A method and system for designing a multi-satellite per rocket layout based on separation safety

Abstract

The application relates to a one-rocket multi-satellite layout method and system based on separation safety design, which comprises the following steps: obtaining an in-orbit attitude deviation at a satellite-rocket separation time, setting an initial separation state; setting mass center coordinates of M groups of satellites relative to a rocket body and separation energy of each satellite in the initial separation state, and completing population initialization; establishing a fitness function by taking the minimum far-field distance of two satellites within half a period to five periods after separation and the total attitude angular velocity of each satellite after separation as optimization indexes; calculating a fitness function value of each particle; updating individual extreme values and global extreme values; updating particle speed and particle position; and outputting one-rocket multi-satellite layout optimization results when a preset ending condition is met. The application solves the layout problem caused by coupling of structure layout and far-field separation with the increase of the number of separation bodies in one-rocket multi-satellite tasks, and provides guidance for structure layout by considering far-field safety in the initial structure layout, so that the structure overall design efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the field of overall launch vehicle technology and relates to a method and system for launching multiple satellites with a single rocket based on separation safety design. Background Technology

[0002] The development and operation costs of large and medium-sized launch vehicles, both domestically and internationally, are extremely high. "Multiple satellites launched in a single launch" has become a crucial way to spread launch costs, improve constellation construction and networking efficiency, and enhance the adaptability of rocket missions. In January 2021, SpaceX achieved the feat of launching 143 satellites in one go using a Falcon 9 rocket, sending 10 Starlink satellites and 133 smaller satellites into orbit, significantly breaking the world record for the number of satellites launched in a single launch. The Starlink satellites are a standardized stacked satellite design by SpaceX, leveraging the advantage of a unified design for both satellites and payload support structures. Furthermore, SpaceX has also routinely launched 60 Starlink satellites in a single launch using the Falcon 9.

[0003] Currently, my country's record for launching multiple satellites in a single launch is held by the Long March 8 Y2 carrier rocket, which launched 22 satellites. This launch employed a conical payload support, a central support cylinder, and a top disc satellite adapter design. The number of satellites launched in a single launch is still significantly lower than the records set by mainstream international rockets. Given the future demands for satellite networks and communication satellites, there is an urgent need to optimize the deployment and distributor for multiple satellite launches.

[0004] To address the significant coupling effects in multi-satellite launch missions, such as spatial layout, separation attitude and timing, and far-field safety, it is crucial to explore optimization methods for multi-satellite launch layout and distributors based on near- and far-field safety requirements. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a multi-satellite launcher layout method and system based on separation safety design. The technical problem solved is that as the number of separation components increases, the difficulty of multi-satellite launcher missions caused by structural layout and far-field separation coupling increases exponentially. By considering far-field safety prediction at the initial stage of structural layout, guidance is provided for structural layout, thereby improving the overall design efficiency of the structure.

[0006] The solution of this invention is as follows: Firstly, a method for deploying multiple satellites in a single launcher based on a separation security design is proposed, comprising the following steps:

[0007] S1. Obtain the orbital attitude deviation at the moment of separation of the satellite and rocket, and set the initial separation state;

[0008] S2. Set the M groups of "the centroid coordinates of each satellite relative to the rocket body and the separation energy of each satellite" in the initial separation state as the initial particle positions, initialize the particle velocities, initialize the individual extreme value pbest(i) of each particle and the global extreme value gbest of the entire particle swarm, i = 1, 2, ..., M, where M is the number of particles;

[0009] S3. Based on the near-field and far-field safety analysis of satellite separation, a fitness function is established with the minimum far-field distance between the two satellites within half to five cycles after separation and the sum of the attitude angular velocities of each satellite after separation as optimization indicators.

[0010] S4. Calculate the fitness function value of each particle based on its current position;

[0011] S5. For each particle, if the fitness function value calculated in S4 is less than the corresponding individual extreme value pbest(i), replace pbest(i) with the calculated fitness function value.

[0012] S6. For each particle, if the fitness function value calculated in S4 is less than the global extremum gbest, replace the global extremum gbest with the fitness function value of that particle.

[0013] S7. Update particle velocity and particle position, and perform boundary processing of particle position according to the spatial envelope and the selectable range of separation energy.

[0014] S8. Repeat S4 to S7 until the preset termination condition is met, and output the optimized layout result of one arrow for multiple satellites.

[0015] Furthermore, the orbital attitude deviation specifically includes:

[0016] The deviations in the position of the entry point, the velocity of the entry point, the pitch, yaw, and roll angles of the entry point.

[0017] Furthermore, when setting the initial separation state, it also includes setting the selectable range of rocket final stage mass characteristics, payload mass characteristics, and separation energy.

