A method and system for constructing a satellite formation minimum safety distance calculation model

Abstract

The present application discloses a method and system for constructing a satellite formation minimum safety distance calculation model, the method comprising: setting each orbital element number of the formation satellites; modeling elliptical motion based on the orbital element number to obtain a first model; bringing the configuration parameters into the minimum safety distance model to obtain a second model; performing monotonicity analysis and linearization processing on the model to obtain a third model; the third model is used to calculate the minimum safety distance of the satellite formation. The present application models and processes each set orbital element vector, and finally establishes a model that can be used to accurately calculate the minimum safety distance of the satellite formation.

Description

Technical Field

[0001] The present application relates to the field of satellite formations, and specifically to a method and system for constructing a satellite formation minimum safety distance calculation model. Background Art

[0002] A satellite formation refers to a collaborative working system composed of two or more satellites in a certain configuration. Through the coordination of multiple satellites, it can break through the bottleneck of the payload scale and performance of a single satellite and form ultra-large-scale and ultra-high-performance space applications. With the development of aerospace technology, satellite formation technology has become an irreplaceable technology in the fields of observation, communication, reconnaissance, etc., and has also become the focus of technological development. Among them, the natural flyby formation of two satellites is the basic application scenario of satellite formation technology.

[0003] In satellite formation technology, modeling, analysis and prediction of inter-satellite safety distance are key links to ensure the safety and reliability of the formation system, and are also the core constraints of satellite formation configuration design. However, due to the complex and highly nonlinear relative motion relationship between formation satellites, existing technologies cannot directly model the dynamic changes of the minimum safety distance, and can only be estimated through numerical iterative estimation, enumeration calculation and other methods. This type of method can only estimate the minimum relative motion distance for existing configuration geometric relationships, and cannot directly establish an analytical relationship between the minimum safety distance and configuration parameters. This is the direct reason why formation configuration design can only be achieved through numerical iteration and safety evaluation methods. Therefore, it is necessary to establish a dynamic model of the minimum safety distance, construct a direct analytical relationship between configuration parameters and the minimum safety distance, speed up formation configuration design, and thus speed up the key technology of the emergency response capability of the formation system. Summary of the invention

[0004] This application proposes a method and system for constructing a satellite formation minimum safety distance calculation model. By modeling and processing the set orbital element vectors, a model that can be used to accurately calculate the minimum safety distance of a satellite formation is finally established.

[0005] To achieve the above purpose, the present application proposes a method for constructing a satellite formation minimum safety distance calculation model, comprising the following steps:

[0006] Set the orbital elements of the formation satellites;

[0007] Perform elliptical motion modeling based on the orbital elements to obtain a first model;

[0008] Substitute the configuration parameters into the first model to obtain the second model;

[0009] The second model is subjected to monotonicity analysis and linearization processing to obtain a third model; the third model is used to calculate the minimum safe distance of the satellite formation.

[0010] Optionally, the orbital elements include: semi-major axis, eccentricity, orbital inclination, right ascension of ascending node, argument of perigee, true anomaly, eccentric anomaly, mean anomaly and argument of mean latitude.

[0011] Optionally, the method for constructing the first model includes:

[0012] S1. Define a set of relative orbital elements;

[0013] S2. Construct the relative motion equation of the formation based on the relative orbital elements;

[0014] S3. Substitute the relative motion equation into the elliptical motion equation to obtain the first model.

[0015] Optionally, the method for defining the relative orbital elements includes: assuming σ is a vector of each orbital element, then the difference between each orbital element of the auxiliary star and the primary star is δσ=σ d -σ, the relative orbital element equation is:

[0016]

[0017] Where a is the semi-major axis, e is the eccentricity, i is the orbital inclination, Ω is the right ascension of the ascending node, ω is the argument of perigee, and e is x = e cos ω, e y =e sinω; if there is a subscript d, it represents a secondary star, and if there is a subscript c or no subscript, it represents a primary star.

