Method and device for determining transfer orbit of spacecraft

Abstract

The present invention provides a method and apparatus for determining a spacecraft's transfer orbit, belonging to the field of orbital transfer technology. The method provided in an embodiment of the present application is applied in a scenario where a first spacecraft is pursuing a second spacecraft. When the first spacecraft lags behind the second spacecraft, the method determines a maximum phase difference based on the first spacecraft's current position and the radius of a central celestial body. The transfer time of the first spacecraft is determined based on the maximum phase difference and the current phase difference between the first and second spacecraft, thereby determining the start and end times of the first spacecraft's orbital transfer. Furthermore, the trajectory information of the target transfer orbit is determined based on the Lambert orbital transfer model. The target transfer orbit determined by this method has an orbital altitude greater than the radius of the central celestial body. A reasonable transfer orbit can be designed for the spacecraft, thereby smoothly adjusting the spacecraft's motion state to enable the spacecraft to complete the pursuit mission.

Description

Technical Field

[0001] The present invention relates to the field of orbit transfer technology, and in particular to a method and device for determining the transfer orbit of a spacecraft. Background Art

[0002] When a spacecraft (such as a satellite) orbits a central celestial body (such as the Earth), it typically follows a given orbit. In some cases, it may be necessary to adjust the spacecraft's motion. Specifically, this can be done by adjusting the spacecraft's orbit.

[0003] At present, when the orbital altitude of a spacecraft is relatively low, the orbital altitude of the adjusted operating orbit (hereinafter referred to as the transfer orbit) may be smaller than the radius of the central celestial body. In this case, the determined transfer orbit is an unreasonable transfer orbit and the motion state of the spacecraft cannot be adjusted. Summary of the Invention

[0004] The present invention proposes a method and device for determining the transfer orbit of a spacecraft. In a scenario where the spacecraft performs a pursuit mission, a reasonable transfer orbit can be designed for the spacecraft, thereby smoothly adjusting the motion state of the spacecraft to enable the spacecraft to complete the pursuit mission.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a method for determining a transfer orbit of a spacecraft, which is applied to a scenario in which a first spacecraft is chasing a second spacecraft, wherein the first spacecraft is transferred from an original orbit to a target transfer orbit to chase the second spacecraft, and the first spacecraft and the second spacecraft move in the same direction around the same central celestial body. The method includes: when the first spacecraft lags behind the second spacecraft, determining the maximum phase difference between the phase of the first spacecraft running on the transfer orbit and the phase of the second spacecraft running on the original orbit when the first spacecraft meets the second spacecraft after running one circle on the transfer orbit, the transfer orbit corresponding to the maximum phase difference is the limit transfer orbit, and the limit transfer orbit is the maximum phase difference between the first spacecraft running on the transfer orbit and the second spacecraft running on the original orbit. The apogee orbital altitude of the limiting transfer orbit is the current orbital altitude of the first spacecraft, and the perigee orbital altitude of the limiting transfer orbit is the radius of the central celestial body; and based on the current phase difference and the maximum phase difference between the first spacecraft and the second spacecraft, the transfer time of the first spacecraft is determined. The transfer time is the time required for the first spacecraft to pursue the second spacecraft, and the transfer time is greater than the orbital period of the limiting transfer orbit; and then based on the Lambert orbit transfer model and the transfer time of the first spacecraft, the trajectory information of the target transfer orbit is determined. The trajectory information of the target transfer orbit includes the speed of the first spacecraft at multiple points on the target transfer orbit.

[0007] In the method for determining the transfer orbit of a spacecraft provided by the present invention, the transfer time determined based on the maximum phase difference and the current phase difference between the first spacecraft and the second spacecraft is greater than the orbital period of the limit transfer orbit, which can ensure that the orbital altitude of the target transfer orbit of the first spacecraft is greater than the radius of the central celestial body, so that a reasonable transfer orbit can be designed for the spacecraft, thereby smoothly adjusting the motion state of the spacecraft to enable the spacecraft to complete the pursuit mission.

[0008] In an implementation of the first aspect, a maximum phase difference between a phase of the first spacecraft operating on the transfer orbit and a phase of the second spacecraft operating on the original orbit satisfies:

[0009]

[0010]

[0011] Where T1 represents the orbital period of the extreme transfer orbit, T2 represents the orbital period of the second spacecraft on the original orbit, represents the maximum phase difference; a represents the semi-major axis of the extreme transfer orbit, μ represents the gravitational constant of the central celestial body, R1 represents the apogee orbital altitude of the extreme transfer orbit, and R2 represents the perigee orbital altitude of the extreme transfer orbit.

[0012] In an implementation of the first aspect, the transfer time of the first spacecraft is determined based on the current phase difference and the maximum phase difference between the first spacecraft and the second spacecraft, including: determining the predicted transfer time of the first spacecraft based on the current phase difference and the maximum phase difference between the first spacecraft and the second spacecraft; and optimizing the predicted transfer time using a gradient descent method to obtain the transfer time of the first spacecraft.

[0013] In an implementation of the first aspect, when a current phase difference between the first spacecraft and the second spacecraft is less than a maximum phase difference, the predicted transfer time of the first spacecraft satisfies:

[0014]

[0015] When the current phase difference between the first spacecraft and the second spacecraft is greater than or equal to the maximum phase difference, the predicted transfer time of the first spacecraft satisfies:

[0016]

[0017] Among them, T trans represents the predicted transfer time of the first spacecraft, T2 represents the orbital period of the second spacecraft on the original orbit, and Δθ represents the current phase difference between the first spacecraft and the second spacecraft.

[0018] In one implementation of the first aspect, trajectory information of a target transfer orbit is determined based on a Lambert orbit transfer model and a transfer time of the first spacecraft, including: determining a starting velocity and an ending velocity of the first spacecraft on the target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft; and interpolating the starting velocity and the ending velocity of the target transfer orbit to obtain velocities of the first spacecraft at multiple points on the target transfer orbit.

[0019] In one implementation of the first aspect, before determining trajectory information of the target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft, the method provided by the present invention further includes: when the first spacecraft is ahead of the second spacecraft, determining a predicted transfer time of the first spacecraft in the event that the first spacecraft encounters the second spacecraft after completing one orbit of the transfer orbit; wherein the predicted transfer time of the first spacecraft satisfies:

[0020]

[0021] Among them, T trans represents the predicted transfer time of the first spacecraft, T2 represents the orbital period of the second spacecraft on the original orbit, and Δθ represents the current phase difference between the first spacecraft and the second spacecraft. The predicted transfer time is optimized using the gradient descent method to obtain the transfer time of the first spacecraft.

