An orbital design method, system and device for a spacecraft to avoid space debris

Abstract

The present invention discloses an orbital design method, system and device for a spacecraft to avoid space debris. The method includes: constructing a dynamic model of the spacecraft and space debris under perturbation; performing data processing on the dynamic models of the spacecraft and space debris to obtain the position information of the spacecraft and space debris; modeling the impulse velocity increment of the spacecraft to obtain a set of initial state increments of the spacecraft; performing data processing on different maneuver impulse velocity increments according to the position information of the spacecraft and space debris to obtain the position information of the spacecraft and space debris in different states; comparing the position information of the spacecraft and space debris in different states and selecting an optimal avoidance scheme for the spacecraft. This method can calculate the impulse velocity increment of the spacecraft, select the optimal avoidance scheme, and ensure the operation accuracy under the consideration of perturbation force, and has universality for orbits at different heights and in different situations.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft, and relates to an orbital design method, system and device for a spacecraft to avoid space debris. Background Art

[0002] With the rapid development of space technology, the number of near-earth orbit space debris has been continuously increasing. According to the data of the European Space Surveillance Network, as of January 2021, there are more than 34,000 space debris with a diameter exceeding 10 cm, and more than 560 dangerous events such as collisions or disintegrations caused by space debris. Generally speaking, due to the extremely high relative speed between space debris and artificial spacecraft, once a space collision occurs, the on-orbit spacecraft will be severely damaged or even explode and disintegrate. In history, there have been many space collision events, such as the collision between the Russian COSMOS 1934 spacecraft and the cataloged space debris No. 13475 in 1991; the collision between the French "Cherry" spacecraft and the cataloged space debris No. 18208 in 1996; the collision between the THOR BURNER 2A rocket body and the cataloged space debris No. 26207 in 2005; the collision between the COSMOS 2251 spacecraft and the IRIDIUM 33 spacecraft in 2009. Each hypervelocity space collision is extremely likely to cause the disintegration of space objects, generate more space debris, and cause a vicious cycle. For example, the collision between the COSMOS 2251 spacecraft and the IRIDIUM 33 spacecraft in 2009 generated a total of 2,201 cataloged debris. The mutual collision between space objects not only poses a huge threat to on-orbit spacecraft, but also becomes the main factor for the current growth of space debris. With the continuous accumulation of debris generated by space collisions and disintegrations, the cascading effect (Kessler phenomenon) of space collisions will become more and more obvious. The Kessler phenomenon will cause the near-earth orbit to be covered by dangerous space debris and lose the orbits that can operate safely. Therefore, how to design the avoidance orbit of a spacecraft for existing space debris is an important prerequisite for reducing space collisions and an important guarantee for space safety.

[0003] Patera and Russell P, in the literature "General Method for Calculating Satellite Collision Probability", based on the probability calculation model, derived the optimal solution of the velocity increment through the one-dimensional collision probability integration method, and used the two-body orbit integration to replace the high-precision orbit integration to study the collision avoidance maneuver strategy. This method obtained an analytical solution for the avoidance orbit design by ignoring some perturbation terms, but the ignored perturbation terms would lead to a significant reduction in the calculation accuracy. To improve the operation accuracy, Lee S C, Kim H D, and Suk J, in the literature "Collision avoidance maneuver planning using GA for LEO and GEO satellite maintained in keeping area", solved the multi-objective optimization problem using the genetic algorithm for fuel consumption and maneuver duration, and obtained the collision avoidance maneuver strategy. This method used a heuristic algorithm to autonomously search for the results, but the heuristic algorithm was prone to falling into the local optimum and had its own limitations such as orbital altitude and orbital shape.

