Spacecraft space urgency degree calculation method based on maneuvering reachable domain

Abstract

The invention relates to a spacecraft space urgency degree calculation method based on a maneuvering reachable domain, which utilizes the theory of the spacecraft maneuvering reachable domain, obtains the concept of space urgency degree through calculation, reflects the degree of threat suffered by a spacecraft in a multi-target pursuit scene, and solves the problem that the degree of threat is not easy to quantify. The specific calculation method comprises the following steps: step 1, determining the orbital elements of a master target and a slave target; 2, calculating maneuvering reachable domains of the master target and the slave target; step 3, calculating the reachability of the slave target; and 4, calculating the space urgency degree. The method has the advantage of wide applicability, can be applied to a multi-target track pursuit game scene, and solves the problem that the threat degree is not easy to quantify in the multi-target track pursuit game scene; and meanwhile, the universality is high, quantitative indexes can be provided for general track pursuit game problems, and the threat degree of the slave target to the master target is quantitatively analyzed.

Description

Technical Field

[0001] The present invention relates to a method for calculating space urgency based on maneuverable reachable domain. The method utilizes the theory of maneuverable reachable domain and obtains the concept of "space urgency" through calculation to evaluate the safety of spacecraft in orbit, belonging to the field of aerospace technology. Background Art

[0002] With the development of human science and technology, human exploration technology for outer space has continued to mature, space activities have become increasingly frequent, and the number of non-cooperative space targets such as non-cooperative satellites and space debris has increased sharply. At the same time, the increasing maturity of space exploration technology and the continuous enhancement of exploration capabilities of various countries have also led to the gradual expansion of strategic competition between countries to the "space domain".

[0003] In this context, it is not uncommon for in-orbit spacecraft to be actively approached by non-cooperative targets such as reconnaissance satellites. In order to protect the safety of space assets, the study of orbital pursuit and escape games has become increasingly important. The maneuverable reachable domain of a spacecraft can effectively evaluate the maneuverability and range of a spacecraft, and has been widely used in the field of orbital pursuit and escape games. Wen Changxuan from the Beijing University of Aeronautics and Astronautics proposed the concepts of absolute position reachable domain and relative position reachable domain, and defined the reachable domain as the set of all possible spatial positions that a spacecraft can access under given orbital maneuvering constraints (Wen C, Zhao Y, Shi P. Precise determination of reachable domain for spacecraft with single impulse [J]. Journal of Guidance, Control, and Dynamics, 2014, 37 (6): 1767-1779.). Du Xiangnan and others from the National University of Defense Technology gave a reachability criterion based on the basic theory and inference of boundary value problems, proposed a solution method for the reachable domain of single-pulse maneuvers using the reachability criterion, and carried out research on threat avoidance maneuver strategies based on the reachable domain theory (Du Xiangnan. Characterization of reachable domain of spacecraft maneuver and threat avoidance [D]. National University of Defense Technology, 2023.).

[0004] However, existing research on maneuverable reachable domain mainly focuses on evaluating the maneuverability and range of spacecraft at the orbital level, which cannot intuitively present the threat level of non-cooperative targets to friendly targets in orbital pursuit scenarios. In addition, existing related research is mostly carried out on a single non-cooperative target, and there are few studies on multiple non-cooperative targets approaching our targets together. Therefore, in the multi-target orbital pursuit game, it is necessary to propose a method to concisely and effectively evaluate the threat level of spacecraft. Summary of the invention

[0005] 1. Purpose

[0006] The present invention provides a concept for evaluating the degree of threat posed to a spacecraft by a non-cooperative target - spatial urgency, to solve the problem that it is difficult to quantify the degree of threat in orbital pursuit games. Spatial urgency reflects the composite threat degree of the threat target to the main target in a multi-target pursuit scenario.

[0007] 2. Technical solution

[0008] In order to achieve the above-mentioned object of the invention, the present invention adopts the following technical solutions.

[0009] A method for calculating space urgency of a spacecraft based on a maneuverable reachable domain comprises the following steps:

[0010] Step 1: Determine the number of master and slave target orbits

[0011] The main target is defined as the spacecraft that is threatened, that is, the "escaping" party in the pursuit and escape scenario; the secondary target poses a threat to the main target, that is, the "chasing" party in the pursuit and escape scenario. In a multi-target pursuit and escape scenario, the main target is unique, and the number of secondary targets may be more than one.