[0022] In an implementation of the first aspect, the Lambert orbital transfer model satisfies:

[0023]

[0024] Where v0 represents the velocity vector of the first spacecraft at the start of the transfer time, v1 represents the velocity vector of the first spacecraft at the end of the transfer time, G(t1,t0) represents the first orbital state transfer function, F(t1,t0) represents the second orbital state transfer function, G t (t1, t0) represents the derivative of the first orbital state transfer function with respect to time, t0 represents the start time of the transfer time, t1 represents the end time of the transfer time, r0 represents the position vector of the first spacecraft at the start time of the transfer time, and r1 represents the position vector of the first spacecraft at the end time of the transfer time.

[0025] In a second aspect, the present invention provides a device for determining a spacecraft transfer orbit, comprising a phase difference determination module, a transfer time determination module, and a transfer orbit determination module; the phase difference determination module is configured to, when a first spacecraft lags behind a second spacecraft, determine the maximum phase difference between the phase of the first spacecraft on the transfer orbit and the phase of the second spacecraft on the original orbit when the first spacecraft encounters the second spacecraft after one revolution on the transfer orbit, wherein the transfer orbit corresponding to the maximum phase difference is a limit transfer orbit; wherein the apoapsis orbital altitude of the limit transfer orbit is the current orbital altitude of the first spacecraft, and the periapsis orbital altitude of the limit transfer orbit is the radius of the central celestial body; the transfer time determination module is configured to determine the transfer time of the first spacecraft based on the current phase difference and the maximum phase difference between the first spacecraft and the second spacecraft; the transfer time is the time required for the first spacecraft to pursue the second spacecraft, and the transfer time is greater than the orbital period of the limit transfer orbit; the transfer orbit determination module is configured to determine trajectory information of a target transfer orbit based on a Lambert orbit transfer model and the transfer time of the first spacecraft; the trajectory information of the target transfer orbit includes the velocities of the first spacecraft at multiple points on the target transfer orbit.

[0026] In one implementation of the second aspect, the transfer time determination module is specifically configured to determine a predicted transfer time of the first spacecraft based on a current phase difference and a maximum phase difference between the first spacecraft and the second spacecraft, and to optimize the predicted transfer time using a gradient descent method to obtain the transfer time of the first spacecraft.

[0027] In one implementation of the second aspect, the transfer orbit determination module is specifically used to determine the starting velocity and the ending velocity of the first spacecraft on the target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft; and interpolate the starting velocity and the ending velocity of the target transfer orbit to obtain the velocity of multiple points of the first spacecraft on the target transfer orbit.

[0028] In one implementation of the second aspect, the transfer time determination module is further configured to, when the first spacecraft is ahead of the second spacecraft, determine a predicted transfer time for the first spacecraft when the first spacecraft encounters the second spacecraft after completing one orbit of the transfer orbit. The predicted transfer time for the first spacecraft satisfies:

[0029]

[0030] Among them, T trans represents the predicted transfer time of the first spacecraft, T2 represents the orbital period of the second spacecraft on the original orbit, and Δθ represents the current phase difference between the first spacecraft and the second spacecraft. The predicted transfer time is optimized using the gradient descent method to obtain the transfer time of the first spacecraft.

[0031] In a third aspect, the present invention provides an electronic device comprising a processor and a memory coupled to the processor; the memory is used to store computer instructions, and when the electronic device is running, the processor executes the computer instructions stored in the memory, so that the electronic device performs the method described in the first aspect or any one of its implementations.

[0032] In a fourth aspect, the present invention provides a computer-readable storage medium comprising computer program instructions, which, when executed by a computer, enable the computer to execute the method as described in the first aspect or any one of its implementations.

[0033] In a fifth aspect, the present invention provides a computer program product, comprising computer program instructions, which, when executed on a computer, enable the computer to execute the method as described in the first aspect or any one of its implementations.

[0034] The technical effects corresponding to the above-mentioned second to fifth aspects and their possible implementation methods can refer to the above-mentioned description of the technical effects of the first aspect and its possible implementation methods, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is one of the schematic diagrams of a method for determining the transfer orbit of a spacecraft provided in an embodiment of the present application;

[0036] Figure 2 is a schematic diagram of the phase relationship between the first spacecraft and the second spacecraft in an embodiment of the present application;

[0037] Figure 3 This is a schematic diagram of changes in the velocity increment and initial phase difference of the first spacecraft provided in an embodiment of the present application;

[0038] Figure 4 This is one of the transfer trajectory schematic diagrams provided in the embodiments of the present application;

[0039] Figure 5 This is the second schematic diagram of the method for determining the transfer orbit of a spacecraft provided in an embodiment of the present application;

[0040] Figure 6 This is the second transfer orbit diagram provided in an embodiment of the present application;

[0041] Figure 7 This is the third schematic diagram of the method for determining the transfer orbit of a spacecraft provided in an embodiment of the present application;

[0042] Figure 8 This is a schematic structural diagram of a device for determining a transfer orbit of a spacecraft provided in an embodiment of the present application. DETAILED DESCRIPTION

[0043] In the description and claims of the present invention, the terms "first" and "second" are used to distinguish different objects rather than to describe a specific order of objects.

[0044] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0045] It should be understood that while the terms "first" and "second" may be used to describe spacecraft in embodiments of this application, the present invention is not limited to these terms. These terms are merely used to distinguish between the two spacecraft. For example, the first spacecraft could be referred to as the second spacecraft, and similarly, the second spacecraft could be referred to as the first spacecraft without departing from the scope of the embodiments of the present invention.

[0046] In the embodiments of this application, spacecraft are used to perform specific space missions, such as scientific experiments, planetary observation, and weather monitoring. Exemplarily, spacecraft include unmanned spacecraft and manned spacecraft. Unmanned spacecraft include artificial satellites and space probes, while manned spacecraft include manned spacecraft, space stations, and space shuttles.