[0004] The current mainstream methods for designing avoidance orbits of on-orbit spacecraft are divided into the following two types: The first is to obtain an analytical form of the avoidance orbit design solution by ignoring the influence of perturbation terms such as lunar gravity, solar gravity, solar radiation pressure, and tenuous atmospheric drag; the second is to autonomously search for the avoidance strategy through a heuristic algorithm. To ensure the accuracy of the avoidance orbit design for on-orbit spacecraft to avoid space debris and minimize the adverse effects caused by calculation deviations, it is necessary to consider the influence of perturbation terms, but this will increase the calculation complexity and make the orbital dynamics equation strongly nonlinear. In addition, it is necessary to avoid being restricted by a series of external factors such as local optimum and orbital altitude during the avoidance orbit design process, or obtaining high-cost search results, so that the proposed avoidance orbit design method has universality. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems in the prior art and provide an orbit design method, system, and device for a spacecraft to avoid space debris; in the case of perturbations, by establishing a dynamic model of the spacecraft and space debris, the position information of the spacecraft and space debris is obtained. When the space debris approaches the spacecraft, the spacecraft avoids the space debris through impulsive maneuvers to ensure the safety of the spacecraft. This method can calculate the impulsive velocity increment of the spacecraft, select the optimal avoidance plan, and ensure the operation accuracy considering the perturbation force, and is applicable to orbits with different altitudes and different situations.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] An orbital design method for a spacecraft to avoid space debris, comprising the following steps:

[0008] Construct a dynamic model of the spacecraft and space debris under perturbation conditions;

[0009] Process the data of the dynamic models of the spacecraft and space debris to obtain the position information of the spacecraft and space debris;

[0010] Model the pulse velocity increment of the spacecraft to obtain a set of initial state increments of the spacecraft;

[0011] According to the position information of the spacecraft and space debris, process the data of different maneuver pulse velocity increments to obtain the position information of the spacecraft and space debris in different states;

[0012] Compare the position information of the spacecraft and space debris in different states, and select the optimal avoidance scheme for the spacecraft.

[0013] A further improvement of the present invention lies in:

[0014] The perturbation conditions include the non-spherical oblateness perturbation of the Earth, the solar gravitational perturbation, the lunar gravitational perturbation, the solar radiation pressure perturbation, and the atmospheric drag perturbation.

[0015] The dynamic models of the spacecraft and space debris are as follows:

[0016]

[0017] Among them, the vector v is the velocity vector of the space object; the vector r is the position vector of the space object; the scalar r is the distance of the space object from the orbit center; the scalar μ = GM is the central celestial body gravitational constant, G is the universal gravitational constant, and M is the mass of the central celestial body; represents the first derivative of the velocity vector; represents the first derivative of the distance vector; is the acceleration change vector caused by the non-spherical oblateness perturbation of the Earth; is the acceleration change vector caused by the solar gravitational perturbation; is the acceleration change vector caused by the lunar gravitational perturbation; is the acceleration change vector caused by the solar radiation pressure perturbation; is the acceleration change vector caused by the atmospheric drag perturbation; Δv is the pulse velocity increment when the spacecraft maneuvers. For space debris, Δv is the 0 vector.

[0018] The specific method for processing the data of the dynamic models of the spacecraft and space debris to obtain the position information of the spacecraft and space debris is as follows:

[0019] Select appropriate perturbations according to the orbital altitude of the space object, take Δv as the zero vector, numerically integrate Equation (1) using the fourth-order Runge-Kutta method to obtain the trajectories of the spacecraft and the space debris, and determine the time t when the distance between the two is the closest when there is no orbital maneuver. f ;

[0020] The fourth-order Runge-Kutta method is as follows:

[0021]

[0022] Specifically,

[0023]

[0024] where h is the time interval; k 1 is the slope at the start of the time period; k 2 is the slope at the midpoint of the time period, and the slope k 1 is processed by the Euler method to determine the value of x at the point ; k 3 is the slope at the midpoint, and the slope k 2 is used to determine the x value; k 4 is the slope at the end of the time period, and its x value is determined by k 3 ; f(·) is the differential equation to be numerically integrated; the subscript n is the nth step of the numerical integration; x n is the independent variable at the nth step of the numerical integration; x n+1 is the independent variable at the (n + 1)th step of the numerical integration; t n is the cumulative time of the nth step of integration; through the Runge-Kutta method, x n+1 is calculated from the current function value x n to obtain the numerical solution of the differential equation.