[0018] Furthermore, the particle position is represented by vector X. i i = 1, 2, ..., M;

[0019] X i ={x(1),…,x(N),y(1),…,y(N),power1(1),…,power1(j),…,

[0020] powerN(1),…,powerN(k)};

[0021] Where x(1), ..., x(N) are the X-axis coordinates of the 1st to Nth satellites in the rocket body coordinate system, y(1), ..., y(N) are the Y-axis coordinates of the 1st to Nth satellites in the rocket body coordinate system, power1(1), ..., power1(j) are the 1st to jth group of separation energy for the 1st satellite, and so on, powerN(1), ..., powerN(k) are the 1st to kth group of separation energy for the Nth satellite; where N is the total number of satellites on the rocket.

[0022] Furthermore, the fitness function is specifically as follows:

[0023]

[0024] Where d is the minimum far-field distance between the two satellites within half to five periods after separation, and ω nx ω ny ω nz η represents the attitude angular velocities of the nth satellite in the x, y, and z directions in the body coordinate system after separation, where n = 1, 2, ..., N; and η is the fitness function value.

[0025] Furthermore, step S4 specifically includes: based on the particle position X i Using the physical quantities in the model as initial conditions, two satellites are randomly selected from N satellites and substituted into the near-field and far-field separation dynamics models for calculation. From the results, the minimum far-field distance d between the two satellites within half to five cycles after separation was selected, and the attitude angular velocities ω of each satellite in the x, y, and z directions in the body coordinate system after separation were calculated. nx ,

[0026] Furthermore, the boundary processing of particle positions described in S7 specifically includes:

[0027] The constraints of x(1)~x(N) and y(1)~y(N) are the installation position envelope on the load support, and the constraints of power1(1)~powerN(k) are the adjustable capability of the separated energy. If the particle position exceeds the constraint conditions, the particle position takes a random value within the constraint conditions.

[0028] Furthermore, the method for launching multiple satellites in one rocket also includes: selecting appropriate fairings and satellite adapters based on satellite envelope size, separation requirements, and available operational space.

[0029] Furthermore, the preset termination condition includes one of the following: the fitness function value is less than a set value, or the preset maximum number of iterations is reached.

[0030] Secondly, a multi-satellite deployment system based on separation safety design is proposed, including a payload adapter selection module, a satellite-rocket separation deviation acquisition module, and an intelligent deployment module.

[0031] The payload adapter selection module is used to select the appropriate fairing and satellite adapter based on the satellite envelope size, separation requirements, and available operational space.

[0032] The satellite-rocket separation deviation acquisition module is used to acquire the orbital attitude deviation at the moment of satellite-rocket separation and to set the initial separation state.

[0033] The intelligent layout module executes an algorithm that includes the following steps:

[0034] T1. Set the M groups of "the centroid coordinates of each satellite relative to the rocket body and the separation energy of each satellite" in the initial separation state as the initial particle positions, initialize the initial particle velocities, initialize the individual extreme value pbest(i) of each particle and the global extreme value gbest of the entire particle swarm, i = 1, 2, ..., M, where M is the number of particles;

[0035] T2. Based on the near-field and far-field safety analysis of satellite separation, a fitness function is established with the minimum far-field distance between the two satellites within half to five cycles after separation and the sum of the attitude angular velocities of each satellite after separation as optimization indicators.

[0036] T3. Calculate the fitness function value of each particle based on its current position;

[0037] T4. For each particle, if the calculated fitness function value is less than the corresponding individual extreme value pbest(i), replace pbest(i) with the calculated fitness function value.

[0038] T5. For each particle, if the calculated fitness function value is less than the global optimum gbest, replace the global optimum gbest with the fitness function value of that particle.

[0039] T6. Update particle velocity and particle position, and perform boundary processing of particle position according to the spatial envelope and the selectable range of separation energy.

[0040] T7. Repeat T3 to T6 until the preset termination condition is met, and output the optimized layout result of one rocket launching multiple satellites.

[0041] The beneficial effects of this invention compared to the prior art are:

[0042] (1) This invention uses a structural layout analysis method based on near-field and far-field safety to optimize the structural layout with near-field and far-field safety indicators. Compared with existing structural layout methods, it solves the structural layout and near-field and far-field separation safety problems of multi-satellite missions.

[0043] (2) This invention provides guidance on the structural layout by considering far-field safety prediction at the initial stage of the structural layout, and uses particle swarm optimization algorithm to simultaneously optimize the centroid coordinates of each satellite relative to the rocket body and the separation energy of each satellite, thus ensuring the design efficiency of the structural layout for a multi-satellite launch mission. Attached Figure Description

[0044] Figure 1 This is a flowchart of a multi-satellite deployment method based on separation security design according to the present invention;

[0045] Figure 2 This is the satellite adapter selection interface according to an embodiment of the present invention;

[0046] Figure 3 This is a simulation diagram illustrating the impact of orbital velocity deviation on far-field safety in an embodiment of the present invention.

[0047] Figure 4 This is a simulation diagram illustrating the impact of the rocket body attitude angular velocity deviation at the separation moment on far-field safety according to an embodiment of the present invention.

[0048] Figure 5 This is a simulation diagram illustrating the impact of load installation orientation deviation on far-field safety in an embodiment of the present invention.

