A method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements

Abstract

The present invention provides a coplanar spacecraft relative motion configuration recognition method based on multiple orbital elements, which belongs to the field of spacecraft relative motion configuration recognition and solves the problem of large computational complexity in spacecraft relative motion configuration recognition. The method comprises: constructing a relative motion configuration set when a target spacecraft is in a circular orbit and a tracking spacecraft is coplanar with the target spacecraft; obtaining constraint conditions corresponding to linear motion polynomials and elliptical motion polynomials in the relative motion equation from the motion characteristics of each relative motion configuration, and forming a multi-orbital element set from the orbital elements in the constraint conditions; extracting input data required for the relative motion equation in mission data, outputting numerical values ​​of the multi-orbital element set through the relative motion equation, inputting the numerical values ​​into the constraint conditions to obtain output results, and identifying the relative motion configuration corresponding to the constraint conditions in the relative motion configuration set through the output results. The present invention reduces the computational complexity and improves recognition efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft relative motion configuration recognition, and in particular relates to a coplanar spacecraft relative motion configuration recognition method based on multiple orbital elements. Background Art

[0002] Spacecraft relative motion configuration identification refers to determining the relative position, speed and motion trend of a spacecraft in orbit through observation and calculation. It is a key technology in space mission planning, orbit control and space operations, and involves the needs of complex tasks such as space debris avoidance, spacecraft formation flying, rendezvous and docking, on-orbit servicing, and space station assembly.

[0003] There are two main methods for traditional spacecraft relative motion configuration identification:

[0004] The first method is to iteratively calculate the motion data of the two spacecraft in the inertial system at a series of future moments using the orbital dynamics model in the inertial system. Then, coordinate transformation is performed to obtain the motion data in the relative coordinate system. Finally, all the motion data are displayed through computer graphics, and the relative motion configuration is obtained by manual interpretation of the graphics.

[0005] The second method is to first obtain the motion equation in the relative coordinate system, and then iteratively calculate the relative motion equation to obtain the relative motion data of the two spacecraft at a series of future moments. Finally, all the motion data are also displayed through computer drawing to manually obtain the relative motion configuration.

[0006] The above two methods are simple and clear in concept, but each new judgment requires continuous orbit forecasting and long-term status data, which is computationally intensive and requires manual interpretation.

[0007] For example, the application publication number is CN116663407A, and the invention is titled "A Neural Network-Based Spacecraft Relative Motion Configuration Identification System and Method." This invention uses data to train a neural network model. Once the neural network model is established, the relative position and velocity of the spacecraft are input to perform relative configuration identification. While this method requires minimal computational effort in the later stages, the initial neural network model development still requires extensive orbital motion data calculations to generate an accurate neural network. Summary of the Invention

[0008] In order to solve the technical problem of large amount of orbit iteration calculation when identifying the relative motion configuration of spacecraft, the present invention proposes a coplanar spacecraft relative motion configuration identification method based on multiple orbit elements. The method constructs a relative motion configuration set when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft; the motion characteristics of each relative motion configuration in the relative motion configuration set are used to obtain the constraint conditions corresponding to the linear motion polynomial and the elliptical motion polynomial in the relative motion equation, and the relative motion configuration in the relative motion configuration set corresponding to the constraint conditions is identified through the constraint conditions; the method does not require a large number of orbit iteration calculations, but only needs to calculate the required orbit elements to identify the coplanar spacecraft relative motion configuration, with low calculation amount and high recognition rate.

[0009] To achieve the above object, the present invention is specifically implemented through the following technical solutions:

[0010] A method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements comprises:

[0011] Step 1: Combine the relative position equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system with the two-body dynamics equation to obtain the relative acceleration equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system, and convert it into the relative acceleration equation of the tracking spacecraft to the target spacecraft in the VVLH coordinate system;

[0012] Step 2: Construct the CW equation of the target spacecraft when it is in a circular orbit from the relative acceleration equation of the tracking spacecraft to the target spacecraft in the VVLH target orbit coordinate system, and obtain the analytical solution equations of the relative position and relative velocity of the CW equation;

[0013] Step 3: Construct the relative motion equation when the tracking spacecraft and the target spacecraft are coplanar by solving the equation analytically, and decompose the relative motion equation into linear motion polynomials and elliptical motion polynomials;

[0014] Step 4: Construct a set of relative motion configurations when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft; obtain the constraints corresponding to the linear motion polynomial and the elliptical motion polynomial in the relative motion equation from the motion characteristics of each relative motion configuration in the relative motion configuration set, and form a multi-orbital element set from the orbital elements in the constraints;

[0015] Step 5: Extract the input data required for the relative motion equation in the mission data, output the numerical value of the multi-orbital element set through the relative motion equation, input the numerical value into the constraint condition to obtain the output result, and identify the relative motion configuration corresponding to the constraint condition in the relative motion configuration set through the output result.

[0016] The beneficial effects of the present invention are:

[0017] 1. The present invention constructs a relative motion equation when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft, which is the superposition of linear motion and elliptical motion, and decomposes the relative motion equation into linear motion polynomials and elliptical motion polynomials; decomposes the relative motion of the spacecraft into linear motion and elliptical motion that can be superimposed, and converts the abstract mathematical expression of the motion equation into physical motion that is easy to understand; and through the superposition of linear motion and elliptical motion, constructs a complete set of relative motion configurations when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft.

