Method and system for evaluating spin separation trajectories and collision probabilities of stacked satellites

Abstract

The present invention provides a method and system for evaluating the spin separation trajectory and collision probability of stacked satellites, and relates to the technical field of separation trajectory and collision probability evaluation. The method includes: step S1: using the principle of relativity of motion to establish a reference system with the fixed coordinates of any satellite body; step S2: establishing the relative velocity vector of other satellites in the same layer to the reference system; step S3: projecting the relative velocity vector into the reference system and integrating it in the reference system to obtain the analytical solution of the motion trajectory of other satellites relative to the reference system; step S4: based on the trajectory, the rotational motion of the satellite itself can be ignored, and the relative motion between satellites is simplified to the translation according to the trajectory, so that the collision probability of the satellite can be estimated. The present invention can significantly reduce the complexity of the collision risk assessment in the satellite separation link, and thus provide a reference for the formulation of separation strategies for stacked satellite groups.

Description

Technical Field

[0001] The present invention relates to the technical field of separation trajectory and collision probability assessment, and in particular to a method and system for assessing the spin separation trajectory and collision probability of stacked satellites. Background Art

[0002] The evaluation method for the spin separation trajectory and collision probability of stacked satellites is directly related to the safety of stacked satellites after separation. Each stacked satellite does not have its own spring or explosive bolt, and cannot rely on the deployment mechanism to provide separation actuation, but is deployed very slowly as the upper stage spins. A single satellite is generally approximated as a two-dimensional flat plate structure, which generally uses spin separation. The disadvantage is that it may cause collisions between satellites, especially between satellites on the same layer, posing serious safety risks to onboard equipment.

[0003] According to the stress state after separation, after the satellite cluster is unlocked, ignoring the friction effect and orbital angular velocity between satellites, each satellite has both translation in the inertial system and uniform rotation. In addition, the complexity of the actual satellite's own shape and contour makes collision analysis difficult. The evaluation method for the spin separation trajectory and collision probability of stacked satellites is used to promote the exploration of a more universal 2-n satellite arrangement scheme with collision-free separation conditions, which will have a positive effect on the launch safety of large-scale stacked satellite clusters.

[0004] The invention patent with the publication number CN102541070A discloses a collision avoidance method for a satellite formation flight ground test system, including the following specific steps: step 1, select the operation mode; step 2, set the collision risk coefficient threshold value P0; step 3, normal operation mode; calculate the collision risk coefficient Pi in each control cycle; detect the collision risk coefficient Pi; step 4, determine Pi>P0; step 5, enter the collision avoidance mode: according to the artificial potential field method, obtain the control force Fi of the i-th simulated satellite, and use the control force Fi to control the i-th simulated satellite to achieve collision avoidance; detect the collision risk coefficient Pi; return to step 3. The invention mainly focuses on the problem of collision avoidance in the ground test of satellite simulated formation flight, specifically controlling the collision risk coefficient threshold value Pi, and applying control force to the satellite when the threshold value is exceeded. The present invention mainly focuses on the separation trajectory and prediction of the collision probability of stacked satellites when they spin separate in space, and simplifies the relative motion between satellites into translation according to the trajectory, so that the collision probability of the satellite can be estimated, and no control force is applied to control the satellite during this period.

[0005] The invention patent with publication number CN107991053B discloses a method and system for predicting the separation trajectory of an aircraft in a high-speed wind tunnel model test. By introducing a formula correction method, the inherent lack of vertical acceleration of the model of the object in the high-speed wind tunnel model test using the light model method can be compensated, thereby overcoming the problem that the model trajectory deviates from the actual trajectory due to the lack of vertical acceleration of the object model caused by the light model method, which causes the vertical displacement and horizontal displacement of the model to be disproportionate when falling, and then causes the vertical displacement to differ from the actual object, thereby achieving accurate prediction of the safety of multi-body separation and separation trajectory of high-speed aircraft. This invention mainly focuses on the compensation of vertical acceleration in the wind tunnel and performs calculation correction on it. The present invention mainly focuses on the prediction of separation trajectory in space.