[0047] In one scenario, to ensure the continuous and stable completion of space missions, a large number of high-value satellites deployed in low-Earth orbit require on-orbit maintenance and servicing, such as propellant replenishment, payload repair, and attitude recovery. Currently, satellites capable of providing maintenance services are often used to perform on-orbit maintenance and servicing of other satellites. The servicing satellites and the high-value satellites orbit the same central celestial body. In this scenario, the servicing satellite needs to adjust its motion state in a relatively short period of time, shifting its orbit to catch up with the serviced satellite. After the two satellites rendezvous, on-orbit maintenance and servicing of the high-value satellite can be performed.

[0048] In the embodiments of this application, a spacecraft performing a pursuit mission may be referred to as a pursuit spacecraft or an action spacecraft, and the spacecraft being pursued may be referred to as a target spacecraft. For example, the pursuit spacecraft or action spacecraft may be a maintenance spacecraft, a service spacecraft, or a resource spacecraft. The embodiments of this application do not limit the name or type of spacecraft performing a pursuit mission.

[0049] In the scenario where a spacecraft performs a pursuit mission, the orbit that the spacecraft runs on before performing the pursuit mission is called the original orbit of the spacecraft; the orbit that the spacecraft runs on during the pursuit mission is called the transfer orbit of the spacecraft. By adjusting the motion state of the spacecraft, the spacecraft is transferred from the original orbit to the transfer orbit to complete the pursuit mission.

[0050] In an embodiment of the present application, before the pursuing spacecraft performs the pursuit mission, the pursuing spacecraft and the target spacecraft are approximately running on the same orbit, that is, before the pursuing spacecraft performs the pursuit mission, the pursuing spacecraft and the target spacecraft are both running on the original orbit.

[0051] In order to solve the problem in the background technology that when the orbital altitude of the spacecraft is low, the orbital altitude of the determined transfer orbit may be smaller than the radius of the central celestial body, resulting in an unreasonable transfer orbit, the embodiment of the present application provides a method and device for determining the transfer orbit of a spacecraft. When the pursuing spacecraft lags behind the target spacecraft, the radius of the central celestial body is used as a constraint condition for the periapsis orbital altitude of the transfer orbit of the pursuing spacecraft, and the transfer time of the first spacecraft is determined, and then the trajectory information of the transfer orbit is determined. This method can ensure that the orbital altitude of the pursuing spacecraft is not less than the radius of the central celestial body, and a reasonable transfer orbit can be designed for the spacecraft, so that the motion state of the spacecraft can be smoothly adjusted to enable the spacecraft to complete the pursuit mission.

[0052] For example, the method for determining a spacecraft transfer orbit provided in an embodiment of the present invention can be performed by an electronic device with processing capabilities, such as a computer or server. For example, the hardware components of a computer may include a processor, memory, a network interface, a user interface, a communication bus, and the like.

[0053] The processor is used to control the electronic device to perform related processing and computing tasks. Specifically, in the embodiment of the present application, the processor is used to determine the transfer time of the pursuit spacecraft and, based on the Lambert orbit transfer model and the transfer time, determine the trajectory information of the target transfer orbit of the pursuit spacecraft. The processor may include a central processing unit (CPU) or other processor. The processor may be single-core or multi-core, for example, the processor may include multiple CPUs.

[0054] The memory is used to store computer instructions and related data. Specifically, in the embodiment of the present application, the memory is used to store phase differences, target transfer trajectory information, etc. The memory can be random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, or optical storage, disk storage media or other magnetic storage devices, or any other medium capable of storing program code or data accessible by a computer. Optionally, the memory can be integrated into the processor, or the memory can be independent of the processor.

[0055] The network interface is used for the computer to communicate with other devices or communication networks. The network interface can be a transceiver with transceiver functions. Optionally, the network interface can include a standard wired interface or a wireless interface (such as a Wi-Fi interface, a Bluetooth interface, or a 5G interface).

[0056] The communication bus is used to achieve connection and communication between different components. For example, the processor, memory, network interface, and user interface mentioned above can be interconnected through the communication bus.

[0057] The user interface may include a display screen and an input unit (such as a keyboard). Optionally, the user interface may also include a standard wired interface and a wireless interface.

[0058] Those skilled in the art will appreciate that the above-mentioned computer may also include more or fewer components, or a combination of certain components, or different arrangements of components, which is not limited in the embodiments of the present application.

[0059] The method for determining the transfer orbit of a spacecraft provided in an embodiment of the present application is applied to a scenario in which a first spacecraft (i.e., an action spacecraft) pursues a second spacecraft (i.e., a target spacecraft). The first spacecraft transfers from its original orbit to a target transfer orbit to pursue the second spacecraft, and the first spacecraft and the second spacecraft move in the same direction around the same central celestial body.

[0060] It should be noted that, in the embodiment of the present application, it is limited that the first spacecraft can catch up with the second spacecraft when it runs one circle on the transfer orbit, that is, the first spacecraft meets the second spacecraft when it runs one circle on the transfer orbit.

[0061] The following describes in detail the method for determining the transfer orbit of a spacecraft provided in the embodiment of the present application. Figure 1 As shown, the method includes S101-S103.

[0062] S101. When the first spacecraft lags behind the second spacecraft, determine the maximum phase difference between the phase of the first spacecraft on the transfer orbit and the phase of the second spacecraft on the original orbit when the first spacecraft meets the second spacecraft after completing one orbit on the transfer orbit. The transfer orbit corresponding to the maximum phase difference is the extreme transfer orbit; wherein the apogee orbital altitude of the extreme transfer orbit is the current orbital altitude of the first spacecraft, and the perigee orbital altitude of the extreme transfer orbit is the radius of the central celestial body.

[0063] In the embodiment of the present application, the positional relationship between the first spacecraft and the second spacecraft is determined by the phase relationship between the first spacecraft and the second spacecraft. Specifically, when the first spacecraft and the second spacecraft are moving in the same direction around the same central celestial body, if the phase of the first spacecraft is greater than that of the second spacecraft, the first spacecraft is ahead of the second spacecraft; if the phase of the first spacecraft is less than that of the second spacecraft, the first spacecraft is behind the second spacecraft.

[0064] Exemplary, reference Figure 2 , the first spacecraft and the second spacecraft move around the central celestial body in the first direction, the phase of the first spacecraft is a1, the phase of the second spacecraft is a2, Figure 2 In (a), a1>a2, the first spacecraft is ahead of the second spacecraft; Figure 2 In (b), a2>a1, then the first spacecraft lags behind the second spacecraft.