[0018] 2. The present invention analyzes the motion characteristics of each relative motion configuration in the relative motion configuration set, and establishes constraint conditions corresponding to the linear motion polynomials and elliptical motion polynomials in the relative motion equation based on the motion characteristics under different relative motion configurations. By extracting the orbital elements in the constraint conditions, a multi-orbital element set is established.

[0019] 3. The present invention experimentally verifies the effectiveness of a method for identifying relative motion configurations of coplanar spacecraft based on multi-orbital elements, solving the problem of large computational complexity and low recognition rate caused by the traditional method that requires a large number of iterative calculations to obtain motion data and then display them graphically before identification. The present invention uses the initial relative position and initial relative velocity of the tracking spacecraft in the mission and the angular velocity of the target spacecraft as input data, outputs the numerical values ​​of the multi-orbital element set through the relative motion equation, inputs the numerical values ​​into the constraints to obtain output results, and identifies the relative motion configuration scheme corresponding to the constraints in the relative motion configuration set through the output results. Compared with the traditional relative configuration identification method, the present invention simplifies the calculation steps, reduces the computational complexity, and improves the recognition efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0021] Figure 1 It is a schematic diagram of the straight-line flying configuration provided by the present invention.

[0022] Figure 2 It is a schematic diagram of the arch line flying configuration provided by the present invention.

[0023] Figure 3 It is a schematic diagram of the teardrop-shaped skimming configuration provided by the present invention.

[0024] Figure 4 It is a schematic diagram of the follow-fly configuration provided by the present invention.

[0025] Figure 5 It is a schematic diagram of the resident configuration provided by the present invention.

[0026] Figure 6 It is a schematic diagram of the fly-around configuration provided by the present invention.

[0027] Figure 7 It is a schematic diagram of the intersection configuration provided by the present invention.

[0028] Figure 8 It is a schematic diagram of the teardrop-shaped flyby configuration trajectory of the tracking spacecraft provided by the present invention.

[0029] Figure 9 It is a schematic diagram of the flyby configuration trajectory of the tracking spacecraft provided by the present invention. DETAILED DESCRIPTION

[0030] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0031] An embodiment of the present invention provides a method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements, comprising:

[0032] Step 1: Combine the relative position equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system with the two-body dynamics equation to obtain the relative acceleration equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system, and convert it into the relative acceleration equation of the tracking spacecraft to the target spacecraft in the VVLH coordinate system;

[0033] The geocentric inertial coordinate system (GVI) is a coordinate system with the Earth's center of mass as its origin. This coordinate system does not rotate with the Earth's rotation or revolution and is therefore an inertial reference system. The VVLH coordinate system, with the target spacecraft's center of mass as its origin, is a rotating coordinate system because the spacecraft orbits the Earth. The VVLH coordinate system has its origin at the target spacecraft's center of mass, with the Z axis pointing toward the Earth's center. The X axis lies within the target spacecraft's orbital plane, perpendicular to the Z axis, and points in the direction of the target spacecraft's motion. The Y axis is determined by the right-hand rule.

[0034] Step 2: Construct the CW equation of the target spacecraft when it is in a circular orbit from the relative acceleration equation of the tracking spacecraft to the target spacecraft in the VVLH target orbit coordinate system, and obtain the analytical solution equations of the relative position and relative velocity of the CW equation;

[0035] Step 3: By solving the equation analytically, the relative motion equation of the tracking spacecraft and the target spacecraft, which is the superposition of linear motion and elliptical motion, is constructed, and the relative motion equation is decomposed into linear motion polynomials and elliptical motion polynomials;

[0036] Step 4: Construct a set of relative motion configurations when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft; obtain the constraints corresponding to the linear motion polynomial and the elliptical motion polynomial in the relative motion equation from the motion characteristics of each relative motion configuration in the relative motion configuration set, and form a multi-orbital element set from the orbital elements in the constraints;

[0037] Step 5: Extract the input data required for the relative motion equation in the mission data, output the numerical value of the multi-orbital element set through the relative motion equation, input the numerical value into the constraint condition to obtain the output result, and identify the relative motion configuration corresponding to the constraint condition in the relative motion configuration set through the output result.

[0038] The input data required for the relative motion equation are: the initial relative position and initial relative velocity of the tracking spacecraft and the angular velocity of the target spacecraft.

[0039] In step 1, the relative acceleration equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system is:

[0040]

[0041] Where, is the relative acceleration vector of the tracking spacecraft to the target spacecraft in the geocentric inertial system, μ is the earth's gravitational constant, is the position vector of the target spacecraft in the geocentric inertial system, is the position vector of the tracking spacecraft in the Earth-centered inertial system; r ti for The modulus value, r ci for The modulus value of .

[0042] In step 1, the relative position equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system is:

[0043]

[0044] The two-body dynamics equation in the geocentric inertial system is:

[0045]

[0046] Substituting the relative position vector equation into the two-body dynamics equation, the relative acceleration equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system is obtained.

[0047] Where, is the relative position vector of the tracking spacecraft to the target spacecraft in the geocentric inertial system; is the acceleration vector of the spacecraft in the geocentric inertial system, is the position vector of the spacecraft in the Earth-centered inertial system, rE for The modulus value of .