[0006] The invention patent with publication number CN104966129A discloses a method for separating vehicle running trajectories, including the following steps: (1) obtaining satellite positioning data of the vehicle running within a set time period, the satellite positioning data including the acquisition time, vehicle position and passenger status corresponding to the satellite positioning data; (2) screening the acquired satellite positioning data according to the passenger status of each satellite positioning data, and forming a corresponding passenger running trajectory according to the screening result; (3) determining the positions of the time jump points and space jump points of the passenger running trajectory, and dividing the passenger running trajectory into a plurality of sub-running trajectories according to the positions of the time jump points and space jump points. This invention mainly simplifies the vehicle running data and improves the accuracy of its data application, which is the application aspect of the data. The present invention mainly focuses on separating the trajectory from the satellite in orbit, which is a prediction of the separation trajectory of the real object.

[0007] The invention patent with publication number CN113232892A discloses a foldable and expandable modular stacked satellite configuration for launching multiple satellites with one rocket, which includes satellite structure design, thermal control design, comprehensive equipment layout, center of mass optimization, etc., so as to ultimately realize the serial launch of multiple satellites with one rocket using modular stacked satellites. Summary of the invention

[0008] In view of the defects in the prior art, the present invention provides a method and system for evaluating the spin separation trajectory and collision probability of stacked satellites.

[0009] According to a method and system for evaluating the spin separation trajectory and collision probability of stacked satellites provided by the present invention, the scheme is as follows:

[0010] In a first aspect, a method for evaluating the spin separation trajectory and collision probability of stacked satellites is provided, the method comprising:

[0011] Step S1: Using the principle of relativity of motion, a reference system is established with the fixed coordinates of any satellite body;

[0012] Step S2: Establishing the relative velocity vectors of other satellites in the same layer to the reference system;

[0013] Step S3: Projecting the relative velocity vector into the reference system and integrating it in the reference system, thereby obtaining an analytical solution of the motion trajectory of other satellites relative to the reference system;

[0014] Step S4: Based on the trajectory, the rotational motion of the satellite itself can be ignored, and the relative motion between the satellites is simplified to the translational motion according to the trajectory, so that the collision probability of the satellites can be estimated.

[0015] Preferably, step S1 is applicable to the spin separation of stacked satellites, and during separation, the separation action cannot be provided by the deployment mechanism, but is deployed with the spin of the upper stage.

[0016] Preferably, during the separation, the center of mass of each satellite performs inertial motion along the speed at the unlocking moment, while the satellite body rotates at a uniform speed maintaining the angular velocity at the unlocking moment.

[0017] Preferably, the number of satellites stacked on the same layer during separation is 2, 3, 4, 5, 6 or even more.

[0018] Preferably, the step S1 defines the system's entire center of mass to perform inertial motion, and defines the inertial reference system at the system's center of mass as OXYZ;

[0019] After unlocking, all satellites will start to do centrifugal motion while maintaining spin. Take any satellite to start, and they will be numbered 1-n in the counterclockwise order around the Z axis;

[0020] The fixed reference system O1X1Y1Z1 is established with the first satellite, and the origin of the coordinates is located at the satellite mass center. At the zero moment of unlocking, the OXYZ coordinate axes are parallel to O1X1Y1Z1 respectively;

[0021] In the launch state, the satellites in the same layer are arranged in a circular array around the central axis, and the distance between each center of mass and the central axis of the satellite cluster is r0. The distance between two adjacent satellites is α. If n satellites are arranged in the same layer, there must be

[0022]

[0023] Preferably, in step S2, after unlocking, the center of mass of each satellite maintains the tangential velocity ωr0 at the unlocking moment relative to the OXYZ coordinate system to perform inertial motion, and the satellite body performs a uniform rotation at an angular velocity ω relative to the OXYZ coordinate system;