[0018] Optionally, the method for constructing the formation relative motion equation includes: constructing the formation relative motion equation based on the e / i vector description, the equation is:

[0019]

[0020] Among them, e represents the eccentricity vector, i represents the inclination vector, δλ0 represents the initial relative longitude, and θ represents the relative eccentricity vector phase angle. represents the phase angle of the relative inclination vector, u represents the mean latitude amplitude, u=ω+M, and M represents the mean anomaly angle.

[0021] Optionally, the method of substituting the elliptical motion equation includes: based on the formation relative motion equation, introducing the elliptical motion equation, and modeling the relative motion in the xoz plane, the elliptical motion equation is:

[0022] Az 2 +Bzx+Cx 2 =1

[0023] Where A+C>0 and B 2 -4AC<0, substituting the relative motion equation into the ellipse equation, we can get:

[0024]

[0025]

[0026]

[0027] The center of this ellipse is at the origin of the coordinate system, the major semi-axis is α, the minor semi-axis is β, and the angles Z∈[0,π) between the major semi-axis and the x-axis are:

[0028]

[0029] Furthermore, the xoz plane projection distance ρ xz The minimum value of is the minor semi-axis β:

[0030]

[0031] Optionally, the method for constructing the second model includes: substituting the configuration parameter into the projection distance ρ xz ; Substitute the formation configuration parameters described by the e / i vector into ρ xz have to:

[0032]

[0033] Let p = 1 / (aδe) 2 , q=1 / (aδi) 2 , Convert the above formula into:

[0034]

[0035] in:

[0036]

[0037] Optionally, the method for constructing the third model includes: according to Take the value to obtain the minimum safe distance model; take the derivative of F(X) to get:

[0038]

[0039] F′(X) is always less than 0, that is, F(X) is a decreasing function within the range; therefore, when or π, ρ xz Take the minimum value:

[0040] (ρ xz ) min =amin{δe,δi}

[0041] when or π, for (ρ xz )min Linearization is performed. Since the amplitude p in the formation configuration plane and the amplitude q outside the plane are symmetrical in the safe distance expression, assuming that p≤q, that is, δi≤δe, let k=δi / δe, then q / p=k 2 When:

[0042]

[0043] When k≤0.5, that is, when δi / δe≤0.5, the safe distance of the formation configuration in the xoz plane is The cosine value has a good linear relationship, and the minimum safe distance of the formation configuration in the xoz plane can be approximated as:

[0044]

[0045] Furthermore, combined with the J2 perturbation stable formation design constraint, that is, when θ = 90°, the linearized safety distance model can be expressed as:

[0046]

[0047] The present application also provides a system for constructing a satellite formation minimum safety distance calculation model, including: a setting module, a first calculation module, a second calculation module and a third calculation module; wherein,

[0048] The setting module is used to set the number of orbital elements of the formation satellites;

[0049] The first calculation module is used to perform elliptical motion modeling based on the orbital elements to obtain a first model;

[0050] The second calculation module is used to bring the configuration parameters into the minimum safety distance model to obtain a second model;

[0051] The third calculation module performs monotonicity analysis and linearization processing on the model to obtain a third model.

[0052] Optionally, the orbital elements set by the setting module include: semi-major axis, eccentricity, orbital inclination, right ascension of ascending node, argument of perigee, true anomaly, eccentric anomaly, mean anomaly and argument of mean latitude.

[0053] Compared with the prior art, the beneficial effects of this application are:

[0054] 1) By adopting the elliptical relative motion model, it is proved that the natural fly-by relative motion is projected as an ellipse in the xoz plane, and the minimum distance between the two stars is the minor axis of the ellipse. This solves the problem that the relative motion law can only be analyzed by simulation in the past, and provides a method to analyze the relative motion distance analytically.