[0012] The orbital elements of the two targets are determined by the space situational awareness system through relevant orbit determination operations.

[0013] Step 2: Calculation of the mobile reachable area of ​​the master and slave targets

[0014] The maneuverable domain is defined as the set of all positions that the spacecraft can reach under a given initial orbit and fuel constraints. The spacecraft uses pulse thrust during orbital maneuvers, which means that the maneuver is considered to occur instantaneously and is manifested as a velocity increment Δv in an arbitrary direction applied to the spacecraft.

[0015] The maneuverable reachable domain of the master and slave targets is defined in the present invention as a reachable domain with free maneuvering time, that is, the maneuvering time of the target is not restricted, the target is allowed to maneuver at any time, and then the area that the target can reach is calculated. This is mainly achieved by the following steps:

[0016] (1) Determine a spatial position by azimuth;

[0017] (2) Determine the accessibility of the location;

[0018] (3) If the direction is reachable, then solve the reachable domain envelope at the direction;

[0019] (4) Traverse all spatial orientations, obtain the approximate envelope surface, and find the reachable domain.

[0020] Step 3: Calculate from target reachability

[0021] The target reachability calculation includes the selection of sample points, coordinate transformation and threat domain calculation.

[0022] The selection of sample points refers to selecting a number of sample points at equal intervals using the Monte Carlo method within the reachable domain of the primary target calculated in step 2 to form a full set for judging the reachability of the secondary target. Within the range allowed by the computing speed, the more sample points are selected, the higher the accuracy.

[0023] The coordinate transformation refers to transforming the selected sample points from the orbital coordinate system where the master target is located to the orbital coordinate system where the slave target is located, so as to facilitate the calculation of the threat domain of the slave target.

[0024] The threat domain refers to the area where the range where the main target may escape when threatened overlaps with the range that the slave target can reach through orbital maneuvers. During the calculation process, if a sample point is within the maneuverable reachable domain of the slave target, then the point belongs to the threat domain of the slave target, which is called a danger point. The set of danger points is the threat domain of the slave target. If there are multiple slave targets in a certain scenario, the threat domains of each slave target are combined to form a composite threat domain in a multi-target pursuit scenario.

[0025] Step 4: Calculate space urgency

[0026] The spatial urgency is defined as the ratio of the composite threat domain of each slave target to the maneuverable domain of the main target, reflecting the threat level of each slave target to the main target in a multi-target pursuit scenario.

[0027] The spatial urgency can be quantified using the sample points selected by the Monte Carlo method in step three, that is, when the number of sample points is large enough, the spatial urgency of the main target is reflected by the proportion of dangerous points to all sample points.

[0028] 3. Advantages and effects

[0029] The present invention proposes the concept of "spatial urgency" based on the maneuverable accessible domain, describes the spatial ratio of risks within the accessible domain of our spacecraft, and designs a method for calculating the spatial urgency; the present invention has wide applicability and can be applied to multi-target orbital pursuit and escape game scenarios, solving the problem that it is difficult to quantify the threat level in multi-target pursuit and escape scenarios; the present invention has strong versatility and can provide quantitative indicators for general orbital pursuit and escape game problems, and quantitatively analyze the threat level of slave targets to the main target. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flowchart of a method for calculating the space urgency of a spacecraft based on a maneuverable reachable domain.

[0031] Figure 2 This is an example diagram of the maneuverable reachable area of ​​a single target.

[0032] Figure 3 This is a schematic diagram of a composite threat domain. DETAILED DESCRIPTION

[0033] The present invention is further described below in conjunction with the accompanying drawings and embodiments of a multi-target orbital pursuit scenario, but this embodiment is not intended to limit the present invention. All similar methods and similar variations of the present invention should be included in the protection scope of the present invention.

[0034] Depend on Figure 1 It can be seen that the present invention provides a method for calculating the space urgency of a spacecraft based on a maneuverable reachable domain, which mainly includes the following steps:

[0035] Step 1: Determine the number of master and slave target orbits

[0036] The main target is defined as the spacecraft under threat, i.e. the "escaping" party in the pursuit scenario; the secondary target poses a threat to the main target, i.e. the "chasing" party in the pursuit scenario. In a multi-target pursuit scenario, the main target is unique, and the number of secondary targets may be more than one. This embodiment includes one main target and three secondary targets, which jointly threaten the main target, forming a "hunting" situation.