[0024] After time t, the mass center of all satellites moves a distance of ωr0t and rotates at an angle of ωt, where r0 represents the distance from the mass center of each satellite to the central axis of the satellite cluster, and ω represents the stable angular velocity obtained by the satellite cluster by relying on the carrier rotation;

[0025] The velocity vector of the first satellite's center of mass relative to the OXYZ coordinate system at time t after unlocking is: The velocity vector of the second satellite's center of mass relative to the OXYZ coordinate system is: The projection to the OXYZ coordinate system is:

[0026]

[0027] Where α represents the interval angle between two adjacent satellites; a represents the velocity identifier of the satellite's center of mass relative to the OXYZ coordinate system; () T represents transpose;

[0028] The velocity of the second satellite's center of mass in the O′X′Y′Z′ coordinate system is:

[0029]

[0030] in, represents the relative velocity of the second satellite's mass center relative to the first satellite in the O′X′Y′Z′ coordinate system;

[0031] e represents the associated velocity identifier of the second satellite relative to the first satellite in the O′X′Y′Z′ coordinate system;

[0032] represents the radius vector from the mass center of the first satellite to the mass center of the second satellite at time t, The angular velocity vectors representing the O′X′Y′Z′ coordinate system relative to the OXYZ coordinate system are projected onto the OXYZ coordinate system:

[0033]

[0034] Preferably, the step S3 is Projection to the OXYZ coordinate system is:

[0035]

[0036] The velocity of the second satellite's center of mass relative to the O′X′Y′Z′ coordinate system is:

[0037]

[0038] Wherein, r represents the velocity identifier of the second satellite in the O′X′Y′Z′ coordinate system;

[0039] Projection to the OXYZ coordinate system is:

[0040]

[0041] The projection to the O′X′Y′Z′ coordinate system is:

[0042]

[0043] Will The time integral relative to the O′X′Y′Z′ coordinate system is calculated to obtain the trajectory of the second satellite's center of mass relative to the O′X′Y′Z′ coordinate system;

[0044] The coordinates of the second satellite's center of mass at time zero are:

[0045]

[0046] The trajectory of the second satellite's center of mass relative to the O′X′Y′Z′ coordinate system or the first satellite can be obtained, that is,

[0047]

[0048] Will Normalize r0 to get

[0049]

[0050] Preferably, the step S4 can obtain the mass center relative motion trajectory as an involute through the step S3;

[0051] The angular velocity of the second satellite and the first satellite relative to the OXYZ coordinate system is ω. With the first satellite as a reference, the second satellite only moves in translation, and the center of mass of the second satellite is Given trajectory motion;

[0052] According to the trajectory line, it can be determined whether any two points on the first satellite and the second satellite will collide during the separation process.

[0053] Preferably, the angle α is universal, and the result of whether all other satellites will collide with the first satellite can be obtained; and the first satellite is selected arbitrarily, and the conclusion of the collision risk can be extended to all satellites.

[0054] Preferably, in actual engineering applications, a safety gap is set based on relevant uncontrollable factors including friction and hooking. When the distance between the second satellite and the first satellite is always greater than the safety gap during translation along the relative trajectory, the risk of separation and collision is acceptable.

[0055] In another aspect, a system for evaluating the spin separation trajectory and collision probability of stacked satellites is provided, the system comprising:

[0056] Module M1: Using the principle of relativity of motion, a reference system is established with the fixed coordinates of any satellite body;

[0057] Module M2: Establishing the relative velocity vectors of other satellites in the same layer to the reference system;

[0058] Module M3: Projecting the relative velocity vector into the reference system and integrating it in the reference system, and obtaining the motion trajectory analytical solution of other satellites relative to the reference system;