[0065] It should be understood that the phase difference between spacecraft is the absolute value of the difference between the phases of the spacecraft, and the above-mentioned maximum phase difference is the absolute value of the difference between the phase of the first spacecraft running on the transfer orbit and the phase of the second spacecraft running on the original orbit.

[0066] In the embodiment of the present application, since the first spacecraft meets the second spacecraft when it runs one circle on the transfer orbit, the position of the first spacecraft at the current moment is the position where the first spacecraft and the second spacecraft meet.

[0067] Through the simulation experiment, the process of the first spacecraft chasing the second spacecraft is simulated to obtain the change of the velocity increment of the first spacecraft and the change of the initial phase difference of the first spacecraft. The initial phase difference of the first spacecraft refers to the phase difference between the phase of the first spacecraft when it is in the transfer orbit when it meets the second spacecraft and the initial phase of the first spacecraft (the phase when the first spacecraft starts chasing). Figure 3 As shown in the figure, the black solid line represents the change curve of the velocity increment of the first spacecraft during the transfer process, and the black dotted line represents the change curve of the initial phase difference. The initial phase difference is zero, which means that the first spacecraft has run an integer number of circles on the transfer orbit. Figure 3It can be seen that when the first spacecraft runs one circle in the transfer orbit and meets the second spacecraft, the speed increment required by the first spacecraft is the smallest. The first spacecraft realizes orbit transfer and catches up with the second spacecraft with the smallest speed increment, which can save fuel and shorten the pursuit time to a certain extent.

[0068] It can be understood that when the first spacecraft meets the second spacecraft after one orbit, the running time of the first spacecraft and the second spacecraft is the same, that is, the running time of the second spacecraft is equal to the orbital period of the transfer orbit of the first spacecraft. Figure 4 As shown, in the case where the first spacecraft lags behind the second spacecraft, since the first spacecraft runs one circle on the transfer orbit and meets the second spacecraft, the second spacecraft runs less than one circle on the original orbit, which means that the motion period of the first spacecraft on the transfer orbit is smaller than the motion period of the second spacecraft on the original orbit. For the first spacecraft, when the speed increment is small, the smaller the orbital period, the lower the orbital altitude. It can be seen that when the motion period of the first spacecraft on the transfer orbit is smaller than the motion period of the second spacecraft on the original orbit, the orbital altitude of the transfer orbit is lower than the orbital altitude of the original orbit. In the embodiment of the present application, usually, the original orbit is a low orbit (for example, when the central celestial body is the earth, the original orbit is a low earth orbit), and the orbital altitude of the transfer orbit of the above-mentioned first spacecraft is lower than the orbital altitude of the original orbit, and there may be a risk of the first spacecraft colliding with the central celestial body.

[0069] Based on the above, we can know that the second spacecraft runs less than one circle on the original orbit, that is, the running time of the second spacecraft is less than one motion cycle. Its running time is:

[0070]

[0071] Where Δθ is the phase difference between the first and second spacecraft, and T2 is the orbital period of the second spacecraft on the original orbit. If the first spacecraft lags behind the second spacecraft, the greater the phase difference between the first and second spacecraft, the shorter the second spacecraft's travel time on the original orbit when the first and second spacecraft meet. Consequently, the shorter the orbital period of the first spacecraft's transfer orbit (the travel time of the second spacecraft is equal to the orbital period of the first spacecraft's transfer orbit), and the smaller the orbital altitude of the first spacecraft's transfer orbit. If the transfer orbit's altitude is lower than the radius of the central celestial body, the transfer orbit is unreasonable and cannot adjust the first spacecraft's motion state.

[0072] To prevent an unreasonable transfer orbit designed for the first spacecraft when the first spacecraft lags behind the second spacecraft, an embodiment of the present application sets a constraint on the orbital altitude of the first spacecraft on the transfer orbit and designs a transfer orbit for the first spacecraft based on the constraint. The orbital altitude constraint is that the orbital altitude of the transfer orbit is greater than the radius of the central celestial body.

[0073] Specifically, the orbital altitude of the first spacecraft at its apogee on the transfer orbit is set as the first spacecraft's current orbital altitude, and the orbital altitude of its perigee on the transfer orbit is set as the radius of the central celestial body. The phase difference between the first spacecraft's phase on the transfer orbit and the second spacecraft's phase on the original orbit is determined. This phase difference is the maximum phase difference between the first spacecraft's phase on the transfer orbit and the second spacecraft's phase on the original orbit. At this point, the transfer orbit has the lowest orbital altitude and is referred to as the extreme transfer orbit. That is, the transfer orbit corresponding to the maximum phase difference is the extreme transfer orbit. In other words, the phase difference between the first spacecraft's phase on the extreme transfer orbit and the second spacecraft's phase on the original orbit is the maximum phase difference.

[0074] According to the above content, the apogee orbital altitude of the extreme transfer orbit is the current orbital altitude of the first spacecraft, and the perigee orbital altitude of the extreme transfer orbit is the radius of the central celestial body. Optionally, when the first spacecraft lags behind the second spacecraft, the maximum phase difference is determined when the first spacecraft meets the second spacecraft after running one circle on the transfer orbit. satisfy:

[0075]

[0076]

[0077] Wherein, T1 represents the orbital period of the extreme transfer orbit, T2 represents the orbital period of the second spacecraft on the original orbit; a represents the semi-major axis of the extreme transfer orbit, μ represents the gravitational constant of the central celestial body, R1 represents the apogee orbital altitude of the extreme transfer orbit, and R2 represents the perigee orbital altitude of the extreme transfer orbit.

[0078] Since the transfer orbit corresponding to the maximum phase difference is the transfer orbit with the lowest orbital altitude, when the first spacecraft lags behind the second spacecraft, the maximum phase difference can be used as a constraint condition to design a transfer orbit with a phase difference smaller than the maximum phase difference as the target transfer orbit of the first spacecraft.

[0079] S102. Determine a transfer time of the first spacecraft based on a current phase difference and a maximum phase difference between the first spacecraft and the second spacecraft; the transfer time is the time required for the first spacecraft to pursue the second spacecraft, and the transfer time is greater than the orbital period of the extreme transfer orbit.

[0080] The current phase difference is the absolute value of the difference between the phase of the first spacecraft running on the original orbit and the phase of the second spacecraft running on the original orbit at the current moment.