[0037] The orbital elements of the two targets are determined by the space situational awareness system through related orbit determination operations. The orbital elements include the position and velocity information of the spacecraft at the initial moment, which can be obtained through common orbital information forms such as two line elements (TLE), including: orbital semi-major axis a, eccentricity e, orbital inclination i, perigee argument ω, ascending node right ascension Ω, true anomaly f. In this embodiment, the orbital elements are as follows:

[0038] Orbital parameters Main goal From Target 1 From Target 2 From Target 3 Orbital semi-major axis a(km) 7000 7000 7000 7000 Eccentricity 0.1 0.1 0.1 0.1 Orbital inclination i(°) 0 0 2 5 Argument of perigee ω(°) 0 10 5 0 Ascending node right ascension Ω(°) 0 30 0 0 True anomaly f 0 90 90 180

[0039] Step 2: Calculation of the mobile reachable area of ​​the master and slave targets

[0040] The maneuverable domain is defined as the set of all positions that the spacecraft can reach under a given initial orbit and fuel constraints. The spacecraft uses pulse thrust during orbital maneuvers, that is, the maneuver is considered to occur instantaneously and is manifested as a velocity increment Δv in an arbitrary direction applied to the spacecraft. The maneuverable domain can be divided into a domain with fixed maneuvering time, a domain with free maneuvering time, and a relative maneuverable domain.

[0041] The maneuverable reachable domain of the master and slave targets is defined in the present invention as a reachable domain with free maneuvering time, that is, the maneuvering time of the target is not restricted, the target is allowed to maneuver at any time, and then the area that the target can reach is calculated. Figure 2It can be seen that the reachable domain is similar to a circular pipe and is symmetrical about the initial orbital plane. The calculation of the reachable domain is mainly achieved through the following steps:

[0042] (1) Determine a spatial position by azimuth

[0043] The spatial orientation can be determined by two azimuth angles γ, is determined by the unit vector In the orbital perigee coordinate system, the origin is the center of mass of the Earth; the x-axis points to the orbital perigee; the z-axis is along the angular momentum direction of the orbital plane and is perpendicular to the orbit; the y-axis is determined by the right-hand rule. When a certain spatial orientation is projected onto the target orbital plane, the angle between the projection line and the x-axis is γ, and the value range is [0,2π]; the angle between the orientation and the orbital plane is The value range is Due to symmetry, The value of only covers the upper half of the reachable domain, and the lower half of the reachable domain can be obtained by symmetry.

[0044] (2) Determine the accessibility of the location

[0045] After determining the spatial position, we need to know whether the spacecraft can reach the position. The position is reachable when the following equation is satisfied:

[0046]

[0047] In the formula, γ, is the azimuth angle, Δv is the applied velocity increment, μ=3.986×10 14 m 3 / s 2 is the earth's gravitational constant, p = a(1-e 2 ) is the orbital semi-diameter, and f is the true anomaly. If the position is reachable, proceed to step (3); if not, skip step (3) and directly proceed to step (4) to traverse the next spatial position.

[0048] (3) Solve the reachable domain envelope at this location

[0049] Depend on Figure 2 It is easy to see that when a certain direction When it is reachable, the ray along this azimuth will pass through the reachable domain and form two intersection points with the boundary of the reachable domain, inner and outer. Therefore, the radius vector extreme value r of these two points in the coordinate system is calculated. min and r max , we can determine that the radius vector value r of all reachable points on this direction satisfies r min ≤r≤r max , and get the reachable domain envelope of the orientation. The specific calculation method is as follows.