[0059] Module M4: Based on the trajectory, the rotational motion of the satellite itself can be ignored, and the relative motion between satellites is simplified to the translational motion according to the trajectory, so that the collision probability of the satellites can be estimated.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] 1. The present invention considers the relative motion trajectory of each satellite under the condition of multiple satellites in the same layer, and converts the complex motion originally including translation and rotation into relative motion without rotation, thereby simplifying the collision risk assessment work, and further provides a reference for the formulation of separation strategy for stacked satellite groups;

[0062] 2. The present invention improves the efficiency of collision analysis by calculating the motion trajectory of other satellites relative to the first satellite reference system. Subsequently, the appropriate distance r0 from the satellite to the center line, the separation angular velocity ω and the safety distance can be selected according to the number of satellites required for each layer to avoid collision between satellites during separation. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0064] Figure 1 is a flow chart of the present invention;

[0065] Figure 2 Schematic diagram of the satellite system at the time of unlocking;

[0066] Figure 3 This is the state diagram at time t after unlocking;

[0067] Figure 4 This is a schematic diagram of collision determination of 4 stars on the same layer;

[0068] Figure 5 This is a schematic diagram of the trajectory of two stars in the same layer;

[0069] Figure 6 This is a schematic diagram of the trajectories of five stars on the same layer;

[0070] Figure 7 This is a schematic diagram of the trajectories of six stars in the same layer. DETAILED DESCRIPTION

[0071] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0072] The embodiment of the present invention provides a method for evaluating the spin separation trajectory and collision probability of stacked satellites, referring to Figure 1 and Figure 2 As shown, the invention specifically includes:

[0073] Step S1: It is known that each satellite in the inertial system is a superposition of uniform linear motion of the center of mass and uniform rotation around the center of mass. Using the principle of relativity of motion, a reference system is established with the fixed coordinates of any satellite body.

[0074] Step S1 is to define the inertial motion of the system's entire center of mass, and define the inertial reference system at the center of mass of the system as OXYZ. After unlocking, all satellites will start to perform centrifugal motion while maintaining spin, starting with any satellite, numbered 1-n in counterclockwise order around the Z axis; the first satellite is used to establish a fixed reference system O1X1Y1Z1, with the origin of the coordinates located at the satellite's center of mass. At the zero moment of unlocking, the OXYZ coordinate axes are parallel to O1X1Y1Z1.

[0075] Step S2: Establish the relative velocity vectors of other satellites in the same layer to the reference system (expressed by the components projected in the inertial system).

[0076] Reference Figure 2 and Figure 3 As shown, after unlocking in this step, the center of mass of each satellite maintains the tangential velocity ωr0 at the unlocking moment relative to the OXYZ coordinate system to perform inertial motion, and the satellite body rotates at a uniform speed of ω relative to the OXYZ coordinate system;

[0077] After time t, the mass center of all satellites moves a distance of ωr0t and rotates at an angle of ωt, where r0 represents the distance from the mass center of each satellite to the central axis of the satellite cluster, and ω represents the stable angular velocity obtained by the satellite cluster by relying on the carrier rotation;

[0078] The velocity vector of the first satellite's center of mass relative to the OXYZ coordinate system at time t after unlocking is: The velocity vector of the second satellite's center of mass relative to the OXYZ coordinate system is: The projection to the OXYZ coordinate system is:

[0079]

[0080] Where α represents the interval angle between two adjacent satellites; a represents the velocity identifier of the satellite's center of mass relative to the OXYZ coordinate system; ()T represents transpose;

[0081] The velocity of the second satellite's center of mass in the O′X′Y′Z′ coordinate system is:

[0082]

[0083] in, represents the relative velocity of the second satellite's mass center relative to the first satellite in the O′X′Y′Z′ coordinate system;

[0084] e represents the associated velocity identifier of the second satellite relative to the first satellite in the O′X′Y′Z′ coordinate system;

[0085] represents the radius vector from the mass center of the first satellite to the mass center of the second satellite at time t, The angular velocity vectors representing the O′X′Y′Z′ coordinate system relative to the OXYZ coordinate system are projected onto the OXYZ coordinate system:

[0086]

[0087] Step S3: Project the relative velocity vector into the reference system and integrate it in the reference system to obtain the analytical solution (involute) of the motion trajectory of other satellites relative to the reference system.