[0081] In the embodiment of the present application, different methods are used to determine the transfer time of the first spacecraft according to the magnitude relationship between the current phase difference and the maximum phase difference between the first spacecraft and the second spacecraft, as shown in S1021-S1022 below.

[0082] Optionally, combined Figure 1 ,like Figure 5 As shown, S102 of the embodiment of the present application includes S1021-S1022.

[0083] S1021: Determine a predicted transfer time of the first spacecraft based on a current phase difference and a maximum phase difference between the first spacecraft and the second spacecraft.

[0084] In an embodiment of the present application, the first spacecraft meets the second spacecraft when it runs one circle on the transfer orbit. The predicted transfer time of the first spacecraft is the motion period of the first spacecraft on the transfer orbit, which is also equal to the running time of the second spacecraft.

[0085] In one implementation, when the current phase difference between the first spacecraft and the second spacecraft is less than the maximum phase difference, the second spacecraft has completed less than one revolution in the original orbit, and the first spacecraft has completed one revolution in the transfer orbit, and the two spacecraft may meet. Then, the predicted transfer time of the first spacecraft satisfies:

[0086]

[0087] Among them, T trans represents the predicted transfer time of the first spacecraft (i.e., the period of motion of the first spacecraft on the transfer orbit), T2 represents the orbital period of the second spacecraft on the original orbit (i.e., the period of motion of the second spacecraft on the original orbit), and Δθ represents the current phase difference between the first and second spacecraft. It can be seen that if the current phase difference between the first and second spacecraft is less than the maximum phase difference, the predicted transfer time of the first spacecraft is less than the orbital period of the first spacecraft on the transfer limit orbit.

[0088] In another implementation, if the current phase difference between the first and second spacecraft is greater than or equal to the maximum phase difference, the second spacecraft may meet the first spacecraft after it has completed one orbit on its original orbit and the first spacecraft has completed one orbit on its transfer orbit.

[0089]

[0090] Among them, T trans represents the predicted transfer time of the first spacecraft, T2 represents the orbital period of the second spacecraft on the original orbit, and Δθ represents the current phase difference between the first spacecraft and the second spacecraft.

[0091] In summary, when the current phase difference between the first spacecraft and the second spacecraft is greater than or equal to the maximum phase difference, the second spacecraft runs more than one circle on the original orbit, that is, the running time of the second spacecraft increases, and the motion period of the first spacecraft on the transfer orbit increases, then the orbital height of the first spacecraft increases. In this way, the orbital height of the transfer orbit is greater than the radius of the central celestial body, which can prevent the first spacecraft from colliding with the central celestial body.

[0092] Furthermore, when the current phase difference between the first spacecraft and the second spacecraft is greater than or equal to the maximum phase difference, the motion period of the first spacecraft on the transfer orbit is greater than the motion period of the first spacecraft on the original orbit, and the motion period of the first spacecraft on the original orbit is greater than the motion period of the first spacecraft on the extreme transfer orbit (the orbital altitude of the above-mentioned extreme transfer orbit is lower than the orbital altitude of the original orbit), then the predicted transfer time of the first spacecraft is greater than the orbital period of the extreme transfer orbit.

[0093] S1022. Use the gradient descent method to optimize the predicted transfer time to obtain the transfer time of the first spacecraft.

[0094] As can be understood, the gradient descent method, as an optimization algorithm, utilizes the gradient information of the objective function and iteratively adjusts the parameters in the opposite direction of the gradient so that the objective function value is less than the set minimum deviation value. In the embodiment of the present application, the parameter in the gradient descent method is the transfer time to be optimized (i.e., the predicted transfer time described above), the objective function is the velocity increment, the gradient value of the objective function is the quotient of the change in the velocity increment and the change in the predicted transfer time, and the direction of the gradient is the optimization direction of the predicted transfer time. The gradient is used to indicate the rate of change and direction of change of the velocity increment.

[0095] Illustratively, in the embodiment of the present application, the process of optimizing the predicted transfer time using the gradient descent method includes SA1-SA4.

[0096] SA1. Initialization parameters: Set the initial value of the transfer time to be optimized to the predicted transfer time and set the minimum deviation value.

[0097] Optionally, the minimum deviation value can be e -4 m / s.

[0098] Optionally, the minimum deviation value may also be any value less than 1 m / s. The embodiment of the present application does not limit the minimum deviation value.

[0099] SA2. Calculate the gradient: Substitute the transfer time to be optimized into the objective function to obtain the speed increment and gradient.

[0100] Optionally, in an embodiment of the present application, the objective function includes a Lambert orbit transfer model and a velocity increment calculation formula. The Lambert orbit transfer model is used to calculate the velocity vector of the first spacecraft at the start time of the transfer time and the velocity vector of the first spacecraft at the end time of the transfer time based on the predicted start time of the transfer time, the predicted end time of the transfer time, the position vector of the first spacecraft at the start time of the transfer time, and the position vector of the first spacecraft at the end time of the transfer time; the velocity increment calculation formula is used to calculate the velocity increment required for the first spacecraft to catch up with the second spacecraft based on the velocity vector of the first spacecraft before the transfer occurs, the velocity vector of the first spacecraft at the start time of the transfer time, the velocity vector of the first spacecraft at the end time of the transfer time, and the velocity vector of the first spacecraft when the first spacecraft and the second spacecraft remain synchronized after the first spacecraft meet.

[0101] The Lambert orbital transfer model satisfies:

[0102]

[0103] The speed increment calculation formula satisfies:

[0104] v in =|v0-v t0 |+|v1-v t1 |

[0105] Where v0 represents the velocity vector of the first spacecraft at the start of the transfer time, v1 represents the velocity vector of the first spacecraft at the end of the transfer time, G(t1,t0) represents the first orbital state transfer function, F(t1,t0) represents the second orbital state transfer function, G t (t1, t0) represents the time derivative of the first orbital state transfer function, t0 represents the start time of the transfer time, t1 represents the end time of the transfer time, r0 represents the position vector of the first spacecraft at the start time of the transfer time, and r1 represents the position vector of the first spacecraft at the end time of the transfer time; v inrepresents the velocity increment, v t0 represents the velocity vector of the first spacecraft before the transfer occurs (the velocity vector is the velocity vector of the first spacecraft on the original orbit before the transfer occurs, and the velocity vector is a known quantity), v t1 It represents the velocity vector of the first spacecraft when the first spacecraft and the second spacecraft keep synchronization after the first spacecraft meets the second spacecraft (the velocity vector is the velocity vector of the second spacecraft at the end of the transfer time, and the velocity vector is a known quantity).