[0048] In step 1, the relative acceleration equation of the tracking spacecraft to the target spacecraft in the VVLH coordinate system is:

[0049]

[0050] Where, is the relative acceleration vector of the tracking spacecraft to the target spacecraft in the VVLH coordinate system; is the relative velocity vector of the tracking spacecraft to the target spacecraft in the VVLH coordinate system; is the relative position vector of the tracking spacecraft to the target spacecraft in the VVLH coordinate system, t is the time variable, is the derivative of the target spacecraft angular velocity vector in the VVLH coordinate system; is the angular velocity vector of the target spacecraft in the geocentric inertial system, is the position vector of the target spacecraft in the VVLH coordinate system, is the position vector of the tracking spacecraft in the VVLH coordinate system, r t for The modulus value, r c for The modulus value, T oi is the transformation matrix from the Earth-centered inertial system to the VVLH coordinate system.

[0051] In step 2, when the target spacecraft is in a circular orbit, is a fixed value, The relative acceleration equation of the tracking spacecraft to the target spacecraft in the VVLH coordinate system is expanded according to the X-axis, Y-axis, and Z-axis in the VVLH coordinate system, and the second-order small quantities are neglected to obtain the CW equation:

[0052]

[0053] Where, is the relative acceleration component of the tracking spacecraft to the target spacecraft on the X-axis in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative acceleration component of the tracking spacecraft to the target spacecraft on the Y axis in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative acceleration component of the tracking spacecraft to the target spacecraft in the Z-axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; is the relative velocity component of the tracking spacecraft to the target spacecraft on the X axis in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative velocity component of the tracking spacecraft to the target spacecraft in the VVLH coordinate system when the target spacecraft is in a circular orbit on the Z axis; y is the relative position component of the tracking spacecraft to the target spacecraft in the VVLH coordinate system when the target spacecraft is in a circular orbit on the Y axis; z is the relative position component of the tracking spacecraft to the target spacecraft in the VVLH coordinate system when the target spacecraft is in a circular orbit on the Z axis; ω is the angular velocity of the target spacecraft in the VVLH coordinate system.

[0054] In step 2, the CW equation is a system of linear differential equations with constant coefficients. By solving the system of differential equations, the analytical solution equation is obtained as follows:

[0055]

[0056] Where x(t) is the relative position component of the tracking spacecraft to the target spacecraft at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit; y(t) is the relative position component of the tracking spacecraft to the target spacecraft at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit; z(t) is the relative position component of the tracking spacecraft to the target spacecraft at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit; is the relative velocity component of the tracking spacecraft to the target spacecraft at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative velocity component of the tracking spacecraft to the target spacecraft on the Y axis at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative velocity component of the tracking spacecraft to the target spacecraft at time t on the Z axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; x0 is the relative position component of the tracking spacecraft to the target spacecraft at the initial time on the X axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; y0 is the relative position component of the tracking spacecraft to the target spacecraft at the initial time on the Y axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; z0 is the relative position component of the tracking spacecraft to the target spacecraft at the initial time on the Z axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; is the relative velocity component of the tracking spacecraft to the target spacecraft on the X axis at the initial moment in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative velocity component of the tracking spacecraft to the target spacecraft on the Y axis at the initial moment in the VVLH coordinate system when the target spacecraft is in a circular orbit, It is the relative velocity component of the tracking spacecraft to the target spacecraft on the Z axis at the initial moment in the VVLH coordinate system when the target spacecraft is in a circular orbit.

[0057] From the analytical solution of the equation, it can be obtained that the relative motion state in the X-axis and Z-axis directions is only controlled by the state quantity of the X-axis, the state quantity of the Z-axis, and the time variable t, and has nothing to do with the state quantity of the Y-axis. At the same time, the relative motion state of the Y-axis is only controlled by the state quantity of the Y-axis and the time variable t, and has nothing to do with the state quantity of the X-axis and the Z-axis. Therefore, the relative motion can be decomposed into two independent parts: the motion within the orbital plane (X-axis Z-axis plane) and the motion perpendicular to the orbital plane (Y-axis direction). The present invention considers the relative motion configuration of coplanar spacecraft, so the relative motion in the Y-axis direction is ignored, and the relative motion equation of the coplanar spacecraft can be obtained by replacing the position and velocity components in the X-axis and Z-axis directions with appropriate parameters; then in step three, the relative motion equation is:

[0058]

[0059] Where,

[0060]

[0061] Among them, x xd (t) represents the position component of the tracking spacecraft on the X axis in the VVLH coordinate system at time t when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft; z xd (t) represents the Z-axis position component of the tracking spacecraft in the VVLH coordinate system at time t when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft; Indicates that the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft. The velocity component of the tracking spacecraft along the X axis in the VVLH coordinate system at time t; Indicates that the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft. The velocity component of the tracking spacecraft on the Z axis in the VVLH coordinate system at time t; C x is x xd (t) Constant coefficient of the expression, C vx is x xd (t) The coefficient of the first-order term in the expression, C z For z xd (t) Constant coefficient of the expression; C0 is x xd (t) expression and z xd (t) The trigonometric function coefficients shared by the expression, ψ0 is x xd (t) expression and z xd (t) The angle values ​​of the trigonometric functions used in the expression.

[0062] The values ​​of each coefficient are determined by the relative position and relative velocity of the tracking spacecraft at the initial moment, and the angular velocity of the target spacecraft. Analysis of the relative motion equation shows that it is a linear differential equation that satisfies the superposition principle. Therefore, the relative motion of coplanar spacecraft can be further decomposed into the superposition of two motions: linear motion and elliptical motion.