[0055] 2) By adopting the method of the present application, a linear expression for the minimum safe distance of relative motion between satellites is derived, which can be used for satellite formation configuration design and maintenance control, providing a key way to overcome the previous numerical iterative configuration design method. The linear expression is simple in form, fast in solution, easy to analyze and computer-implemented. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solution of the present application, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0057] Figure 1 Schematic diagram of a method for constructing a satellite formation minimum safety distance calculation model in the first embodiment;

[0058] Figure 2 This is a schematic diagram of the system structure for constructing a satellite formation minimum safety distance calculation model in the second embodiment. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0060] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0061] Embodiment 1

[0062] like Figure 1 The figure is a schematic diagram of a method for constructing a satellite formation minimum safety distance calculation model in an embodiment of the present application, comprising the following steps:

[0063] Step 1: Set the orbital elements of the satellites in the formation:

[0064] First, assume that a, e, i, Ω, ω, f, E, and M represent the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, true anomaly, eccentric anomaly, and mean anomaly, respectively, and u = ω + M represents the argument of mean latitude. For these orbital elements, if there is a subscript d, it means the auxiliary satellite, and if there is a subscript c or no subscript, it means the primary satellite.

[0065] Step 2: Model the elliptical motion based on the orbital elements to obtain the first model:

[0066] S1. Define a set of relative orbital elements

[0067] Let σ be the vector of the orbital elements, then the difference between the orbital elements of the auxiliary star and the primary star is δσ = σ d -σ, based on which a set of relative orbital elements are defined as:

[0068]

[0069] The semi-major axis difference has been normalized to represent the relative mean longitude, and e x = e cos ω, e y =e sinω.

[0070] S2. Construct the relative motion equation of the formation based on the relative orbital elements

[0071] Afterwards, the relative motion equation of the formation is constructed based on the e / i vector description, which is:

[0072]

[0073] Among them, e represents the eccentricity vector, i represents the inclination vector, δλ0 represents the initial relative longitude, and θ represents the relative eccentricity vector phase angle. represents the phase angle of the relative inclination vector, u represents the mean latitude amplitude, u=ω+M, and M represents the mean anomaly angle.

[0074] S3. Substitute the relative motion equation into the elliptical motion equation

[0075] Finally, the elliptical motion equation is introduced to model the relative motion in the xoz plane. The elliptical motion equation is:

[0076] Az 2 +Bzx+Cx 2 =1

[0077] Where A+C>0 and B 2 -4AC<0. Substituting the relative motion equation into the ellipse equation, we get:

[0078]

[0079]

[0080]

[0081] The center of this ellipse is at the origin of the coordinate system, the major semi-axis is α, the minor semi-axis is β, and the angles between the major semi-axis and the x-axis are (χ∈[0,π)):

[0082]

[0083] Furthermore, the minimum value ρ of the xoz plane projection distance xz is the minor semi-axis β:

[0084]

[0085] Substituting the configuration parameters into the minimum safety distance model, the second model is obtained:

[0086] Substitute the configuration parameters into the projection distance ρ xz Substitute the formation configuration parameters described by the e / i vector into ρ xz have to:

[0087]

[0088] Let p = 1 / (aδe) 2 , q=1 / (aδi) 2 , Convert the above formula into:

[0089]

[0090] in:

[0091]

[0092] The model is subjected to monotonicity analysis and linearization processing to obtain the third model:

[0093] according to Take the value to obtain the minimum safe distance model. Derivative F(X) yields:

[0094]

[0095] F′(X) is always less than 0, that is, F(X) is a decreasing function in the range of x∈(0,1]. Therefore, when or π, ρ xz Take the minimum value:

[0096] (ρ xz ) min =amin{δe,δi}

[0097] when or π, for (ρ xz ) min Linearization is performed. Since the amplitude p in the formation configuration plane and the amplitude q outside the plane are symmetrical in the safe distance expression, assuming that p≤q, that is, δi≤δe, let k=δi / δe, then q / p=k 2 ,have:

[0098]

[0099] When k≤0.5, that is, when δi / δe≤0.5, the safe distance of the formation configuration in the xoz plane is The cosine value has a good linear relationship. The minimum safe distance of the formation configuration in the xoz plane can be approximated as:

[0100]