[0088] This step S3 is Projection to OXYZ coordinate system:

[0089]

[0090] The velocity of the second satellite's center of mass relative to the O′X′Y′Z′ coordinate system is:

[0091]

[0092] Wherein, r represents the velocity identifier of the second satellite in the O′X′Y′Z′ coordinate system;

[0093] Projection to the OXYZ coordinate system is:

[0094]

[0095] The projection to the O′X′Y′Z′ coordinate system is:

[0096]

[0097] Will The time integral relative to the O′X′Y′Z′ coordinate system is calculated to obtain the trajectory of the second satellite's center of mass relative to the O′X′Y′Z′ coordinate system;

[0098] The coordinates of the second satellite's center of mass at time zero are:

[0099]

[0100] The trajectory of the second satellite's center of mass relative to the O′X′Y′Z′ coordinate system or the first satellite can be obtained, that is,

[0101]

[0102] Will Normalize r0 to get

[0103]

[0104] Step S4: Based on the trajectory, the rotational motion of the satellite itself can be ignored, and the relative motion between the satellites is simplified to the translational motion according to the trajectory, so that the collision probability of the satellites can be estimated.

[0105] This step can be obtained by step S3 that the relative motion trajectory of the center of mass is an involute; the angular velocity of the second satellite and the first satellite relative to the OXYZ coordinate system is ω, and the first satellite is used as a reference, and the second satellite only moves in translation, and the center of mass of the second satellite is according to Given a trajectory motion; based on the trajectory line, it can be determined whether any two points on the first satellite and the second satellite will collide during the separation process.

[0106] Among them, the angle α is universal, and the result of whether all other satellites will collide with the first satellite can be obtained; and the first satellite is selected arbitrarily, and the conclusion of collision risk can be extended to all satellites.

[0107] In actual engineering applications, a safety gap can be set based on relevant uncontrollable factors such as friction and hooking. When the distance between the second satellite and the first satellite is always greater than the safety gap during the translation process along the relative trajectory, the separation and collision risk is acceptable.

[0108] Specifically, in step S1, the stacked satellites are separated by spin. During separation, the deployment mechanism cannot be relied upon to provide separation actuation, but the satellites are deployed very slowly as the upper stage spins. During separation, the center of mass of each satellite moves inertially along the speed at the time of unlocking, while the satellite body rotates at a constant angular speed at the time of unlocking. During separation, the number of satellites stacked on the same layer is 2, 3, 4, 5, 6 or even more. Figure 4 and Figure 5 , respectively, are the collision judgment of 4 stars in the same layer and the trajectory of 2 stars in the same layer; refer to Figure 6 and Figure 7 , which are the trajectories of 5 stars and 6 stars in the same layer respectively.

[0109] The embodiment of the present invention provides a method and system for evaluating the spin separation trajectory and collision probability of stacked satellites, and proposes a simplified motion analysis method to meet the engineering needs of mass satellite collision risk assessment. The relative motion trajectory of each satellite under the layout of multiple satellites in the same layer is considered, and the complex motion originally including translation and rotation is converted into relative motion without rotation, thereby simplifying the collision risk assessment work.

