the orbital time calculated by the strategy. bg The position of the trajectory change point during the first trajectory change is obtained as R. bg Then the speed increments for the two orbital changes are:

[0109]

[0110]

[0111] Therefore, the orbital change strategy is: 1) The first orbital change occurs at time T. bg Afterwards, the velocity increment in the orbital system is [Δv1 0 0]; 2) The time of the second orbital change is T. bg +T mid The velocity increment in the orbital system is [Δv2 0 0].

[0112] Step five, the long-term drift correction strategy, further includes the following steps:

[0113] The current orbital period is T s The terminal orbital period is T T If T bg >T s If T, then the spacecraft has a gliding time greater than one track before changing orbit; similarly, if T ed >T T If the aircraft has a glide time of more than one track before reaching the window after changing its course, then a correction control is added when the glide time is greater than one track to reduce the trajectory recursion error that increases with the recursion time.

[0114] If T bg >T s Then in T bg ≤T s If necessary, the strategy is recalculated from the beginning of step one.

[0115] If T ed >T T After the orbital change is completed according to the orbital change strategy in step four, the following phase adjustment control is performed.

[0116] The orbit after the orbital change is described by orbital elements: a ed e ed i ed Ω ed ω ed f ed The remaining task time is T. last The remaining phase is u last =u t -u ed The latitude argument u corresponding to the orbit after the orbital change ed =ω ed +f ed , will u last Convert to [0, 2π];

[0117] Calculate the phase u of the current orbit. last Time required:

[0118]

[0119] in, It is the orbital angular velocity;

[0120] Using the orbital recursion method for t ed The iterative correction process is as follows:

[0121] 1) The time t is derived from the orbit after the orbit change is completed.ed The orbital phase u is obtained. t ;

[0122] 2) Calculate the time correction amount Before calculation Switch to [-π,π] and adjust time t. ed =t ed +Δt. If Δt≤0.001, exit the iteration; otherwise, go to step 1).

[0123] Depend on Rounding R gives the number of revolutions on the final track. n The target orbit period for phase adjustment and orbit change is calculated as follows:

[0124]

[0125] The semi-major axis of the phase-modulated target orbit is obtained as follows:

[0126]

[0127] The semi-major axis of the target orbit is corrected using a recursive orbital method, and the steps are as follows:

[0128] 1) The phase-adjusting track is described by the number of track elements: a tx , i tx =i ed Ω tx =Ω ed ω tx =ω ed f tx =f ed ;

[0129] 2) The orbit determined by the above orbital elements is used as the initial value for orbital recursion, with a recursion time of T. tx The recursive latitude argument is obtained as follows:

[0130] 3) Calculate the correction time as follows Before calculation Go to [-π,π], where u tx =ω tx +f tx , The corrected semi-major axis of the track is If Δt≤0.001, exit the iteration; otherwise, go to step 1.

[0131] The speed increment for phase-shifting and track changing is:

[0132]

[0133] The orbit is changed under the orbit system, and the orbit change speed increment is [Δv tx 0 0].

[0134] After the strategy calculation is completed, the orbit change can be performed, and after the orbit change is completed, the R n circle is run, and then the orbit change [-Δv tx 00] can be performed to return to the terminal orbit, and finally glide to the mission window.

[0135] Although the present application has been described in detail by the above preferred embodiments, it should be appreciated that the above description should not be considered as limiting the present application. Various modifications and alternatives will be apparent to those skilled in the art after reading the above description. Therefore, the scope of the present application should be defined by the appended claims.

Claims

1. A trajectory planning method for target window intersection, characterized in that, Includes the following steps: Step 1: Calculate the achievable range of latitude angles; Step 2: Preliminary calculation of the strategy change time; Step 3: Correct the orbit change time using a recursive orbital method; Step 4: Calculate the trajectory change strategy; Step 5: Long-term drift correction strategy; The step one, calculating the latitude argument range, further includes: The time T during the journey in the intermediate orbit mid For half an orbital period, the semi-major axis of the orbit is a. mid =0.5(a) s +a t Then we have: Among them, a s Let a be the semi-major axis of the initial orbit. t For the semi-major axis of the window track, The angular velocity of the intermediate orbit is μ = 3.986004415e14, and the gravitational constant is 3.986004415e14. The intermediate orbit running time T is calculated using a recursive orbital method. mid The correction process is as follows: 1) The semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and true anomaly of the intermediate orbit are respectively: a mid , i mid =i s Ω mid =Ω s ω mid =0,f mid =0; where i s Ω represents the current orbital inclination. s The right ascension of the ascending node of the current orbit; 2) The orbit determined by the above orbital elements is used as the initial value for recursion, and the recursion time is T. mid The latitude argument u of the recursive orbit is obtained. dt ; 3) Calculate the time correction amount Update T mid =T mid -Δt, if Δt≤0.001, then exit the iteration; otherwise, go to step 2); T mid The rendezvous time is the corrected fixed time, and the rendezvous time is T. a Then time T needs to be... a -T mid Assigned to T cs and T ed If the latitudinal argument reaches its two extreme values ​​when all time is allocated to the initial orbit or the final orbit, then the latitudinal argument limit achievable by this strategy is: u1=u0+n t ·(T a -T mid )+π u2=u0+n s ·(T a -T mid )+π Where u0 is the initial latitude argument; The initial orbital angular velocity; This represents the angular velocity of the final orbit.