[0106] Alternatively, F(t1, t0), G(t1, t0) and G in the above Lambert orbit transfer model t (t1,t0) satisfies:

[0107]

[0108]

[0109]

[0110] Where A represents the first intermediate parameter (known quantity), y0 represents the second intermediate parameter (known quantity), μ represents the gravitational constant of the central body, Δθ represents the angle between r0 and r1, z represents the universal variable, S(z) represents the orbital equation of the universal variable z, and C(z) represents the Kepler time equation of the universal variable z.

[0111] The specific forms of the above S(z) and C(z) can be referred to the existing technical materials and will not be described in detail in the embodiments of this application.

[0112] SA3. Update parameters: Adjust the value of the transfer time to be optimized according to the opposite direction of the gradient and reduce the speed increment.

[0113] SA4. Iterate to obtain the optimal value: Repeat SA2 and SA3 until the velocity increment value is less than the minimum deviation value. At this time, the transfer time to be optimized is the optimal value of the gradient descent method. The optimal value is determined as the transfer time of the first spacecraft.

[0114] Optionally, the predicted transfer time may be optimized by using an evolutionary algorithm, a particle swarm optimization algorithm, a Newton method, a conjugate gradient method, a simplex method or a Bayesian optimization method.

[0115] The above S101-S102 describe the time required for the first spacecraft to catch up with the second spacecraft when the first spacecraft lags behind the second spacecraft, that is, the transfer time.

[0116] Alternatively, as Figure 6As shown in the figure, when the first spacecraft is ahead of the second spacecraft, in order for the first spacecraft to meet the second spacecraft after one circle of the transfer orbit, the second spacecraft must run more than one circle on the original orbit and the first spacecraft must run one circle on the transfer orbit so that the two can meet. Then the predicted transfer time of the first spacecraft satisfies:

[0117]

[0118] Among them, T trans represents the predicted transfer time of the first spacecraft, T2 represents the orbital period of the second spacecraft on the original orbit, and Δθ represents the current phase difference between the first spacecraft and the second spacecraft.

[0119] After the predicted transfer time of the first spacecraft is obtained, the predicted transfer time of the first spacecraft is optimized using the optimization process described in S1022 above.

[0120] S103 : Determine trajectory information of a target transfer orbit based on a Lambert orbit transfer model and the transfer time of the first spacecraft; the trajectory information of the target transfer orbit includes velocities of the first spacecraft at multiple points on the target transfer orbit.

[0121] In the embodiment of the present application, determining the trajectory information of the target transfer orbit is to determine the position vectors and velocity vectors of multiple points on the target orbit.

[0122] Optionally, combined Figure 5 ,like Figure 7 As shown, S103 of the embodiment of the present application includes S1031-S1032.

[0123] S1031. Determine the starting velocity and the ending velocity of the first spacecraft on the target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft.

[0124]

[0125] In the embodiment of the present application, when the first spacecraft performs the pursuit mission, the starting time t0 of the first spacecraft is set, so that the position vector r0 of the first spacecraft at the starting time (i.e., the starting position vector) can be known, and it is stipulated that the first spacecraft runs one circle on the transfer orbit to meet the second spacecraft, that is, the position vector r1 of the first spacecraft at the end time (i.e., the end position vector) is set, and when the starting time of the transfer time is known, according to the transfer time determined in S102 above, the end time t1 of the transfer time can be determined (t1-t0 is the transfer time), and t0, t1, r0, and r1 are substituted into the above-mentioned Lambert orbit transfer model to obtain v0 and v1, where v0 is the velocity vector of the first spacecraft at the starting position of the target transfer orbit (i.e., the starting velocity), and v1 is the velocity vector of the first spacecraft at the end position of the target transfer orbit (i.e., the end velocity).

[0126] S1032: Perform interpolation processing on the starting point velocity and the ending point velocity of the target transfer orbit to obtain the velocities of the first spacecraft at multiple points on the target transfer orbit.

[0127] Optionally, the Newton interpolation algorithm is used to interpolate the starting position (r0), end position (r1), starting velocity (v0) and end velocity (v1) of the target transfer orbit to obtain the position vector and velocity vector of multiple points of the first spacecraft on the target transfer orbit during the transfer time, that is, the trajectory information of the target transfer orbit is obtained. At this point, the design of the target transfer orbit is completed.

[0128] It can be understood that the Newton interpolation algorithm is a numerical method for interpolation, which constructs an interpolation polynomial by using known data points to interpolate between given data points.

[0129] Illustratively, in an embodiment of the present application, the starting velocity and the ending velocity of the transfer trajectory are interpolated using a Newton interpolation algorithm, including SB1-SB2.

[0130] SB1. Construct an interpolation polynomial based on the transfer time, the starting velocity of the first spacecraft on the target transfer orbit, and the terminal velocity: Given a set of data points (x i ,y i ), where x i represents the i-th moment of the transfer time, y i Represents the position vector and velocity vector of the first spacecraft on the target transfer orbit corresponding to the i-th moment of the transfer time. According to the data point (x i ,y i )Construct an interpolation polynomial.

[0131] Optionally, the above interpolation polynomial satisfies:

[0132] P(n,x)=a0+a1(x-x0)+a2(x-x0)(x-x1)+…+a n (x-x0)…(xx n-1 ),

[0133] Among them, P(n,x) represents the interpolation polynomial, a,a1…a n Represents the coefficients of the interpolation polynomial, x0, x1…x n-1 Indicates each moment within the transfer time.

[0134] SB2. Solve the interpolation polynomial coefficients by using the difference quotient: i ,y i ) determines the difference quotient between each data point, and recursively calculates other high-order difference quotients through the difference quotient until all coefficients a, a1…a are obtained. n The interpolation polynomial obtained so far indicates the relationship between the position and vector velocity of the first spacecraft on the target transfer orbit. The position and velocity vector of the first spacecraft on the target transfer orbit corresponding to any time within the transfer time can be obtained through the above interpolation polynomial.

[0135] Optionally, the above difference quotient satisfies:

[0136]

[0137] Among them, f(x i ,x i+1 ) represents the difference quotient between the i+1th moment and the i-th moment, x i+1 Indicates the i+1th moment of the transfer time, y i+1 represents the position vector and velocity vector of the first spacecraft on the target transfer orbit corresponding to the i+1th moment of the transfer time.