[0063] In step 3, the linear motion polynomial is:

[0064]

[0065] The polynomial representing elliptical motion in the relative motion equation is:

[0066]

[0067] When C0≠0, the elliptical motion polynomial can be expressed as:

[0068]

[0069] Where x line is the X-axis position component in linear motion, z line is the Z-axis position component in linear motion, is the X-axis velocity component in linear motion, is the Z-axis velocity component in linear motion, x oval is the X-axis position component in the elliptical motion, z oval is the Z-axis position component in the elliptical motion, is the X-axis velocity component in elliptical motion, is the Z-axis velocity component in elliptical motion. line Contains two items, of which C vx t is related to the time variable t, which is called the velocity term.

[0070] In step 4, a relative motion configuration set is constructed when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft, including a main set and a subset corresponding to each relative motion configuration in the main set;

[0071] The main set is: flyby configuration, accompanying configuration and rendezvous configuration;

[0072] The subsets of the skimming configurations are: straight-line skimming configuration, arch-line skimming configuration, and teardrop-shaped skimming configuration;

[0073] The subsets of accompanying flight configurations are: following flight configuration, staying configuration and flying around configuration;

[0074] There is no subset of the intersection configuration; among them,

[0075] A flyby configuration refers to a relative motion configuration in which the tracking spacecraft and the target spacecraft have different orbital periods, and the tracking spacecraft first approaches and then moves away from the target spacecraft, or directly moves away from the target spacecraft, but the two spacecraft never touch each other. When the flyby configuration is formed, the linear motion in the relative motion includes forward motion, and there is no requirement for elliptical motion in the relative motion. At this time, the linear motion becomes the dominant relative motion.

[0076] like Figure 1 As shown in the figure, the straight-line flyby configuration refers to the tracking spacecraft passing the target spacecraft by flying above or below the target spacecraft orbit. At this time, there is no elliptical motion in the relative motion, and it moves forward in a straight line.

[0077] like Figure 2 As shown in the figure, the apsidal flyby configuration refers to the situation where the tracking spacecraft passes by the target spacecraft in a flyby manner. In the relative motion, there is an elliptical motion. The superposition of the elliptical motion and the linear motion manifests as an apsidal advance.

[0078] like Figure 3 As shown in the figure, the teardrop-shaped flyby configuration refers to the existence of elliptical motion in the relative motion of the tracking spacecraft when it passes the target spacecraft in a flyby manner. The superposition of the elliptical motion and the linear motion is manifested as a teardrop-shaped back-and-forth forward movement. The back-and-forth trajectory is defined as the trajectory in which the tracking spacecraft retreats relative to the target spacecraft during its forward movement and then turns forward again.

[0079] The accompanying flight configuration refers to a relative motion configuration in which the tracking spacecraft and the target spacecraft have the same orbital period, the tracking spacecraft's spatial position relative to the target spacecraft changes periodically, but the relative distance is always non-zero. When the accompanying flight configuration is formed, the linear motion in the relative motion does not have forward motion, and there is no requirement for elliptical motion in the relative motion. At this time, the elliptical motion becomes the dominant relative motion, and the relative motion manifests as periodic motion or relative stillness.

[0080] like Figure 4 As shown in the figure, the following configuration means that the tracking spacecraft is located to one side of the target spacecraft and is stationary relative to the target spacecraft; the relative motion of the tracking spacecraft is neither linear nor elliptical, and is characterized by a fixed point;

[0081] like Figure 5 As shown in the figure, the stationary configuration means that the tracking spacecraft is always located on one side of the target spacecraft, flying in a closed elliptical shape, with the relative distance maintained within a certain range, and the target spacecraft is located outside the elliptical trajectory of the tracking spacecraft;

[0082] like Figure 6As shown in the figure, the fly-by configuration refers to the tracking spacecraft performing a closed elliptical relative motion around the target spacecraft, with the relative distance maintained within a certain range and the target spacecraft located inside the tracking spacecraft's elliptical trajectory;

[0083] like Figure 7 As shown, the rendezvous configuration refers to a relative motion configuration in which the tracking spacecraft reaches the same spatial position as the target spacecraft at a preset time, and the relative distance is zero; when the rendezvous configuration is formed, no requirements are made for linear motion and elliptical motion in the relative motion, and only the relative distance between the tracking spacecraft and the target spacecraft is required to be zero at the preset time.

[0084] The characteristics of the flyby configuration are: the orbital periods of the tracking spacecraft and the target spacecraft are different, that is, the semi-major axes of the orbits are different; the closest distance is not zero, that is, the two spacecraft will not rendezvous;

[0085] The constraints of the flyby configuration are: That is, the velocity polynomial C in linear motion vx t≠0, and the relative motion trajectory does not pass through the origin;

[0086] Where z xd (t x＝0 ) is the relative motion equation t=t x＝0 Time xd The value of (t). x＝0 Represents x in the relative motion equation xd The solution for the time variable t where (t)=0.