[0101] Furthermore, combined with the J2 perturbation stable formation design constraint, that is, when θ = 90°, the linearized safety distance model can be expressed as:

[0102]

[0103] Embodiment 2

[0104] like Figure 2 As shown, it is a schematic diagram of the construction method of the satellite formation minimum safety distance calculation model in this embodiment, including: a setting module, a first calculation module, a second calculation module and a third calculation module; wherein the setting module is used to set the orbital elements of the formation satellites; the first calculation module is used to perform elliptical motion modeling based on the orbital elements to obtain a first model; the second calculation module is used to bring the configuration parameters into the minimum safety distance model to obtain a second model; the third calculation module performs monotonicity analysis and linearization processing on the model to obtain a third model.

[0105] The following describes in detail the structural composition and functional implementation of each device part in conjunction with this embodiment.

[0106] The setting module is used to set the orbital elements of the formation satellites:

[0107] First, assume that a, e, i, Ω, ω, f, E, and M represent the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, true anomaly, eccentric anomaly, and mean anomaly, respectively, and u = ω + M represents the argument of mean latitude. For these orbital elements, if there is a subscript d, it means the auxiliary satellite, and if there is a subscript c or no subscript, it means the primary satellite.

[0108] The first calculation module is used to perform elliptical motion modeling based on the orbital elements to obtain a first model. The specific workflow includes:

[0109] Define a set of relative orbital elements

[0110] Let σ be the vector of the orbital elements, then the difference between the orbital elements of the auxiliary star and the primary star is δσ = σ d -σ, based on which a set of relative orbital elements are defined as:

[0111]

[0112] The semi-major axis difference has been normalized to represent the relative mean longitude, and e x = e cos ω, e y =e sinω.

[0113] According to the relative orbital roots, the relative motion equation of the formation is constructed

[0114] Afterwards, the relative motion equation of the formation is constructed based on the e / i vector description, which is:

[0115]

[0116] Among them, e represents the eccentricity vector, i represents the inclination vector, δλ0 represents the initial relative longitude, and θ represents the relative eccentricity vector phase angle. represents the phase angle of the relative inclination vector, u represents the mean latitude amplitude, u=ω+M, and M represents the mean anomaly angle.

[0117] Substituting the relative motion equation into the elliptical motion equation, we get the first model

[0118] Finally, the elliptical motion equation is introduced to model the relative motion in the xoz plane. The elliptical motion equation is:

[0119] Az 2 +Bzx+Cx 2 =1

[0120] Where A+C>0 and B 2 -4AC<0. Substituting the relative motion equation into the ellipse equation, we get:

[0121]

[0122]

[0123]

[0124] The center of this ellipse is at the origin of the coordinate system, the major semi-axis is α, the minor semi-axis is β, and the angles between the major semi-axis and the x-axis are (χ∈[0,π)):

[0125]

[0126] Furthermore, the minimum value ρ of the xoz plane projection distance xz is the minor semi-axis β:

[0127]

[0128] The second calculation module is used to bring the configuration parameters into the minimum safety distance model to obtain a second model:

[0129] Substitute the configuration parameters into the projection distance ρxz Substitute the formation configuration parameters described by the e / i vector into ρ xz have to:

[0130]

[0131] Let p = 1 / (aδe) 2 , q=1 / (aδi) 2 , Convert the above formula into:

[0132]

[0133] in:

[0134]

[0135] The third calculation module is used to perform monotonicity analysis and linearization processing on the model to obtain a third model:

[0136] according to Take the value to obtain the minimum safe distance model. Derivative F(X) yields:

[0137]

[0138] F′(X) is always less than 0, that is, F(X) is a decreasing function in the range of x∈(0,1]. Therefore, when or π, ρ xz Take the minimum value:

[0139] (ρ xz ) min =amin{δe,δi}

[0140] when or π, for (ρ xz ) min Linearization is performed. Since the amplitude p in the formation configuration plane and the amplitude q outside the plane are symmetrical in the safe distance expression, assuming that p≤q, that is, δi≤δe, let k=δi / δe, then q / p=k 2 ,have:

[0141]

[0142] When k≤0.5, that is, when δi / δe≤0.5, the safe distance of the formation configuration in the xoz plane is The cosine value has a good linear relationship. The minimum safe distance of the formation configuration in the xoz plane can be approximated as:

[0143]

[0144] Furthermore, combined with the J2 perturbation stable formation design constraint, that is, when θ = 90°, the linearized safety distance model can be expressed as:

[0145]

[0146] The embodiments described above are only descriptions of the preferred methods of the present application, and are not intended to limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements made to the technical solutions of the present application by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present application.

Claims

1. A method for constructing a satellite formation minimum safety distance calculation model, characterized in that: The following steps are involved: Set the orbital elements of the formation satellites; Perform elliptical motion modeling based on the orbital elements to obtain a first model; The method for constructing the first model comprises: S1. Define a set of relative orbital elements; the method of defining the relative orbital elements comprises: let σ be the vector of each orbital element, then the difference between each orbital element of the auxiliary star and the primary star is expressed as δσ=σ d -σ, based on which a set of relative orbital elements are defined as: Where a is the semi-major axis, e is the eccentricity, i is the orbital inclination, Ω is the right ascension of the ascending node, ω is the argument of perigee, and e is x =ecosω,e y =esinω; if there is a subscript d, it represents the auxiliary star, and if there is a subscript c or no subscript, it represents the primary star; S2. Constructing a formation relative motion equation according to the relative orbital elements; the method for constructing the formation relative motion equation comprises: constructing a formation relative motion equation based on the e / i vector description, the equation is: Among them, e represents the eccentricity vector, i represents the inclination vector, δλ0 represents the initial relative longitude, and θ represents the relative eccentricity vector phase angle. represents the phase angle of the relative inclination vector, u represents the mean latitude argument, u=ω+M, M represents the mean anomaly; S3. Substituting the relative motion equation into the elliptical motion equation to obtain a first model; the method of substituting the elliptical motion equation into the elliptical motion equation includes: based on the relative motion equation of the formation, introducing the elliptical motion equation, modeling the relative motion in the xoz plane, the elliptical motion equation is: The 2 +Bzx+Cx 2 =1 Where A+C>0 and B 2 -4AC<0, substituting the relative motion equation into the ellipse equation, we can get: The center of this ellipse is at the origin of the coordinate system, the major semi-axis is α, the minor semi-axis is β, and the angles χ∈[0,π) between the major semi-axis and the x-axis are: Furthermore, the xoz plane projection distance ρ xz The minimum value of is the minor semi-axis β: Substituting the configuration parameters into the first model to obtain a second model; the method for constructing the second model includes: substituting the configuration parameters into the projection distance ρ xz ; Substitute the formation configuration parameters described by the e / i vector into ρ xz have to: in: Performing monotonicity analysis and linearization processing on the second model to obtain a third model; the method for constructing the third model includes: Take the value to obtain the minimum safe distance model; take the derivative of F(X) to get: F′(X) is always less than 0, that is, F(X) is a decreasing function within the range; therefore, when or π, ρ xz Take the minimum value: (r xz ) min =amin{δe,δi} when or π, for (ρ xz ) min Linearization is performed. Since the amplitude p in the formation configuration plane and the amplitude q outside the plane are symmetrical in the safe distance expression, assuming that p≤q, that is, δi≤δe, let k=δi / δe, then q / p=k 2 When: When k≤0.5, that is, when δi / δe≤0.5, the safe distance of the formation configuration in the xoz plane is The cosine value has a good linear relationship, and the minimum safe distance of the formation configuration in the xoz plane can be approximated as: Furthermore, combined with the J2 perturbation stable formation design constraint, that is, when θ = 90°, the linearized safety distance model is expressed as: The third model is used to calculate the minimum safety distance of the satellite formation.