[0025] The specific method for modeling the impulse velocity increment of the spacecraft and obtaining the set of initial state increments of the spacecraft is as follows:

[0026] Arbitrarily select three points P 1 (x 1 , y 1 , z 1 ) in the orbital plane, P 2 (x 2 , y 2 , z 2 ) and P 3 (x 3 , y 3 , z 3 ), then P 1 P 2 (x 1 - x 2 , y 1-y 2 ,z 1 -z 2 ), P 1 P 3 (x 1 -x 3 ,y 1 -y 3 ,z 1 -z 3 ), the normal vector of the orbital plane is denoted as

[0027] Initial state increment The components on the x, y, and z axes in the ECI system are as follows:

[0028]

[0029] Among them, U represents a uniform distribution; the ECI system is the geocentric inertial coordinate system OXYZ; Δvx - and Δvx + respectively represent the maximum pulse velocity increments that the spacecraft can provide in the negative and positive directions of the x-axis, which are determined by the spacecraft itself; Δvy - and Δvy + Similarly;

[0030] According to the maximum pulse velocity increment and the minimum pulse interval provided by the pulse engine carried by the spacecraft, Monte Carlo shooting is performed to model the velocity increment, and the initial state increment set of the spacecraft is obtained as

[0031]

[0032] According to the position information of the spacecraft and the space debris, the specific method for processing data of different maneuver pulse velocity increments to obtain the position information of the spacecraft and the space debris in different states is as follows:

[0033] First, perform Taylor polynomial approximation decomposition on formula (1), and use a polynomial Runge-Kutta integrator to map the initial polynomial state to the orbital state at a specific moment along the time axis, obtaining a polynomial-form solution [x 0 with the initial state increment Δx f as a variable:

[0034]

[0035] Among them, j = j 1 +…+j 6 represents the order of each term of the polynomial approximate solution; d represents the index value of the state vector, x f = Φ(t f ; t 0 , x0 ) represents the state of the spacecraft corresponding to the initial standard orbital state x at time t f ; P represents the set of polynomial state vectors; [x 0 represents the polynomial solution; f represents the corresponding Taylor expansion coefficients, directly given by the polynomial calculation tool; the time axis is used to represent the position of the spacecraft at each time; Then, the formula (1) is numerically integrated by the fourth-order Runge-Kutta method, and the state vector of the spacecraft at the close approach time t

[0036] is obtained. The state difference between the spacecraft and the space debris at the close approach time t f is represented by formula (4): f The state difference between the spacecraft and the space debris at the close approach time t

[0037]

[0038] where the subscript s represents the spacecraft, the subscript d represents the space debris, the subscript f represents the close approach time, and the subscript 0 represents the initial time;

[0039] Finally, each state increment in the initial state set Ω of the spacecraft is sequentially substituted into the polynomial [x f_s2d in formula (5) to obtain the distance between the spacecraft and the space debris at time t f in different states.

[0040] By comparing the position information of the spacecraft and the space debris in different states, the criterion for selecting the optimal avoidance scheme for the spacecraft is: among the maneuvering schemes that satisfy the safety constraints, select the maneuvering scheme with the minimum fuel consumption as the optimal scheme for the spacecraft to maneuver and avoid.

[0041] An orbital design system for a spacecraft to avoid space debris includes

[0042] a first construction module for constructing the dynamic models of the spacecraft and the space debris under perturbation;

[0043] a first data processing module for processing the data of the dynamic models of the spacecraft and the space debris to obtain the position information of the spacecraft and the space debris;

[0044] a second construction module for modeling the pulse velocity increment of the spacecraft to obtain the set of initial state increments of the spacecraft;

[0045] a second data processing module for processing the data of different maneuvering pulse velocity increments according to the position information of the spacecraft and the space debris to obtain the position information of the spacecraft and the space debris in different states;

[0046] A comparison module for comparing the position information of the spacecraft and space debris in different states and selecting the optimal avoidance scheme for the spacecraft.