[0050] Assuming that the spacecraft maneuvers from position r0 to r1 at a speed v1, based on the two-body orbital dynamics model, the size of r1 can be calculated as:

[0051]

[0052] In the formula, h is the size of the transfer orbital angular momentum, which is given by h=||h||=r0v 1y OK; v 1x 、v 1y are the components of velocity v1 on the two coordinate axes respectively; θ is the true anomaly change, which is related to the azimuth vector and the true anomaly f have the following relationship: Since the initial orbital parameters are known and the velocity increment Δv is fixed, the terminal radius vector r1 is only related to the direction of the velocity pulse. Define α as the angle between the spacecraft velocity direction before and after the velocity pulse increment is applied, then:

[0053]

[0054] Where Δv is the applied velocity increment, and β is the azimuth vector and the true anomaly f are determined by the following relationship: From this, we can determine the one-to-one correspondence between the terminal radius vector r1 and α under the conditions of known azimuth and given orbital elements.

[0055] Defining Expressions Solve the expression for the zeros and record them as α1 and α2. Find the terminal radius vector r1 corresponding to α1 and α2, and record the larger of the two as r max , the smaller one is denoted as r min , which is the extreme value of the terminal radius vector.

[0056] (4) Traverse all spatial locations

[0057] Repeat the above three steps to traverse all γ, From step (3), we can get the inner and outer envelope points of all reachable directions. Under the same γ value, different The reachable domain envelope of the value together forms an elliptical plane shape, which is the section of the tubular reachable domain. The reachable domain can be obtained by connecting the sections under different γ values.

[0058] This method is used to calculate the reachable domains of the main target and all the slave targets respectively, completing the calculation work of step 2.

[0059] Step 3: Calculate from target reachability

[0060] The target reachability calculation includes the selection of sample points, coordinate transformation and threat domain calculation.

[0061] The selection of sample points refers to selecting a number of sample points within the reachable domain of the main target calculated in step 2 using the Monte Carlo method to form a complete set for judging the reachability of the slave target. Points are evenly selected at equal intervals in the circumferential and normal directions of the orbital plane of the main target. This way, the entire reachable domain is refined into individual sample points, and points are used instead of regions, solving the problem that three-dimensional regions are not easy to represent. Generally speaking, the more sample points are selected, the higher the accuracy. When selecting sample points, it is performed in the orbit pericenter coordinate system, considering the circumferential, normal and radial dimensions. The coordinates of the sample points can be obtained by Indicates that, γ, is the azimuth angle mentioned above, and r is the distance between the sample point and the origin of the coordinate system. The selection method is as follows:

[0062] (1) Take points of equal arc length on the elliptical orbit and draw rays from the origin to the directions of each point. This is the circumferential direction. In this embodiment, the arc length interval is 10 km.

[0063] (2) Perform normal extension. Since the orbital plane is the xy plane in the orbital pericentric coordinate system, the ray connecting the origin and the circumferential points has no normal component, that is, the azimuth By adding the normal azimuth Components, normal extension is performed to fill the entire upper half space with rays. To ensure the uniformity of sample points, the azimuth difference between every two lines has the following relationship:

[0064]

[0065] in, is the standard interval value, which is 0.01 rad in this embodiment. is the azimuth of the current ray, is the azimuth of the next ray. The calculation is repeated within the range to obtain a ray beam that fills the entire upper half space.

[0066] (3) Points are taken at appropriate intervals on each ray of the ray beam. The interval difference is expressed as follows:

[0067]

[0068] r'=r+Δr

[0069] Where r0 is the standard interval value, which is 10 km in this embodiment, r is the distance from the current point to the origin, and r' is the distance from the next point to the origin. The calculation is repeated within the range of (a is the semi-major axis of the main target orbit) to obtain a sample point set covering a sufficiently large range around the main target orbit.

[0070] (4) Screening of sample points. The sample points obtained by the above method can form a point set. The part of the point set in the reachable domain of the main target is retained to obtain the full set of sample points used for subsequent dangerous point judgment. In this embodiment, a total of 57,214 sample points are selected in the reachable domain of the main target.

[0071] The coordinate transformation refers to transforming the selected sample points from the orbital coordinate system of the master target to the orbital coordinate system of the slave target, so as to facilitate the calculation of the threat domain of the slave target. The coordinate transformation is to transform the geocentric inertial system to the pericentric coordinate system of the slave target.

[0072] The coordinate origin of the geocentric inertial system is the center of mass of the earth; the x-axis is located in the equatorial plane and points to the vernal equinox; the z-axis points to the North Pole along the earth's rotation axis; and the y-axis is determined by the right-hand rule. The sample points are selected in the geocentric inertial system. The coordinates of a point in this coordinate system are expressed as:

[0073] S i =[x i ,y i ,z i ] T

[0074] where x i ,y i 、z i are the coordinate components of the point on the x-axis, y-axis, and z-axis in the geocentric inertial system.