[0110] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0111] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for evaluating the spin separation trajectory and collision probability of stacked satellites, characterized in that: include: Step S1: Using the principle of relativity of motion, a reference system is established with the fixed coordinates of any satellite body; Step S2: Establishing the relative velocity vectors of other satellites in the same layer to the reference system; Step S3: Projecting the relative velocity vector into the reference system and integrating it in the reference system, thereby obtaining an analytical solution of the motion trajectory of other satellites relative to the reference system; Step S4: Based on the trajectory, the rotational motion of the satellite itself can be ignored, and the relative motion between the satellites is simplified to the translational motion according to the trajectory, so that the collision probability of the satellites can be estimated; The step S1 defines the system's entire mass center to perform inertial motion, and defines the inertial reference system at the system's mass center as OXYZ; After unlocking, all satellites will start to do centrifugal motion while maintaining spin. Take any satellite to start, and they will be numbered 1-n in the counterclockwise order around the Z axis; The fixed reference system O1X1Y1Z1 is established with the first satellite, and the origin of the coordinates is located at the satellite mass center. At the zero moment of unlocking, the OXYZ coordinate axes are parallel to O1X1Y1Z1 respectively; In the launch state, the satellites in the same layer are in a circular array around the central axis, and the distance from each center of mass to the central axis of the satellite cluster is r0; two adjacent satellites are separated by an angle α; if n satellites are arranged in the same layer, then: The step S2 is that after unlocking, the center of mass of each satellite maintains the tangential velocity ωr0 at the unlocking moment relative to the OXYZ coordinate system to perform inertial motion, and the satellite body performs a uniform rotation at an angular velocity ω relative to the OXYZ coordinate system; After time t, the mass center of all satellites moves a distance of ωr0t and rotates at an angle of ωt, where r0 represents the distance from the mass center of each satellite to the central axis of the satellite cluster, and ω represents the stable angular velocity obtained by the satellite cluster by relying on the carrier rotation; The velocity vector of the first satellite's center of mass relative to the OXYZ coordinate system at time t after unlocking is: The velocity vector of the second satellite's center of mass relative to the OXYZ coordinate system is: The projection to the OXYZ coordinate system is: Where α represents the interval angle between two adjacent satellites; a represents the velocity identifier of the satellite's center of mass relative to the OXYZ coordinate system; () T represents transpose; The velocity of the second satellite's center of mass in the O′X′Y′Z′ coordinate system is: in, represents the relative velocity of the second satellite's mass center relative to the first satellite in the O′X′Y′Z′ coordinate system; e represents the associated velocity identifier of the second satellite relative to the first satellite in the O′X′Y′Z′ coordinate system; represents the radius vector from the mass center of the first satellite to the mass center of the second satellite at time t, The angular velocity vectors representing the O′X′Y′Z′ coordinate system relative to the OXYZ coordinate system are projected onto the OXYZ coordinate system:

2. The method for evaluating the spin separation trajectory and collision probability of stacked satellites according to claim 1, characterized in that: The step S1 is applicable to the spin separation of stacked satellites. During separation, the deployment mechanism cannot be relied upon to provide separation actuation, but the satellites are deployed with the spin of the upper stage.

3. The method for evaluating the spin separation trajectory and collision probability of stacked satellites according to claim 2, characterized in that: During the separation, the center of mass of each satellite performs inertial motion along the speed at the unlocking moment, while the satellite body rotates at a uniform speed while maintaining the angular speed at the unlocking moment.

4. The method for evaluating the spin separation trajectory and collision probability of stacked satellites according to claim 2, characterized in that: During the separation, the number of satellites stacked on the same layer is 2, 3, 4, 5, 6 or even more.

5. The method for evaluating the spin separation trajectory and collision probability of stacked satellites according to claim 1, characterized in that: The step S3 is Projection to the OXYZ coordinate system is: The velocity of the second satellite's center of mass relative to the O′X′Y′Z′ coordinate system is: Wherein, r represents the velocity identifier of the second satellite in the O′X′Y′Z′ coordinate system; Projection to the OXYZ coordinate system is: The projection to the O′X′Y′Z′ coordinate system is: Will The time integral relative to the O′X′Y′Z′ coordinate system is calculated to obtain the trajectory of the second satellite's center of mass relative to the O′X′Y′Z′ coordinate system; The coordinates of the second satellite's center of mass at time zero are: The trajectory of the second satellite's center of mass relative to the O′X′Y′Z′ coordinate system or the first satellite can be obtained, that is, Will Normalize r0 to get 6. The method for evaluating the spin separation trajectory and collision probability of stacked satellites according to claim 5, characterized in that: The step S4 can obtain the mass center relative motion trajectory as an involute through the step S3; The angular velocity of the second satellite and the first satellite relative to the OXYZ coordinate system is ω. With the first satellite as a reference, the second satellite only moves in translation, and the center of mass of the second satellite is Given trajectory motion; According to the trajectory line, it can be determined whether any two points on the first satellite and the second satellite will collide during the separation process; The angle α is universal, and the result of whether all other satellites will collide with the first satellite can be obtained; and the first satellite is selected arbitrarily, and the conclusion of the collision risk can be extended to all satellites.