[0087] The orbital elements of the flyby configuration are:

[0088] Among the subset of flyby configurations, the motion characteristics of the straight-line flyby configuration are as follows: the magnitude of the relative velocity between the tracking spacecraft and the target spacecraft remains constant;

[0089] The constraints of the straight-line flyby configuration are: That is, the elliptical motion polynomial is equal to zero;

[0090] The orbital elements of the straight flyby configuration are:

[0091] The motion characteristics of the apsidal flyby configuration are as follows: in the VVLH coordinate system, the tracking spacecraft's relative velocity has a magnitude change in the X-axis component but no direction change;

[0092] The constraints of the apsidal flyby configuration are:

[0093] The orbital elements of the apsidal flyby configuration are:

[0094] The motion characteristics of the teardrop-shaped flyby configuration are as follows: in the VVLH coordinate system, the tracking spacecraft's relative velocity has a direction change in the X-axis component;

[0095] The constraints of the teardrop-shaped skimming configuration are:

[0096] The orbital elements of the teardrop-shaped flyby configuration are:

[0097] The motion characteristics of the accompanying flight configuration are: the orbital period of the tracking spacecraft and the target spacecraft is the same and the closest distance is not zero;

[0098] The constraints of the accompanying flight configuration are: That is, the velocity term C in the linear motion polynomial vx t=0, and the relative motion trajectory does not pass through the origin;

[0099] The orbital element set of the accompanying flight configuration is:

[0100] Among the subset of accompanying flight configurations, the motion characteristics of the following flight configuration are as follows: the tracking spacecraft and the target spacecraft remain relatively stationary;

[0101] The constraints of the follow-flight configuration are: That is, the elliptical motion polynomial is zero;

[0102] The orbital element set of the follow-fly configuration is:

[0103] The motion characteristics of the stationary configuration are: the relative motion trajectory of the tracking spacecraft is an ellipse, and the target spacecraft is outside the elliptical trajectory of the tracking spacecraft;

[0104] The constraints of the resident configuration are:

[0105] The set of orbital elements of the resident configuration is:

[0106] The motion characteristics of the fly-by configuration are: the relative motion trajectory of the tracking spacecraft is an ellipse, and the target spacecraft is within the elliptical trajectory of the tracking spacecraft;

[0107] The constraints of the fly-around configuration are:

[0108] The orbital element set of the flyby configuration is:

[0109] The motion characteristics of the rendezvous configuration are: the closest distance between the pursuit spacecraft and the target spacecraft is equal to zero;

[0110] The constraints of the rendezvous configuration are:xd (t x＝0 )=0; that is, the relative motion trajectory passes through the origin;

[0111] The orbital element set of the rendezvous configuration is: [t x＝0 ];

[0112] In the relative motion configuration set, the orbital element set of the main set Track element collection with subsets Combined, the constructed multi-track element set is:

[0113] In step 5, the initial relative position and initial relative velocity of the tracking spacecraft in the mission and the angular velocity of the target spacecraft are used as input data. The numerical values ​​of the multi-orbital element set are output through the relative motion equation. The numerical values ​​are input into the constraint conditions to obtain the output results. The method for identifying the relative motion configuration corresponding to the constraint conditions in the relative motion configuration set through the output results is as follows:

[0114] (1) Method for identifying the main set of relative motion configurations:

[0115] For example: The first constraint is: z xd (t x＝0 )=0, the second constraint is:

[0116] When the first constraint condition is true, the relative motion configuration is determined to be an intersection configuration.

[0117] When the first constraint condition is false, the second constraint condition is determined; if the second constraint condition is true, the relative motion configuration is determined to be a fly-by configuration; if the second constraint condition is false, the relative motion is determined to be a fly-by configuration. The determination method is shown in Table 1:

[0118] Table 1

[0119]

[0120] (2) Identification method of relative motion configuration subset

[0121] Since there are subsets for both the skimming and accompanying configurations, once these two main sets are identified, the subsets to which they belong can be further identified based on the constraints of the subsets. The constraints corresponding to the skimming configuration subset identification method are shown in Table 2; the constraints corresponding to the accompanying configuration subset identification method are shown in Table 3.

[0122] Table 2

[0123]

[0124] Table 3

[0125]

[0126]

[0127] In order to analyze the effect of the technical solution disclosed in the present invention, a simulation experiment is provided for illustration:

[0128] Simulation Experiment 1

[0129] There are two spacecraft in space: a target spacecraft and a tracking spacecraft. The two spacecraft are coplanar. The target spacecraft's position in the J2000 geocentric inertial frame is [42166000, 0, 0], and its velocity is [0, 3074.59, 0]. The tracking spacecraft's position in the J2000 geocentric inertial frame is [42166000, -50000, 0], and its velocity is [3.64, 3080.239, 0]. Based on the initial state data of the two spacecraft, the relative motion configuration of the tracking spacecraft with respect to the target spacecraft is identified.

[0130] (1) Relative motion recognition method based on multi-track elements

[0131] 1. Get the value of a multi-track element set:

[0132] According to the motion state coordinates of the two spacecraft in the J2000 geocentric inertial system, the initial position coordinates of the tracking spacecraft in the target spacecraft VVLH relative coordinate system [x0, y0, z0] = [-50*1000, 0, 100*1000] and the initial velocity coordinates can be obtained from the coordinate conversion relationship. The angular velocity of the target spacecraft is 7.29*10 -5 Substituting the above data into the relative motion equation:

[0133]

[0134] The solution is that the moment t when the X axis is equal to 0 in relative motion x＝0 =3897.05. Therefore, the multi-track element set

[0135] 2. Identify the main set orbital configuration

[0136] Substitute the corresponding elements in the multi-track element set into the first constraint: z xd (t x＝0 )=0; Second constraint: Make a judgment.

[0137] Get z xd (t x＝0 )=97800, Therefore, the first constraint is false, and the second constraint is also false, so the motion is judged to be a flyby configuration.

[0138] 3. Identify subset orbital configurations

[0139] Substitute the corresponding elements in the multi-track feature set into the third constraint of the subset: The fourth constraint: Fifth constraint: Make a judgment.