[0075] The origin of the pericentric coordinate system is the center of mass of the Earth; the x-axis points to the perigee of the orbit; the z-axis is along the angular momentum direction of the orbital plane and is perpendicular to the orbit; the y-axis is determined by the right-hand rule. The coordinates of a point in this coordinate system are expressed as:

[0076] S o =[x o ,y o ,z o ] T

[0077] where x o ,y o 、z o are the coordinate components of the point on the x-axis, y-axis, and z-axis in the pericenter coordinate system, respectively.

[0078] The coordinate transformation is performed by the coordinate transfer matrix L oi Realization, L oi It is related to the orbital inclination i, the perigee argument ω, and the right ascension Ω of the ascending node from the target. The transformation method is:

[0079] S o =Loi S i

[0080]

[0081] The threat domain refers to the area where the range where the main target may escape when threatened overlaps with the range that the secondary target can reach through orbital maneuvers. The size of the threat domain directly reflects the urgency of the space threat. Assuming that there are j threat targets in a certain scenario, the threat domain of each threat target is represented by θ j The composite threat domain can be expressed as:

[0082]

[0083] In this embodiment, the three slave targets all pose a threat to the master target. Each target has its own threat domain. The composite threat domain in this scenario can be obtained by taking the union of the threat domains of the three slave targets.

[0084] The threat domain is calculated by using the sample points after coordinate transformation. If the sample point is within the maneuverable reachable domain of the slave target, the point belongs to the threat domain of the slave target and is called a dangerous point. The set of dangerous points is the threat domain of the slave target. During the calculation process, all selected sample points are traversed to determine whether they are dangerous points one by one.

[0085] In this embodiment, after calculation, the first secondary target has 24574 dangerous points, the second secondary target has 12315 dangerous points, and the third secondary target has 5641 dangerous points. Taking the union of the dangerous points of the three secondary targets, there are 28709 dangerous points in total, and the space they fill is the composite threat domain.

[0086] Step 4: Calculate space urgency

[0087] The spatial urgency S is defined as the ratio of the composite threat domain Θ of each slave target to the mobile reachable domain Ψ of the main target, which reflects the composite threat degree of each slave target to the main target in the multi-target pursuit scenario, and can be expressed by calculating the regional volume:

[0088]

[0089] Among them, Θ is the composite threat domain formed by multiple slave targets, Ψ is the mobile reachable domain of the main target, and the volume integral of these two irregular areas is calculated, and the ratio is the spatial urgency S.

[0090] The spatial urgency can be quantified using the sample points selected by the Monte Carlo method in step 3, that is, the proportion of dangerous points in the entire set of sample points is used instead of the proportion of the secondary target's composite threat domain Θ in the primary target's maneuverable reachable domain Ψ to obtain the spatial urgency. It is easy to see that the spatial urgency is a rational number between 0 and 1.

[0091] In this embodiment, the spatial urgency of the first secondary target is 0.4295, the spatial urgency of the second secondary target is 0.2152, and the spatial urgency of the third secondary target is 0.0986. In the multi-target pursuit scenario under the combined effect of the three, the spatial urgency is 0.5018. At this time, under the combined threat of multiple targets, the main target has a certain operational risk, which should be avoided considering the actual situation.

[0092] Finally, it should be noted that the embodiments described above are only used as illustrations of the technical solutions of the present invention and do not limit the protection scope of the present invention. Those skilled in the art who apply the present invention should understand that they can make appropriate modifications to the technical solutions or make equivalent replacements for some technical details, but the technical solutions after these operations do not deviate from the scope of protection of this patent.