[0047] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the above method are implemented.

[0048] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the steps of the above method are implemented.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] Based on the actual engineering requirements, the present invention proposes an orbital design method, system and device for a spacecraft to avoid space debris. Without being restricted by the orbit type and without ignoring the perturbation force, this method is applicable to different perturbation models. For different central celestial bodies, only the parameters of the central celestial body need to be changed in the orbital dynamics equation.

[0051] The technical solution proposed by the present invention can accelerate the traversal of the position states of the spacecraft at the moment of close contact for different pulse magnitudes, so as to obtain a way with less fuel consumption. The Taylor polynomial is used to represent different velocity pulse increments as a single set, and the Runge-Kutta integration method in the form of a first-order polynomial is used to replace a large number of repetitive pulse maneuver orbit integrations. When the result in polynomial form is obtained, a large number of pulse maneuver orbit evolutions will become a numerical substitution process with extremely fast speed, which will greatly reduce the overall computational efficiency and can achieve an acceleration effect of several orders of magnitude, realizing the effect of traversal optimization.

[0052] The present invention adopts high-order Taylor expansion. The operation accuracy of the technical solution proposed by the present invention can theoretically reach the same accuracy as the traditional Monte Carlo shooting method, and does not reduce the operation accuracy too much due to improving the operation efficiency. When the order of Taylor expansion is four, the operation error is less than 0.01 meters, effectively avoiding sacrificing a large amount of operation accuracy due to polynomial approximation processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required to be used in the embodiments. It should be understood that the following drawings only show some embodiments of the present invention, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings.

[0054] Figure 1Schematic flow chart of the orbital design method for a spacecraft to avoid space debris according to an embodiment of the present invention;

[0055] Figure 2 Schematic structural diagram of the orbital design system for a spacecraft to avoid space debris according to an embodiment of the present invention;

[0056] Figure 3 Simulation orbit of the orbital design method for a spacecraft to avoid space debris according to an embodiment of the present invention;

[0057] Figure 4 Illustration of the ECI coordinate system according to an embodiment of the present invention.

[0058] Wherein, 1 - Motion trajectory of space debris; 2 - Motion trajectory of the spacecraft without maneuvering to avoid; 3 - Motion trajectory of the spacecraft adopting the optimal avoidance strategy. Detailed implementation manners

[0059] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations.

[0060] Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0061] It should be noted that: Similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0062] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper", "lower", "horizontal", "inner", etc. are used to indicate the orientation or positional relationship, it is based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship when the product of the present invention is placed habitually. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be construed as a limitation to the present invention. In addition, terms such as "first", "second", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance.

[0063] In addition, when the term "horizontal" appears, it does not mean that the component is required to be absolutely horizontal, but it can be slightly inclined. For example, "horizontal" only means that its direction is more horizontal relative to "vertical", and does not mean that the structure must be completely horizontal, but it can be slightly inclined.

[0064] In the description of the embodiments of the present invention, it should also be noted that unless otherwise clearly specified and limited, when the terms "arranged", "installed", "connected", and "coupled" appear, they should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected, or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0065] The present invention will be further described in detail below with reference to the accompanying drawings:

[0066] See Figure 1 , Figure 1 A method for designing an orbit for a spacecraft to avoid space debris is disclosed, which specifically includes the following steps:

[0067] S101, construct a dynamic model of the spacecraft and space debris under perturbation conditions.

[0068] Perturbation means that when a celestial body moves around another celestial body, the deviation generated in the orbit due to the attraction of other celestial bodies or other factors. Perturbation conditions include the non-spherical oblateness perturbation of the Earth, the solar gravitational perturbation, the lunar gravitational perturbation, the solar radiation pressure perturbation, and the atmospheric drag perturbation.