[0140] It is concluded that the fifth constraint is true, so the motion configuration is a teardrop-shaped flying configuration.

[0141] (2) Using traditional methods to identify relative motion configurations

[0142] 1. The relative motion state value of the tracking spacecraft is iteratively calculated with a step size of 1 second to obtain the relative motion state data for the next 48 hours. The relative motion state data is plotted on the coordinate axis, and its relative motion trajectory is obtained as a teardrop-shaped flyby configuration. The relative motion trajectory of the tracking spacecraft is as follows: Figure 8 shown.

[0143] (3) Experimental conclusion

[0144] The relative motion recognition method based on multi-orbital elements can use the constructed multi-orbital element set to identify the relative configuration of coplanar spacecraft in this scenario. The recognition result is a teardrop-shaped flyby configuration, which is consistent with the configuration recognition of traditional methods and does not require a large number of iterative calculations.

[0145] Simulation Experiment 2

[0146] There are two spacecraft in space: a target spacecraft and a tracking spacecraft. They are coplanar. The target spacecraft's position in the J2000 geocentric inertial frame is [42166000, 0, 0], and its velocity is [0, 3074.59, 0]. The tracking spacecraft's position in the J2000 geocentric inertial frame is [42066000, -50000, 0], and its velocity is [-6.35, 3081.88, 0]. Based on the initial state data of the two spacecraft, the relative motion configuration of the tracking spacecraft with respect to the target spacecraft is identified.

[0147] (1) Relative motion recognition method based on multi-track elements

[0148] 1. Get the data value of a multi-track feature set

[0149] According to the motion state coordinates of the two spacecraft in the J2000 geocentric inertial system, the initial position coordinates of the tracking spacecraft in the target spacecraft VVLH relative coordinate system [x0, y0, z0] = [-50*1000, 0, 100*1000] and the initial velocity coordinates can be obtained from the coordinate conversion relationship. The angular velocity of the target spacecraft is 7.29*10 -5 Substituting the above data into the relative motion equation:

[0150]

[0151] The solution is that the moment t when the X axis is equal to 0 in relative motion x＝0 = 3003.33. Therefore, the multi-track element set

[0152] 2. Identify the main set orbital configuration

[0153] Substitute the corresponding elements in the multi-track element set into the first constraint of the main set: z xd (t x＝0 )=0; Second constraint: Make a judgment.

[0154] Get z xd (t x＝0 )=134444, Therefore, the first constraint is false and the second constraint is true, so the motion is judged to be a companion flight configuration.

[0155] 3. Identify subset orbital configurations

[0156] Substitute the corresponding elements in the multi-track element set into the sixth constraint of the subset:

[0157] Seventh constraint:

[0158] The eighth constraint: Make a judgment.

[0159] It is concluded that the eighth constraint condition is true, so the motion configuration is a fly-by configuration.

[0160] (2) Using traditional methods to identify relative motion configurations

[0161] 1. The relative motion state value of the tracking spacecraft is iteratively calculated with a step length of 1 second to obtain the relative motion state data for the next 24 hours, and the relative motion state data is plotted on the coordinate axis to obtain its relative motion trajectory as a fly-by configuration. The relative motion trajectory of the tracking spacecraft is as follows: Figure 9 shown.

[0162] (3) Experimental conclusion

[0163] The relative motion recognition method based on multi-orbital elements can use the constructed multi-orbital element set to identify the relative configuration of coplanar spacecraft in this scenario. The recognition result is a fly-by configuration, which is consistent with the configuration recognition of traditional methods and does not require a large number of iterative calculations.

[0164] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements, characterized in that: include: Step 1: Combine the relative position equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system with the two-body dynamics equation to obtain the relative acceleration equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system, and convert it into the relative acceleration equation of the tracking spacecraft to the target spacecraft in the VVLH coordinate system; Step 2: Construct the CW equation of the target spacecraft when it is in a circular orbit from the relative acceleration equation of the tracking spacecraft to the target spacecraft in the VVLH target orbit coordinate system, and obtain the analytical solution equations of the relative position and relative velocity of the CW equation; Step 3: Construct the relative motion equation when the tracking spacecraft and the target spacecraft are coplanar by solving the equation analytically, and decompose the relative motion equation into linear motion polynomials and elliptical motion polynomials; Step 4: Construct a set of relative motion configurations when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft; obtain the constraints corresponding to the linear motion polynomial and the elliptical motion polynomial in the relative motion equation from the motion characteristics of each relative motion configuration in the relative motion configuration set, and form a multi-orbital element set from the orbital elements in the constraints; Step 5: Extract the input data required for the relative motion equation in the mission data, output the numerical value of the multi-orbital element set through the relative motion equation, input the numerical value into the constraint condition to obtain the output result, and identify the relative motion configuration corresponding to the constraint condition in the relative motion configuration set through the output result.

2. The method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements according to claim 1, characterized in that: In step 1, the relative acceleration equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system is: Where, is the relative acceleration vector of the tracking spacecraft to the target spacecraft in the geocentric inertial system, μ is the earth's gravitational constant, is the position vector of the target spacecraft in the geocentric inertial system, is the position vector of the tracking spacecraft in the Earth-centered inertial system; r ti for The modulus value, r ci for The modulus value of .

3. The method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements according to claim 2, wherein: In step 1, the relative position equation of the tracking spacecraft to the target spacecraft in the geocentric inertial system is: The two-body dynamics equation is: Where, is the relative position vector of the tracking spacecraft to the target spacecraft in the geocentric inertial system; is the acceleration vector of the spacecraft in the geocentric inertial system, is the position vector of the spacecraft in the Earth-centered inertial system, r E for The modulus value of .