Claims

1. A method for calculating the space urgency of a spacecraft based on a maneuverable reachable domain, characterized in that: The following steps are involved: Step 1: Determine the number of master and slave target orbits The primary target is defined as the spacecraft that is threatened, i.e. the "escaping" party in the pursuit-escape scenario; the secondary target poses a threat to the primary target, i.e. the "chasing" party in the pursuit-escape scenario; in the multi-target pursuit-escape scenario, the primary target is unique, and the number of secondary targets is more than one; the orbital elements of both targets are determined by the space situational awareness system through related orbit determination operations; Step 2: Calculation of the mobile reachable area of ​​the master and slave targets The maneuverable domain is defined as the set of all positions that the spacecraft can reach under a given initial orbit and fuel constraints. The spacecraft uses pulse thrust during orbital maneuvers, which means that the maneuver is considered to occur instantaneously and is manifested as a velocity increment Δv in an arbitrary direction imposed on the spacecraft. The maneuverable domain of the master and slave targets is a maneuverable domain with free maneuvering time, that is, the maneuvering time of the target is not restricted, the target is allowed to maneuver at any time, and then the area reached by the target is calculated; This is accomplished by following these steps: 2.1 Determine a certain spatial position by azimuth; 2.2 Determine the accessibility of the location; 2.3 If the direction is reachable, then solve the reachable domain envelope at the direction; 2.4 Traverse all spatial orientations, obtain the envelope surface, and find the reachable domain; Step 3: Calculate from target reachability The target reachability calculation includes sample point selection, coordinate transformation and threat domain calculation; The selection of sample points refers to selecting a number of sample points with equal spacing within the reachable domain of the main target calculated in step 2 using the Monte Carlo method to form a full set for judging the reachability of the secondary target; within the range allowed by the computing speed, the more sample points are selected, the higher the accuracy will be; Coordinate transformation refers to transforming the selected sample points from the orbital coordinate system where the master target is located to the orbital coordinate system where the slave target is located, so as to facilitate the calculation of the threat domain of the slave target; The threat domain refers to the area where the range where the main target may escape when threatened overlaps with the range that the slave target can reach through orbital maneuvers; in the calculation process, if the sample point is within the maneuverable reachable domain of the slave target, then the point belongs to the threat domain of the slave target, which is called a danger point. The set of danger points is the threat domain of the slave target; if there are multiple slave targets in a certain scenario, the union of the threat domains of each slave target is calculated to form a composite threat domain in the multi-target pursuit scenario; Step 4: Calculate space urgency The spatial urgency is defined as the ratio of the composite threat domain of each subordinate target to the maneuverable domain of the main target, which reflects the threat level of each subordinate target to the main target in the multi-target pursuit scenario; the spatial urgency is quantified by the sample points selected by the Monte Carlo method in step three, that is, when the number of sample points is large enough, the ratio of dangerous points to all sample points is used to reflect the spatial urgency of the main target.

2. The method for calculating the space urgency of a spacecraft based on a maneuverable reachable domain according to claim 1, characterized in that: In step one, the orbital elements of both targets are determined by the space situational awareness system through relevant orbit determination operations; the orbital elements include the position and velocity information of the spacecraft at the initial moment, which are obtained in the form of common orbital information of two-line orbital elements TLE, including: orbital semi-major axis a, eccentricity e, orbital inclination i, perigee argument ω, ascending node right ascension Ω, true anomaly f.

3. The method for calculating the space urgency of a spacecraft based on a maneuverable reachable domain according to claim 1, characterized in that: In step 2.1, the spatial orientation is determined by two azimuth angles γ, is determined by the unit vector Indicates; in the orbital pericenter coordinate system, the origin of the coordinates is the center of mass of the earth; the x-axis points to the orbital perigee; the z-axis is along the angular momentum direction of the orbital plane and is perpendicular to the orbit; the y-axis is determined by the right-hand rule; when a certain spatial orientation is projected onto the target orbital plane, the angle between the projection line and the x-axis is γ, and the value range is [0,2π]; the angle between the orientation and the orbital plane is The value range is Due to symmetry, The value of only covers the upper half of the reachable domain, and the lower half of the reachable domain is obtained by symmetry.

4. The method for calculating the space urgency of a spacecraft based on a maneuverable reachable domain according to claim 3, characterized in that: In step 2.2, after determining the spatial position, it is necessary to determine whether the spacecraft can reach the position. The position is reachable when the following equation is satisfied: In the formula, γ, is the azimuth angle, Δv is the applied velocity increment, μ=3.986×10 14 m 3 / s 2 is the earth's gravitational constant, p = a(1-e 2 ) is the orbit semi-path, f is the true anomaly; if the position is reachable, proceed to step 2.3; if not reachable, skip step 2.3 and directly proceed to step 2.4 to traverse the next spatial position.