[0069] The dynamic model of the spacecraft and space debris is:

[0070]

[0071] Among them, the vector v is the velocity vector of the space object; the vector r is the position vector of the space object; the scalar r is the distance of the space object from the orbit center; the scalar μ = GM is the central celestial body gravitational constant, G is the universal gravitational constant, and M is the mass of the central celestial body; represents the first derivative of the velocity vector; represents the first derivative of the distance vector; is the acceleration change vector caused by the non-spherical oblateness perturbation of the Earth; is the acceleration change vector caused by the solar gravitational perturbation; is the acceleration change vector caused by the lunar gravitational perturbation; is the acceleration change vector caused by the solar radiation pressure perturbation; The acceleration change vector caused by atmospheric drag perturbation; Δv is the impulse velocity increment when the spacecraft maneuvers. For space debris, Δv is the zero vector.

[0072] S102. Perform data processing on the dynamic models of the spacecraft and space debris to obtain the position information of the spacecraft and space debris.

[0073] Select appropriate perturbations according to the orbital altitude of the space object, take Δv as the zero vector, numerically integrate formula (1) by using the fourth-order Runge-Kutta method to obtain the motion trajectories of the spacecraft and space debris, and determine the moment t when the distance between the two is the closest when there is no orbital maneuver. f ;

[0074] The fourth-order Runge-Kutta method is as follows:

[0075]

[0076] Specifically

[0077]

[0078] where h is the time interval; k 1 is the slope at the start of the time period; k 2 is the slope at the midpoint of the time period, and the value of x at the point 1 is determined by the Euler method according to the slope k ; k 3 is the slope at the midpoint, but the value of x is determined by using the slope k 2 ; k 4 is the slope at the end of the time period, and its value of x is determined by k 3 ; f(·) is the differential equation to be numerically integrated; the subscript n is the nth step of the numerical integration; x n is the independent variable at the nth step of the numerical integration; x n+1 is the independent variable at the (n + 1)th step of the numerical integration; t n is the cumulative time of the nth step of the integration; through the Runge-Kutta method, x n+1 is calculated from the current function value x n to obtain the numerical solution of the differential equation.

[0079] S103. Model the impulse velocity increment of the spacecraft to obtain the set of initial state increments of the spacecraft.

[0080] Arbitrarily select three points P 1 (x 1 , y 1 , z 1 ) in the orbital plane, P 2 (x 2 , y 2 , z2 ) and P 3 (x 3 , y 3 , z 3 ), then P 1 P 2 (x 1 - x 2 , y 1 - y 2 , z 1 - z 2 ), P 1 P 3 (x 1 - x 3 , y 1 - y 3 , z 1 - z 3 ), so the normal vector of the orbital plane is denoted as

[0081] Initial state increment The components on the x, y, and z axes in the ECI system are as follows:

[0082]

[0083] Among them, U represents a uniform distribution; the ECI system is the geocentric inertial coordinate system OXYZ; Δvx - and Δvx + respectively represent the maximum pulse velocity increments that the spacecraft can provide in the negative and positive directions of the x-axis, which are determined by the spacecraft itself; Δvy - and Δvy + Similarly.

[0084] According to the maximum pulse velocity increment and the minimum pulse interval provided by the pulse engine carried by the spacecraft, Monte Carlo shooting is performed, and the velocity increment is modeled to obtain the initial state increment set of the spacecraft as

[0085]

[0086] S104. According to the position information of the spacecraft and the space debris, data processing is performed on different maneuver pulse velocity increments to obtain the position information of the spacecraft and the space debris in different states.

[0087] First, perform a Taylor polynomial approximation decomposition on formula (1), and use a polynomial form of the Runge-Kutta integrator to map the initial polynomial state to the orbital state at a specific moment along the time axis, obtaining a polynomial form of the solution [x 0 as a variable as: f is:

[0088]

[0089] where \(j = j\) 1 +\(\cdots\)+ \(j\) 6 represents the order of each term of the polynomial approximate solution; \(d\) represents the index value of the state vector, \(x\) f =\(\varPhi(t\) f ; \(t\) 0 , \(x\) 0 ) represents the state of the spacecraft corresponding to the initial standard orbit state \(x\) f at time \(t\) 0 ; \(P\) represents the set of polynomial state vectors; \([x\) f represents the polynomial solution; represents the corresponding Taylor expansion coefficient, which is directly given by the polynomial calculation tool; the time axis is used to represent the position of the spacecraft at each time;