4. The method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements according to claim 3, wherein: In step 1, the relative acceleration equation of the tracking spacecraft to the target spacecraft in the VVLH coordinate system is: Where, is the relative acceleration vector of the tracking spacecraft to the target spacecraft in the VVLH coordinate system; is the relative velocity vector of the tracking spacecraft to the target spacecraft in the VVLH coordinate system; is the relative position vector of the tracking spacecraft to the target spacecraft in the VVLH coordinate system; t is the time variable; is the angular velocity vector of the target spacecraft in the VVLH coordinate system, is the derivative of the target spacecraft angular velocity vector in the VVLH coordinate system; is the position vector of the target spacecraft in the VVLH coordinate system, is the position vector of the tracking spacecraft in the VVLH coordinate system, r t for The modulus value, r c for The modulus value, T oi is the transformation matrix from the Earth-centered inertial system to the VVLH coordinate system.

5. The method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements according to claim 4, characterized in that: In step 2, the CW equation is: Where, is the relative acceleration component of the tracking spacecraft to the target spacecraft on the X-axis in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative acceleration component of the tracking spacecraft to the target spacecraft on the Y axis in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative acceleration component of the tracking spacecraft to the target spacecraft in the Z-axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; is the relative velocity component of the tracking spacecraft to the target spacecraft on the X axis in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative velocity component of the tracking spacecraft to the target spacecraft in the VVLH coordinate system when the target spacecraft is in a circular orbit on the Z axis; y is the relative position component of the tracking spacecraft to the target spacecraft in the VVLH coordinate system when the target spacecraft is in a circular orbit on the Y axis; z is the relative position component of the tracking spacecraft to the target spacecraft in the VVLH coordinate system when the target spacecraft is in a circular orbit on the Z axis; ω is the angular velocity of the target spacecraft in the VVLH coordinate system.

6. The method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements according to claim 5, characterized in that: In step 2, the analytical solution equation is: Where x(t) is the relative position component of the tracking spacecraft to the target spacecraft at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit; y(t) is the relative position component of the tracking spacecraft to the target spacecraft at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit; z(t) is the relative position component of the tracking spacecraft to the target spacecraft at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit; is the relative velocity component of the tracking spacecraft to the target spacecraft at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative velocity component of the tracking spacecraft to the target spacecraft on the Y axis at time t in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative velocity component of the tracking spacecraft to the target spacecraft at time t on the Z axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; x0 is the relative position component of the tracking spacecraft to the target spacecraft at the initial time on the X axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; y0 is the relative position component of the tracking spacecraft to the target spacecraft at the initial time on the Y axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; z0 is the relative position component of the tracking spacecraft to the target spacecraft at the initial time on the Z axis in the VVLH coordinate system when the target spacecraft is in a circular orbit; is the relative velocity component of the tracking spacecraft to the target spacecraft on the X axis at the initial moment in the VVLH coordinate system when the target spacecraft is in a circular orbit, is the relative velocity component of the tracking spacecraft to the target spacecraft on the Y axis at the initial moment in the VVLH coordinate system when the target spacecraft is in a circular orbit, It is the relative velocity component of the tracking spacecraft to the target spacecraft on the Z axis at the initial moment in the VVLH coordinate system when the target spacecraft is in a circular orbit.

7. The method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements according to claim 6, characterized in that: In step 3, the relative motion equation is: Among them, x xd (t) represents the position component of the tracking spacecraft on the X axis in the VVLH coordinate system at time t when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft; z xd (t) represents the Z-axis position component of the tracking spacecraft in the VVLH coordinate system at time t when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft; Indicates that the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft. The velocity component of the tracking spacecraft along the X axis in the VVLH coordinate system at time t; Indicates that the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft. The velocity component of the tracking spacecraft on the Z axis in the VVLH coordinate system at time t; C x is x xd (t) Constant coefficient of the expression, C vx is x xd (t) The coefficient of the first-order term in the expression, C z For z xd (t) Constant coefficient of the expression; C0 is x xd (t) expression and z xd (t) The trigonometric function coefficients shared by the expression, ψ0 is x xd (t) expression and z xd (t) The angle values ​​of the trigonometric functions used in the expression.

8. The method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements according to claim 7, characterized in that: In step 3, the linear motion polynomial is: The elliptical motion polynomial is: Where x line is the X-axis position component in linear motion, z line is the Z-axis position component in linear motion, is the X-axis velocity component in linear motion, is the Z-axis velocity component in linear motion, x oval is the X-axis position component in the elliptical motion, z oval is the Z-axis position component in the elliptical motion, is the X-axis velocity component in elliptical motion, is the Z-axis velocity component in the elliptical motion.