2. The trajectory planning method for target window intersection as described in claim 1, characterized in that, Step two, which involves the preliminary calculation of the strategy change time, further includes: Determine the fixed-point phase u t +k·2π (k is an integer) is within the interval formed by u1 and u2; Based on the calculation results from step one, if all the time is allocated to the final orbit, the resulting phase is u1. Therefore, the time to be allocated to the initial orbit can be calculated as follows: Δu=u t -u1 Transform Δu to [0, 2π], if n s -n t If < 0, then Δu = Δu - 2π, and the orbital change time T bg Calculated by the following formula: Then, during the final orbital travel time T ed for: T ed =T a -T mid -T bg 。 3. The trajectory planning method for target window intersection as described in claim 2, characterized in that, The aforementioned step three, orbit change time correction, further includes: The orbit at the moment of orbit change strategy calculation is described by orbital elements: a s e s i s Ω s ω s f s The final orbit under window constraints is described by orbital elements at the rendezvous time: a t e t =0, i t =i s Ω t =Ω s ω t =0,f t =u t ; The strategy calculated in steps one and two yields an initial orbital travel time of T. bg The travel time in the intermediate orbit is T. mid During the end orbit travel time T ed The following section corrects T using a trajectory recursion algorithm. bg During the correction process, keep T mid Keep it unchanged, keep T bg With T ed The sum remains unchanged, and T is iteratively corrected. bg The steps are as follows: 1) The time T is calculated from the orbital time using the strategy. bg The latitude argument u of the spacecraft during the first orbital change was obtained. bg1 Time T is calculated by reversing the orbital time from the rendezvous point. ed The latitude argument u of the spacecraft during the second orbital change was obtained. bg2 ; 2) Calculate the time correction amount Before calculation, (u) bg2 -u bg1 -π) redirects to [-π,π]; after correction, T bg =T bg -Δt,T ed =T ed +Δt; if Δt≤0.001, exit the iteration; otherwise, go to step 1).

4. The trajectory planning method for target window intersection as described in claim 3, characterized in that, Step four, calculating the trajectory change strategy, further includes: The recursive time T is derived from the orbital time calculated by the strategy. bg The position of the orbit change point during the first orbit change was obtained as follows: Therefore, the speed increments for the two orbital changes are: Therefore, the orbital change strategy is: 1) The first orbital change occurs at time T. bg Afterwards, the velocity increment in the orbital system is [Δv1 0 0]; 2) The time of the second orbital change is T. bg +T mid The velocity increment in the orbital system is [Δv2 0 0].

5. The trajectory planning method for target window intersection as described in claim 1, characterized in that, The aforementioned step five, the long-term drift correction strategy, further includes: If T bg >T s T s Given the current orbital period, then at T bg ≤T s If necessary, recalculate the strategy from step one. If T ed >T T T T For the final orbital period, after completing the orbital change according to the orbital change strategy in step four, the following phase adjustment control is performed: The orbit after the orbital change is described by orbital elements: a ed e ed i ed Ω ed ω ed f ed The remaining task time is T. last The remaining phase is u last =u t -u ed , where u ed =ω ed +f ed , will u last Convert to [0, 2π]; Calculate the phase u of the current orbit. last Time required: in, It is the orbital angular velocity; Using the orbital recursion method for t ed The iterative correction process is as follows: 1) The time t is derived from the orbit after the orbit change is completed. ed The orbital phase u is obtained. t ; 2) Calculate the time correction amount Before calculation Switch to [-π,π] and adjust time t. ed =t ed +Δt; if Δt≤0.001, then exit the iteration; otherwise, go to step 1); Depend on Rounding R gives the number of revolutions on the final track. n The target orbit period for phase adjustment and orbit change is calculated as follows: The semi-major axis of the phase-modulated target orbit is obtained as follows: The semi-major axis of the target orbit is corrected using a recursive orbital method, and the steps are as follows: 1) The phase-adjusting track is described by the number of track elements: a tx , i tx =i ed Ω tx =Ω ed ω tx =ω ed f tx =f ed ; 2) The orbit determined by the above orbital elements is used as the initial value for orbital recursion, with a recursion time of T. tx The recursive latitude argument is obtained as follows: 3) Calculate the correction time as follows Before calculation Go to [-π,π], where u tx =ω tx +f tx , The corrected semi-major axis of the track is If Δt≤0.001, exit the iteration; otherwise, go to step 1. The speed increment for phase-shifting and track changing is: A change in orbital configuration is performed, with the velocity increment being [Δv]. tx 0 0]; Once the strategy calculation is complete, the trajectory change can be performed. After the trajectory change is complete, R is run. n After circling, change orbit again [-Δv] tx [0 0] It can return to the end track and eventually glide to the mission window.

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