2. The method for constructing a satellite formation minimum safety distance calculation model according to claim 1, characterized in that: The orbital elements include: semi-major axis, eccentricity, orbital inclination, right ascension of ascending node, argument of perigee, true anomaly, eccentric anomaly, mean anomaly and argument of mean latitude.

3. A system for constructing a satellite formation minimum safety distance calculation model, characterized in that: include: A setting module, a first calculation module, a second calculation module and a third calculation module; wherein, The setting module is used to set the number of orbital elements of the formation satellites; The first calculation module is used to perform elliptical motion modeling based on the orbital elements to obtain a first model; and the method for constructing the first model includes: S1. Define a set of relative orbital elements; the method of defining the relative orbital elements comprises: let σ be the vector of each orbital element, then the difference between each orbital element of the auxiliary star and the primary star is expressed as δσ=σ d -σ, where the equation for the relative orbital elements is: Where a is the semi-major axis, e is the eccentricity, i is the orbital inclination, Ω is the right ascension of the ascending node, ω is the argument of perigee, and e is x =ecosω,e y =esinω; if there is a subscript d, it represents the auxiliary star, and if there is a subscript c or no subscript, it represents the primary star; S2. Constructing a formation relative motion equation according to the relative orbital elements; the method for constructing the formation relative motion equation comprises: constructing a formation relative motion equation based on the e / i vector description, the equation is: Among them, e represents the eccentricity vector, i represents the inclination vector, δλ0 represents the initial relative longitude, and θ represents the relative eccentricity vector phase angle. represents the phase angle of the relative inclination vector, u represents the mean latitude argument, u=ω+M, M represents the mean anomaly; S3. Substituting the relative motion equation into the elliptical motion equation to obtain a first model; the method of substituting the elliptical motion equation into the elliptical motion equation includes: based on the relative motion equation of the formation, introducing the elliptical motion equation, modeling the relative motion in the xoz plane, the elliptical motion equation is: The 2 +Bzx+Cx 2 =1 Where A+C>0 and B 2 -4AC<0, substituting the relative motion equation into the ellipse equation, we can get: The center of this ellipse is at the origin of the coordinate system, the major semi-axis is α, the minor semi-axis is β, and the angles χ∈[0,π) between the major semi-axis and the x-axis are: Furthermore, the xoz plane projection distance ρ xz The minimum value of is the minor semi-axis β: The second calculation module is used to bring the configuration parameters into the first model to obtain a second model; the method for constructing the second model includes: bringing the configuration parameters into the projection distance ρ xz ; Substitute the formation configuration parameters described by the e / i vector into ρ xz have to: Let p = 1 / (aδe) 2 , q=1 / (aδi) 2 , Convert the above formula into: in: The third calculation module performs monotonicity analysis and linearization processing on the second model to obtain a third model; the method for constructing the third model includes: according to Take the value to obtain the minimum safe distance model; take the derivative of F(X) to get: F′(X) is always less than 0, that is, F(X) is a decreasing function within the range; therefore, when or π, ρ xz Take the minimum value: (r xz ) min =amin{δe,δi} when or π, for (ρ xz ) min Linearization is performed. Since the amplitude p in the formation configuration plane and the amplitude q outside the plane are symmetrical in the safe distance expression, assuming that p≤q, that is, δi≤δe, let k=δi / δe, then q / p=k 2 When: When k≤0.5, that is, when δi / δe≤0.5, the safe distance of the formation configuration in the xoz plane is The cosine value has a good linear relationship, and the minimum safe distance of the formation configuration in the xoz plane can be approximated as: Furthermore, combined with the J2 perturbation stable formation design constraint, that is, when θ = 90°, the linearized safety distance model is expressed as: The third model is used to calculate the minimum safety distance of the satellite formation.

4. The system for constructing a satellite formation minimum safety distance calculation model according to claim 3, characterized in that: The orbital elements set by the setting module include: semi-major axis, eccentricity, orbital inclination, right ascension of ascending node, argument of perigee, true anomaly, eccentric anomaly, mean anomaly and argument of mean latitude.

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