9. The method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements according to claim 8, wherein: In step 4, a relative motion configuration set is constructed when the target spacecraft is in a circular orbit and the tracking spacecraft is coplanar with the target spacecraft, including a main set and a subset corresponding to each relative motion configuration in the main set; The main set is: flyby configuration, accompanying configuration and rendezvous configuration; The subsets of the skimming configurations are: straight-line skimming configuration, arch-line skimming configuration, and teardrop-shaped skimming configuration; The subsets of accompanying flight configurations are: following flight configuration, staying configuration and flying around configuration; There is no subset of the intersection configuration; among them, A flyby configuration refers to a relative motion configuration in which the tracking spacecraft and the target spacecraft have different orbital periods, and the tracking spacecraft first approaches and then moves away from the target spacecraft, or directly moves away from the target spacecraft, but the two spacecraft never touch each other. When the flyby configuration is formed, the linear motion in the relative motion includes forward motion, and there is no requirement for elliptical motion in the relative motion. At this time, the linear motion becomes the dominant relative motion. The straight-line flyby configuration refers to the tracking spacecraft passing the target spacecraft by flying above or below the target spacecraft's orbit. At this time, there is no elliptical motion in the relative motion, and it moves forward in a straight line. The arch-line flyby configuration refers to the situation where the tracking spacecraft passes by the target spacecraft in a flyby manner, and there is elliptical motion in the relative motion. The superposition of the elliptical motion and the linear motion manifests as an arch-line forward motion. A teardrop-shaped flyby configuration refers to a tracking spacecraft that flies past a target spacecraft in a flyby manner. The elliptical motion in the relative motion is superimposed on the linear motion, resulting in a teardrop-shaped back-and-forth. The back-and-forth trajectory is defined as the trajectory of the tracking spacecraft retreating relative to the target spacecraft and then reversing to forward motion. The accompanying flight configuration refers to a relative motion configuration in which the tracking spacecraft and the target spacecraft have the same orbital period, the tracking spacecraft's spatial position relative to the target spacecraft changes periodically, but the relative distance is always non-zero. When the accompanying flight configuration is formed, the linear motion in the relative motion does not have forward motion, and there is no requirement for elliptical motion in the relative motion. At this time, the elliptical motion becomes the dominant relative motion, and the relative motion manifests as periodic motion or relative stillness. The tracking configuration refers to the tracking spacecraft being located to one side of the target spacecraft and being stationary relative to the target spacecraft. The tracking spacecraft's relative motion is neither linear nor elliptical, and appears to be a fixed point. The stationary configuration means that the tracking spacecraft is always located to one side of the target spacecraft, flying in a closed elliptical shape, with the relative distance maintained within a certain range, and the target spacecraft is located outside the tracking spacecraft's elliptical trajectory; The fly-by configuration refers to the tracking spacecraft performing a closed elliptical relative motion around the target spacecraft, with the relative distance maintained within a certain range and the target spacecraft located inside the tracking spacecraft's elliptical trajectory. Rendezvous configuration refers to a relative motion configuration in which the tracking spacecraft reaches the same spatial position as the target spacecraft at a preset time, and the relative distance is zero; when the rendezvous configuration is formed, there are no requirements for linear motion and elliptical motion in the relative motion, only the relative distance between the tracking spacecraft and the target spacecraft is required to be zero at the preset time.

10. The method for identifying relative motion configurations of coplanar spacecraft based on multiple orbital elements according to claim 9, characterized in that: The motion characteristics of the flyby configuration are: the orbital periods of the tracking spacecraft and the target spacecraft are different and the closest distance is not zero; The constraints of the flyby configuration are: The orbital elements of the flyby configuration are: Where z xd (t x＝0 ) is the relative motion equation t=t x＝0 Time xd The value of (t), t x＝0 Represents x in the relative motion equation xd The solution for the time variable t where (t) = 0; Among the subset of flyby configurations, the motion characteristics of the straight-line flyby configuration are as follows: the magnitude of the relative velocity between the tracking spacecraft and the target spacecraft remains constant; The constraints of the straight-line flyby configuration are: The orbital elements of the straight flyby configuration are: The motion characteristics of the apsidal flyby configuration are as follows: in the VVLH coordinate system, the tracking spacecraft's relative velocity has a magnitude change in the X-axis component but no direction change; The constraints of the apsidal flyby configuration are: The orbital elements of the apsidal flyby configuration are: The motion characteristics of the teardrop-shaped flyby configuration are as follows: in the VVLH coordinate system, the tracking spacecraft's relative velocity has a direction change in the X-axis component; The constraints of the teardrop-shaped skimming configuration are: The orbital elements of the teardrop-shaped flyby configuration are: The motion characteristics of the accompanying flight configuration are: the orbital period of the tracking spacecraft and the target spacecraft is the same and the closest distance is not zero; The constraints of the accompanying flight configuration are: The orbital element set of the accompanying flight configuration is: Among the subset of accompanying flight configurations, the motion characteristics of the following flight configuration are as follows: the tracking spacecraft and the target spacecraft remain relatively stationary; The constraints of the follow-flight configuration are: The orbital element set of the follow-fly configuration is: The motion characteristics of the stationary configuration are: the relative motion trajectory of the tracking spacecraft is an ellipse, and the target spacecraft is outside the elliptical trajectory of the tracking spacecraft; The constraints of the resident configuration are: The set of orbital elements of the resident configuration is: The motion characteristics of the fly-by configuration are: the relative motion trajectory of the tracking spacecraft is an ellipse, and the target spacecraft is within the elliptical trajectory of the tracking spacecraft; The constraints of the fly-around configuration are: The orbital element set of the flyby configuration is: The motion characteristics of the rendezvous configuration are: the closest distance between the pursuit spacecraft and the target spacecraft is equal to zero; The constraints of the rendezvous configuration are: xd (t x＝0 )=0; The orbital element set of the rendezvous configuration is: [t x＝0 ]; In the relative motion configuration set, the orbital element set of the main set is combined with the orbital element set of the subset to construct a multi-orbital element set:

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