7. The method for evaluating the spin separation trajectory and collision probability of stacked satellites according to claim 6, characterized in that: In actual engineering applications, a safety gap is set based on relevant uncontrollable factors such as friction and hooking. When the distance between the second satellite and the first satellite is always greater than the safety gap during the translation along the relative trajectory, the risk of separation and collision is acceptable.

8. A system for evaluating the spin separation trajectory and collision probability of stacked satellites, characterized in that: include: Module M1: Using the principle of relativity of motion, a reference system is established with the fixed coordinates of any satellite body; Module M2: Establishing the relative velocity vectors of other satellites in the same layer to the reference system; Module M3: Projecting the relative velocity vector into the reference system and integrating it in the reference system, and obtaining the motion trajectory analytical solution of other satellites relative to the reference system; Module M4: Based on the trajectory, the rotational motion of the satellite itself can be ignored, and the relative motion between the satellites is simplified to the translational motion according to the trajectory, so that the collision probability of the satellites can be estimated; The module M1 defines the inertial motion of the system's entire mass center, and defines the inertial reference system at the system's mass center as OXYZ; After unlocking, all satellites will start to do centrifugal motion while maintaining spin. Take any satellite to start, and they will be numbered 1-n in the counterclockwise order around the Z axis; The fixed reference system O1X1Y1Z1 is established with the first satellite, and the origin of the coordinates is located at the satellite mass center. At the zero moment of unlocking, the OXYZ coordinate axes are parallel to O1X1Y1Z1 respectively; In the launch state, the satellites in the same layer are in a circular array around the central axis, and the distance from each center of mass to the central axis of the satellite cluster is r0; two adjacent satellites are separated by an angle α; if n satellites are arranged in the same layer, then: After unlocking, the module M2 makes the center of mass of each satellite maintain the tangential velocity ωr0 at the unlocking moment relative to the OXYZ coordinate system to perform inertial motion, while the satellite body rotates at a uniform speed of ω relative to the OXYZ coordinate system; After time t, the mass center of all satellites moves a distance of ωr0t and rotates at an angle of ωt, where r0 represents the distance from the mass center of each satellite to the central axis of the satellite cluster, and ω represents the stable angular velocity obtained by the satellite cluster by relying on the carrier rotation; The velocity vector of the first satellite's center of mass relative to the OXYZ coordinate system at time t after unlocking is: The velocity vector of the second satellite's center of mass relative to the OXYZ coordinate system is: The projection to the OXYZ coordinate system is: Where α represents the interval angle between two adjacent satellites; a represents the velocity identifier of the satellite's center of mass relative to the OXYZ coordinate system; () T represents transpose; The velocity of the second satellite's center of mass in the O′X′Y′Z′ coordinate system is: in, represents the relative velocity of the second satellite's mass center relative to the first satellite in the O′X′Y′Z′ coordinate system; e represents the associated velocity identifier of the second satellite relative to the first satellite in the O′X′Y′Z′ coordinate system; represents the radius vector from the mass center of the first satellite to the mass center of the second satellite at time t, The angular velocity vectors representing the O′X′Y′Z′ coordinate system relative to the OXYZ coordinate system are projected onto the OXYZ coordinate system:

Images