[0090] Then, the formula (1) is numerically integrated by the fourth-order Runge-Kutta method, and the state vector of the spacecraft at the close approach time \(t\) f can be represented by formula (4). The state difference between the spacecraft and the space debris at the close approach time \(t\) f is:

[0091]

[0092] where the subscript \(s\) represents the spacecraft, the subscript \(d\) represents the space debris, the subscript \(f\) represents the close approach time, and the subscript \(0\) represents the initial time;

[0093] Finally, each state increment in the initial state set \(\varOmega\) of the spacecraft is successively substituted into the polynomial \([x\) f_s2d in formula (5) to obtain the distance between the spacecraft and the space debris at time \(t\) f .

[0094] S105. Compare the position information of the spacecraft and the space debris in different states, and select the optimal avoidance plan for the spacecraft.

[0095] The criterion for selecting the optimal avoidance plan for the spacecraft is: select the maneuver plan with the minimum fuel consumption among the maneuver plans that satisfy the safety constraints as the optimal plan for the spacecraft to maneuver and avoid.

[0096] See Figure 2 , Figure 2 which discloses an orbital design system for a spacecraft to avoid space debris, including:

[0097] A first construction module for constructing the dynamic models of the spacecraft and the space debris under perturbation;

[0098] The first data processing module is used to process the data of the dynamic models of the spacecraft and space debris, and obtain the position information of the spacecraft and space debris;

[0099] The second construction module is used to model the impulse velocity increment of the spacecraft, and obtain the set of initial state increments of the spacecraft;

[0100] The second data processing module is used to process the data of different maneuver impulse velocity increments according to the position information of the spacecraft and space debris, and obtain the position information of the spacecraft and space debris in different states;

[0101] The comparison module is used to compare the position information of the spacecraft and space debris in different states, and select the optimal avoidance plan for the spacecraft.

[0102] See Figure 3 , Figure 3 which is the simulation orbit diagram of the orbit design method for a spacecraft to avoid space debris according to an embodiment of the present invention. As can be seen from Figure 3 , there is a coincidence point between the motion trajectory 2 of the spacecraft without maneuvering avoidance and the motion trajectory 1 of the space debris, which means that the spacecraft will collide with the space debris; there is no coincidence point between the motion trajectory 3 of the spacecraft adopting the optimal avoidance strategy and the motion trajectory 1 of the space debris, which means that the spacecraft has avoided the space debris and the two have not collided. The evaluation index is that the safety distance between the spacecraft and the space debris at the close contact point is greater than 300 meters. In Figure 3 , the motion trajectory 2 of the spacecraft without maneuvering avoidance coincides with the motion trajectory 3 of the spacecraft adopting the optimal avoidance strategy, because the maneuver displacement of the spacecraft to avoid space debris is 500 meters, and for a geostationary orbit (orbital altitude 35786 km), the distance of the maneuver displacement of the spacecraft is very small, so the two orbits seem to overlap.

[0103] When the distance between the spacecraft and the space debris is 12 hours before collision, the orbit evolution of one million groups of initial velocity increments of the spacecraft is carried out. The operation time of using the Monte Carlo shooting method is 13315.5 seconds, while the operation time of using the polynomial integration method proposed by the present invention is 28.4186 seconds, which greatly saves the operation time and ensures that the spacecraft has sufficient time to avoid when threatened by space debris in the universe.

[0104] See Figure 4 , Figure 4 which is the illustration of the ECI coordinate system according to an embodiment of the present invention. To accurately describe the orbital motion of the space debris group, the geocentric inertial coordinate system OXYZ is defined as the ECI system, where the coordinate origin O is located at the center of the earth; the OX axis points to the vernal equinox point at J2000; the OZ axis points to the north pole of the earth; the OY axis is determined by the right-hand rule; P is a certain on-orbit spacecraft.