[0138] Optionally, the starting velocity and the terminal velocity of the target transfer trajectory can also be interpolated by Lagrange interpolation, spline interpolation, polynomial regression, least squares method or Fourier series fitting algorithms. This application does not further limit the above interpolation algorithms.

[0139] The method for determining a spacecraft transfer orbit provided in an embodiment of the present application can be applied in a scenario where a first spacecraft (i.e., the action spacecraft) is pursuing a second spacecraft (i.e., the target spacecraft). In the event that the first spacecraft lags behind the second spacecraft, the radius of the central celestial body is used as the periapsis orbital altitude of the first spacecraft's transfer orbit. A limit transfer orbit with the lowest orbital altitude is set. Based on the limit transfer orbit, the maximum phase difference between the first spacecraft's phase on the transfer orbit and the second spacecraft's phase on the original orbit is determined. Based on the relationship between this maximum phase difference and the current phase difference between the first and second spacecraft, the transfer time of the first spacecraft is determined when it encounters the second spacecraft after one orbital rotation. Furthermore, trajectory information of the transfer orbit is determined based on the Lambert orbit transfer model. In this method, because the transfer time determined based on the maximum phase difference and the current phase difference between the first and second spacecraft is greater than the orbital period of the limit transfer orbit, the orbital altitude of the first spacecraft's target transfer orbit is ensured to be greater than the radius of the central celestial body. This allows for the design of a reasonable transfer orbit for the spacecraft, thereby smoothly adjusting the spacecraft's motion state and enabling it to complete the pursuit mission.

[0140] Accordingly, the embodiment of the present application provides a device for determining the transfer orbit of a spacecraft, such as Figure 8 As shown, it includes a phase difference determination module 801, a transfer time determination module 802 and a transfer trajectory determination module 803.

[0141] Phase difference determination module 801 is configured to, when a first spacecraft lags behind a second spacecraft, determine the maximum phase difference between the first spacecraft's phase on the transfer orbit and the second spacecraft's phase on the original orbit, when the first spacecraft encounters the second spacecraft after one orbit. The transfer orbit corresponding to the maximum phase difference is the limiting transfer orbit. The apoapsis of the limiting transfer orbit is the current orbital altitude of the first spacecraft, and the periapsis of the limiting transfer orbit is the radius of the central celestial body. For example, phase difference determination module 801 is configured to implement S101 of the above-described method for determining the spacecraft's transfer orbit.

[0142] Transfer time determination module 802 is configured to determine a transfer time for the first spacecraft based on the current phase difference and the maximum phase difference between the first spacecraft and the second spacecraft. The transfer time is the time required for the first spacecraft to pursue the second spacecraft, and the transfer time is greater than the orbital period of the extreme transfer orbit. For example, transfer time determination module 802 is configured to implement S102 of the above-described method for determining the spacecraft's transfer orbit.

[0143] The transfer orbit determination module 803 is configured to determine trajectory information of a target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft. The target transfer orbit trajectory information includes the velocities of the first spacecraft at multiple points along the target transfer orbit. For example, the transfer orbit determination module 803 is configured to implement step S103 of the above-described method.

[0144] Optionally, the transfer time determination module 802 is specifically configured to determine a predicted transfer time for the first spacecraft based on the current phase difference and the maximum phase difference between the first spacecraft and the second spacecraft. The predicted transfer time is optimized using a gradient descent method to obtain the transfer time for the first spacecraft. For example, the transfer time determination module 802 is specifically configured to implement S1021-S1022 of the above-described method for determining a spacecraft transfer orbit.

[0145] Optionally, the transfer time determination module 802 is further configured to: when the first spacecraft is ahead of the second spacecraft, determine a predicted transfer time of the first spacecraft when the first spacecraft encounters the second spacecraft after completing one orbit of the transfer orbit. The predicted transfer time of the first spacecraft satisfies:

[0146]

[0147] Among them, T trans represents the predicted transfer time of the first spacecraft, T2 represents the orbital period of the second spacecraft on the original orbit, and Δθ represents the current phase difference between the first spacecraft and the second spacecraft. The predicted transfer time is optimized using the gradient descent method to obtain the transfer time of the first spacecraft.

[0148] Optionally, the transfer orbit determination module 803 is specifically configured to: determine the starting velocity and terminal velocity of the first spacecraft on the target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft; and interpolate the starting velocity and terminal velocity of the target transfer orbit to obtain the velocities of the first spacecraft at multiple points on the target transfer orbit. For example, the transfer orbit determination module 803 is specifically configured to implement S1031-S1032 of the above-described method for determining the spacecraft's transfer orbit.

[0149] The various modules of the above-mentioned spacecraft transfer orbit determination device can also be used to execute other steps in the above-mentioned method embodiment. All relevant contents involved in the above-mentioned method embodiment can be referred to the functional description of the corresponding functional module and will not be repeated here.

[0150] The present application also provides an electronic device, including: a processor and a memory coupled to the processor; the memory is configured to store computer instructions, and when the electronic device is in operation, the processor executes the computer instructions stored in the memory, causing the electronic device to perform the method of the above embodiment. The processor can implement the above-mentioned phase difference determination module 801, transfer time determination module 802, and transfer orbit determination module 803; the memory can also be configured to store the phase difference between the first spacecraft and the second spacecraft, the maximum phase difference, the Lambert orbit transfer model, the starting and ending velocities of the first spacecraft on the transfer orbit, and trajectory information of the transfer orbit.

[0151] An embodiment of the present application further provides a computer-readable storage medium, which includes a computer program. When the computer program runs on a computer, the method described in the above embodiment is executed.

[0152] An embodiment of the present application further provides a computer program product, which includes computer program instructions. When the computer program instructions are run on a computer, the method described in the above embodiment is executed.