5. The method for calculating the space urgency of a spacecraft based on a maneuverable reachable domain according to claim 4, characterized in that: In step 2.3, when a certain position When it is reachable, the ray along this azimuth will pass through the reachable domain and form two intersection points with the boundary of the reachable domain, inner and outer. Therefore, the radius vector extreme value r of these two points in the coordinate system is calculated. min and r max , we can determine that the radius vector value r of all reachable points on this direction satisfies r min ≤r≤r max , and obtain the reachable domain envelope of the orientation.

6. The method for calculating space urgency of a spacecraft based on a maneuverable reachable domain according to claim 5, characterized in that: In step 2.4, repeat steps 2.1-2.3 to traverse all γ, value; from step 2.3, we can get the inner and outer envelope points on all reachable directions. Under the same γ value, different The envelope of the accessible domain of the values ​​together form an elliptical plane shape, that is, the section of the tubular accessible domain; the accessible domain is obtained by connecting the sections under different γ values.

7. The method for calculating space urgency of a spacecraft based on a maneuverable reachable domain according to claim 1, characterized in that: In step 3, when selecting sample points, the coordinates are selected in the orbit pericenter coordinate system, considering the circumferential, normal and radial dimensions. The coordinates of the sample points are given by Indicates that, γ, is the azimuth, and r is the distance between the sample point and the origin of the coordinate system; the selection is as follows: (1) Select points of equal arc length on the elliptical orbit to form a ray ring centered at the origin; (2) Perform normal extension to form a ray beam that fills the entire upper half space; (3) Pick a point on the beam; (4) Filter out the target point set that is within the reachable domain of the main target.

8. The method for calculating space urgency of a spacecraft based on a maneuverable reachable domain according to claim 1 or 7, characterized in that: In step 3, the coordinate transformation is to transform the geocentric inertial system into the pericentric coordinate system to which the target belongs; the coordinate origin of the geocentric inertial system is the center of mass of the earth; the x-axis is located in the equatorial plane and points to the vernal equinox; the z-axis points to the North Pole along the earth's rotation axis; the y-axis is determined by the right-hand rule; the sample point is selected in the geocentric inertial system, and the coordinates of a point in this coordinate system are expressed as: S i =[x i ,y i ,z i ] T where x i ,y i 、z i are the coordinate components of the point on the x-axis, y-axis, and z-axis in the geocentric inertial system respectively; The origin of the pericentric coordinate system is the center of mass of the Earth; the x-axis points to the perigee of the orbit; the z-axis is along the angular momentum direction of the orbital plane, perpendicular to the orbit; the y-axis is determined by the right-hand rule; the coordinates of a point in this coordinate system are expressed as: S o =[x o ,y o ,z o ] T where x o ,y o 、z o are the coordinate components of the point on the x-axis, y-axis, and z-axis in the pericenter coordinate system respectively; The coordinate transformation is done by using the coordinate transfer matrix L oi Realization, L oi It is related to the orbital inclination i, the perigee argument ω, and the right ascension Ω of the ascending node from the target. The transformation method is: S o =L oi S i 9. A method for calculating spacecraft space urgency based on a maneuverable reachable domain according to claim 1 or 8, characterized in that: In step 3, suppose there are j threat targets in a certain scenario, and the threat domain of each threat target is θ j The composite threat domain is represented as:

10. The method for calculating space urgency of a spacecraft based on a maneuverable reachable domain according to claim 1, characterized in that: The spatial urgency S is defined as the ratio of the composite threat domain Θ of each slave target to the mobile reachable domain Ψ of the master target, which is expressed by calculating the regional volume: Among them, Θ is the composite threat domain formed by multiple slave targets, Ψ is the mobile reachable domain of the main target, and the volume integral of these two irregular areas is calculated, and the ratio is the spatial urgency S; The spatial urgency is quantified by the sample points selected by the Monte Carlo method in step 3, that is, the ratio of dangerous points to the whole set of sample points is used instead of the ratio of the composite threat domain Θ of the secondary target to the maneuverable reachable domain Ψ of the primary target to obtain the spatial urgency. It is easy to see that the spatial urgency is a rational number between 0 and 1.

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