[0105] Schematic diagram of a terminal device provided by an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps in the above-mentioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of each module / unit in the above-mentioned device embodiments are implemented.

[0106] The computer program can be divided into one or more modules / units, and the one or more modules / units are stored in the memory and executed by the processor to complete the present invention.

[0107] The terminal device can be a computing device such as a desktop computer, a notebook, a palm computer, and a cloud server. The terminal device may include, but is not limited to, a processor and a memory.

[0108] The processor may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0109] The memory can be used to store the computer program and / or module, and the processor realizes various functions of the terminal device by running or executing the computer program and / or module stored in the memory, and by calling the data stored in the memory.

[0110] If the modules / units integrated in the terminal device are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, to implement all or part of the processes in the above-described embodiment methods of the present invention, it can also be completed by a computer program instructing relevant hardware. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-described various method embodiments can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file, or some intermediate form, etc. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disc, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the content included in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0111] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An orbital design method for a spacecraft to avoid space debris, characterized in that, it includes the following steps: Construct a dynamic model of the spacecraft and space debris under perturbation; The dynamic models of the spacecraft and space debris are: where the vector v is the velocity vector of the space object; the vector r is the position vector of the space object; the scalar r is the distance of the space object from the orbit center; the scalar μ = GM is the gravitational constant of the central celestial body, G is the universal gravitational constant, and M is the mass of the central celestial body; represents the first derivative of the velocity vector; represents the first derivative of the distance vector; is the acceleration change vector caused by the non-spherical oblateness perturbation of the Earth; is the acceleration change vector caused by the solar gravitational perturbation; is the acceleration change vector caused by the lunar gravitational perturbation; is the acceleration change vector caused by the solar radiation pressure perturbation; is the acceleration change vector caused by the atmospheric drag perturbation; Δv is the impulse velocity increment during the maneuver of the spacecraft. For space debris, Δv is the 0 vector; Perform data processing on the dynamic models of the spacecraft and space debris to obtain the position information of the spacecraft and space debris; Model the pulse velocity increment of the spacecraft to obtain the set of initial state increments of the spacecraft; According to the position information of the spacecraft and space debris, perform data processing on different maneuver pulse velocity increments to obtain the position information of the spacecraft and space debris in different states; specifically including: First, perform a Taylor polynomial approximation decomposition on formula (1). Use a Runge-Kutta integrator in polynomial form to map the initial polynomial state to the orbital state at a specific moment along the time axis, obtaining a solution in polynomial form with the initial state increment Δx 0 as the variable [x f : where j = j 1 +…+j 6 represents the order of each term of the polynomial approximate solution; d represents the index value of the state vector, x f = Φ(t f ; t 0 , x 0 ) represents the state of the spacecraft corresponding to the initial standard orbit state x f at time t 0 ; P represents the set of polynomial state vectors; [x f represents the polynomial solution; represents the corresponding Taylor expansion coefficient, which is directly given by the polynomial calculation tool; the time axis is used to represent the position of the spacecraft at each time; Then, the fourth-order Runge-Kutta method is used to perform numerical integration on formula (1), and the state vector of the spacecraft at the close approach time t f is obtained. The state difference between the spacecraft and the space debris at the close approach time tf is expressed by formula (4) as: where the subscript s represents the spacecraft, the subscript d represents the space debris, the subscript f represents the moment of close approach, and the subscript 0 represents the initial moment; Finally, substitute each state increment in the initial state set Ω of the spacecraft into the polynomial [x f_s2d in formula (5) in turn, and obtain the distances between the spacecraft and the space debris at different states at time t f ; Compare the position information of the spacecraft and space debris in different states, and select the optimal avoidance plan for the spacecraft.

2. The orbital design method for a spacecraft to avoid space debris according to claim 1, characterized in that, the perturbation cases include the non-spherical oblateness perturbation of the Earth, the solar gravitational perturbation, the lunar gravitational perturbation, the solar radiation pressure perturbation, and the atmospheric drag perturbation.