[0153] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for determining a transfer orbit of a spacecraft, characterized in that: Applied to a scenario where a first spacecraft is pursuing a second spacecraft, the first spacecraft is transferred from an original orbit to a target transfer orbit to pursue the second spacecraft, and the first spacecraft and the second spacecraft are moving in the same direction around the same central celestial body, the method comprising: When the first spacecraft lags behind the second spacecraft, the maximum phase difference between the phase of the first spacecraft on the transfer orbit and the phase of the second spacecraft on the original orbit is determined when the first spacecraft encounters the second spacecraft after one orbit in the transfer orbit. The transfer orbit corresponding to the maximum phase difference is the limiting transfer orbit. The apogee orbital altitude of the limiting transfer orbit is the current orbital altitude of the first spacecraft, and the perigee orbital altitude of the limiting transfer orbit is the radius of the central celestial body. The maximum phase difference satisfies: Wherein, T1 represents the orbital period of the extreme transfer orbit, T2 represents the orbital period of the second spacecraft on the original orbit, represents the maximum phase difference; a represents the semi-major axis of the extreme transfer orbit, μ represents the gravitational constant of the central celestial body, R1 represents the apogee orbital altitude of the extreme transfer orbit, and R2 represents the perigee orbital altitude of the extreme transfer orbit; Determining a transfer time of the first spacecraft based on a current phase difference and a maximum phase difference between the first spacecraft and the second spacecraft; the transfer time is a time required for the first spacecraft to pursue the second spacecraft, and the transfer time is greater than an orbital period of the extreme transfer orbit; determining the transfer time of the first spacecraft based on the current phase difference and the maximum phase difference between the first spacecraft and the second spacecraft includes: determining a predicted transfer time of the first spacecraft based on a current phase difference between the first spacecraft and the second spacecraft and the maximum phase difference; When the current phase difference between the first spacecraft and the second spacecraft is less than the maximum phase difference, the predicted transfer time of the first spacecraft satisfies: When the current phase difference between the first spacecraft and the second spacecraft is greater than or equal to the maximum phase difference, the predicted transfer time of the first spacecraft satisfies: Among them, T trans represents the predicted transfer time of the first spacecraft, T2 represents the orbital period of the second spacecraft on the original orbit, and Δθ represents the current phase difference between the first spacecraft and the second spacecraft; Optimizing the predicted transfer time using a gradient descent method to obtain a transfer time of the first spacecraft; Based on the Lambert orbit transfer model and the transfer time of the first spacecraft, trajectory information of the target transfer orbit is determined; the trajectory information of the target transfer orbit includes the speed of multiple points of the first spacecraft on the target transfer orbit.

2. The method according to claim 1, wherein Determining the trajectory information of the target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft includes: determining a starting velocity and a terminal velocity of the first spacecraft on the target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft; Interpolation processing is performed on the starting point velocity and the ending point velocity of the target transfer orbit to obtain the velocities of multiple points of the first spacecraft on the target transfer orbit.

3. The method according to claim 1, wherein Before determining the trajectory information of the target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft, the method further includes: When the first spacecraft is ahead of the second spacecraft, a predicted transfer time of the first spacecraft is determined when the first spacecraft encounters the second spacecraft after completing one orbit of the transfer orbit; wherein the predicted transfer time of the first spacecraft satisfies: Among them, T trans represents the predicted transfer time of the first spacecraft, T2 represents the orbital period of the second spacecraft on the original orbit, and Δθ represents the current phase difference between the first spacecraft and the second spacecraft; The predicted transfer time is optimized using a gradient descent method to obtain the transfer time of the first spacecraft.

4. A device for determining a transfer orbit of a spacecraft, characterized in that: Applied to a scenario where a first spacecraft is pursuing a second spacecraft, the first spacecraft is transferred from an original orbit to a target transfer orbit to pursue the second spacecraft, and the first spacecraft and the second spacecraft are moving in the same direction around the same central celestial body. The device includes a phase difference determination module, a transfer time determination module, and a transfer orbit determination module; The phase difference determination module is configured to, when the first spacecraft lags behind the second spacecraft, determine a maximum phase difference between a phase of the first spacecraft on the transfer orbit and a phase of the second spacecraft on the original orbit when the first spacecraft encounters the second spacecraft after one orbit of the transfer orbit, wherein the transfer orbit corresponding to the maximum phase difference is a limit transfer orbit; wherein the apoapsis orbital altitude of the limit transfer orbit is the current orbital altitude of the first spacecraft, and the periapsis orbital altitude of the limit transfer orbit is the radius of the central celestial body; and the maximum phase difference satisfies: Wherein, T1 represents the orbital period of the extreme transfer orbit, T2 represents the orbital period of the second spacecraft on the original orbit, represents the maximum phase difference; a represents the semi-major axis of the extreme transfer orbit, μ represents the gravitational constant of the central celestial body, R1 represents the apogee orbital altitude of the extreme transfer orbit, and R2 represents the perigee orbital altitude of the extreme transfer orbit; The transfer time determination module is configured to determine a transfer time of the first spacecraft based on a current phase difference and a maximum phase difference between the first spacecraft and the second spacecraft; the transfer time is a time required for the first spacecraft to pursue the second spacecraft, and the transfer time is greater than an orbital period of the extreme transfer orbit; determining the transfer time of the first spacecraft based on the current phase difference and the maximum phase difference between the first spacecraft and the second spacecraft includes: determining a predicted transfer time of the first spacecraft based on a current phase difference between the first spacecraft and the second spacecraft and the maximum phase difference; When the current phase difference between the first spacecraft and the second spacecraft is less than the maximum phase difference, the predicted transfer time of the first spacecraft satisfies: When the current phase difference between the first spacecraft and the second spacecraft is greater than or equal to the maximum phase difference, the predicted transfer time of the first spacecraft satisfies: Among them, T trans represents the predicted transfer time of the first spacecraft, T2 represents the orbital period of the second spacecraft on the original orbit, and Δθ represents the current phase difference between the first spacecraft and the second spacecraft; Optimizing the predicted transfer time using a gradient descent method to obtain a transfer time of the first spacecraft; The transfer orbit determination module is used to determine the trajectory information of the target transfer orbit based on the Lambert orbit transfer model and the transfer time of the first spacecraft; the trajectory information of the target transfer orbit includes the velocity of multiple points of the first spacecraft on the target transfer orbit.

5. An electronic device, characterized in that: The electronic device comprises a processor and a memory coupled to the processor; the memory is used to store computer instructions, and when the electronic device is running, the processor executes the computer instructions stored in the memory, so that the electronic device executes the method according to any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that The method comprises computer program instructions, which, when executed by a computer, cause the computer to perform the method according to any one of claims 1 to 3.

7. A computer program product, characterized in that The method comprises computer program instructions, which, when executed on a computer, cause the computer to perform the method according to any one of claims 1 to 3.

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