3. The orbital design method for a spacecraft to avoid space debris according to claim 1, characterized in that, the specific way of performing data processing on the dynamic models of the spacecraft and space debris to obtain the position information of the spacecraft and space debris is: Select appropriate perturbations according to the orbital altitude of the space object, take Δv as the zero vector, numerically integrate formula (1) using the fourth-order Runge-Kutta method to obtain the trajectories of the spacecraft and the space debris, and determine the time t when the distance between the two is the closest when there is no orbital maneuver f ; The fourth-order Runge-Kutta method is: Specifically, where h is the time interval; k 1 is the slope at the start of the time period; k 2 is the slope at the midpoint of the time period, and the slope k 1 is processed by the Euler method to determine the value of x at the point ; k 3 is the slope at the midpoint, and the slope k 2 is used to determine the value of x; k 4 is the slope at the end of the time period, and its x value is determined by k 3 ; f(·) is the differential equation for which numerical integration is to be performed; the subscript n is the nth step of the numerical integration; x n is the independent variable at the nth step of the numerical integration; x n+1 is the independent variable at the (n + 1)th step of the numerical integration; t n is the cumulative time of the nth step of the integration; by the Runge-Kutta method, x n+1 is calculated from the current function value x n to obtain the numerical solution of the differential equation.

4. The orbital design method for a spacecraft to avoid space debris according to claim 1, characterized in that, the specific way of modeling the pulse velocity increment of the spacecraft to obtain the set of initial state increments of the spacecraft is: Arbitrarily select three points \(P\) 1 (x 1 ,y 1 ,z 1 ), \(P\) 2 (x 2 ,y 2 ,z 2 ) and \(P\) 3 (x 3 ,y 3 ,z 3 ), then \(P\) 1 \(P\) 2 (x 1 - x 2 ,y 1 - y 2 ,z 1 - z 2 ), \(P\) 1 \(P\) 3 (x 1 - x 3 ,y 1 - y 3 ,z 1 - z 3 ), and the normal vector of the orbital plane is denoted as Initial state increment The components on the x, y, and z axes in the ECI system are as follows: Among them, U represents a uniform distribution; the ECI system is the geocentric inertial coordinate system OXYZ; Δvx - and Δvx + respectively represent the maximum pulse velocity increments that the spacecraft can provide in the negative and positive directions of the x-axis, which are determined by the spacecraft itself; Δvy - and Δvy + Similarly; Perform Monte Carlo shooting according to the maximum pulse velocity increment and the minimum pulse interval that the pulse engine carried by the spacecraft can provide, model the velocity increment, and obtain the set of initial state increments of the spacecraft as 5. The orbital design method for a spacecraft to avoid space debris according to claim 1, characterized in that, the criterion for comparing the position information of the spacecraft and space debris in different states and selecting the optimal avoidance plan for the spacecraft is: select the maneuver plan with the minimum fuel consumption among the maneuver plans that meet the safety constraints as the optimal plan for the spacecraft's maneuvering avoidance.

6. An orbital design system for a spacecraft to avoid space debris, characterized in that, based on the orbital design method for a spacecraft to avoid space debris according to any one of claims 1 to 5, it includes: The first construction module, which is used to construct a dynamic model of the spacecraft and space debris under perturbation; The first data processing module, which is used to perform data processing on the dynamic models of the spacecraft and space debris to obtain the position information of the spacecraft and space debris; The second construction module, which models the pulse velocity increment of the spacecraft to obtain the set of initial state increments of the spacecraft; The second data processing module, which is used to perform data processing on different maneuver pulse velocity increments according to the position information of the spacecraft and space debris to obtain the position information of the spacecraft and space debris in different states; A comparison module, which is used to compare the position information of the spacecraft and space debris in different states and select the optimal avoidance scheme for the spacecraft.

7. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein, when the processor executes the computer program, the steps of the method according to any one of claims 1-5 are implemented.

8. A computer-readable storage medium storing a computer program, wherein, when the computer program is executed by a processor, the steps of the method according to any one of claims 1-5 are implemented.

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