[0049] Figure 6(a) is a schematic diagram of the first multi-star layout optimization result in the embodiment of the present invention;

[0050] Figure 6(b) is a schematic diagram of the fourth multi-star layout optimization result in the embodiment of the present invention;

[0051] Figure 6(c) is a schematic diagram of the seventh multi-star layout optimization result in the embodiment of the present invention;

[0052] Figure 6(d) is a schematic diagram of the 14th multi-star layout optimization result in the embodiment of the present invention; Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0054] Example 1

[0055] In this embodiment, a 14-star configuration is adopted with a central support cylinder for a certain mission. The configuration aims to ensure that the mass centers of multiple stars are located in the center of the central support cylinder and to ensure the safety of far-field separation.

[0056] First, select the appropriate fairing and satellite adapter based on factors such as satellite envelope size, separation requirements, and available operational space. See the selection interface below. Figure 2 In this embodiment, the structural components to be selected include the satellite adapter and the rocket fairing. For the separation speed requirements, the key parameters to be selected include the type and quantity of the separation energy source.

[0057] After selecting the fairing and satellite adapters, execute the following multi-satellite deployment procedure, such as... Figure 1 As shown, it includes the following steps:

[0058] S1. Obtain the orbital attitude deviation at the moment of separation of the satellite and rocket, and set the initial separation state.

[0059] Specifically, the orbital attitude deviation includes the orbital insertion point position deviation, orbital insertion point velocity deviation, orbital insertion point pitch, yaw and roll angle deviations. When setting the initial separation state, it also includes setting the selectable range of rocket final stage mass characteristics, payload mass characteristics and separation energy.

[0060] In this embodiment, the position and velocity of the orbital insertion point are in the inertial frame:

[0061] The positions are [3214659.2; -399985.8; 1758182.9];

[0062] The speeds are [5472.6485; -3954.7604; 3351.6751];

[0063] Pitch, yaw, and roll program angles [-87.0081, -11.2957, 0];

[0064] The separation force adjustment range for the energy separation is 790N±50N, and the working stroke is 40mm.

[0065] The initial separation state is set as follows: the position deviation of the insertion point is taken as the nominal value, the velocity deviation of the insertion point is also taken as the nominal value, and the pitch, yaw and roll angles are all taken as the upper deviation; the mass characteristics of the rocket's final stage and the mass characteristics of the payload are all taken as the nominal values, and the selectable range of the separation energy is 790N±50N.

[0066] S2. Set the M groups of "the centroid coordinates of each satellite relative to the rocket body and the separation energy of each satellite" in the initial separation state as the initial particle positions, initialize the particle velocities, initialize the individual extreme value pbest(i) of each particle and the global extreme value gbest of the entire particle swarm, i = 1, 2, ..., M, where M is the number of particles.

[0067] In this embodiment, the number of particles is set to M = 30, and the position of each particle is represented by a column vector X. i If i = 1, 2, ..., 30, then:

[0068] X i ={x(1),…,x(14),y(1),…,y(14),power1(1),…,power1(j),…,

[0069] power14(1),...,power14(k)};

[0070] Where x(1), ..., x(14) are the X-axis coordinates of the 1st to 14th satellites in the rocket body coordinate system, y(1), ..., y(14) are the Y-axis coordinates of the 1st to 14th satellites in the rocket body coordinate system, power1(1), ..., power1(j) are the 1st to jth groups of separation energy for the 1st satellite, and so on, power14(1), ..., power14(k) are the 1st to kth groups of separation energy for the 14th satellite.

[0071] In this embodiment, the initial particle velocity V is:

[0072]

[0073] The individual extreme value pbest(i) of each particle is initialized as follows:

[0074]

[0075] The global extremum gbest of the entire particle swarm is initialized to -65.9.

[0076] S3. Based on the near-field and far-field safety analysis of satellite separation, a fitness function is established with the minimum far-field distance between the two satellites within half to five cycles after separation and the sum of the attitude angular velocities of each satellite after separation as optimization indicators.

[0077] Figures 3-5 The effects of orbital velocity deviation, rocket body attitude angular velocity deviation at separation, and load installation azimuth deviation on far-field safety are presented respectively.

[0078] The fitness function established is as follows:

[0079]

[0080] Where d is the minimum far-field distance between the two satellites within half to five periods after separation, and ω nx ω ny ω nz η represents the attitude angular velocities of the nth satellite in the x, y, and z directions in the body coordinate system after separation, where n = 1, 2, ..., N; and η is the fitness function value.

[0081] S4. Calculate the fitness function value of each particle based on its current position.

[0082] Step S4 specifically includes: using the particle position X i Using the physical quantities in the model as initial conditions, two satellites are randomly selected from the N satellites. The far-field distance and separation attitude angular velocity between the satellites are calculated based on the far-field separation dynamics and near-field dynamics models. The fitness function of each particle is also calculated.

[0083] In this embodiment, the fitness function values ​​of each particle calculated in a certain iteration are as follows:

[0084]

[0085]

[0086] S5. For each particle, if the fitness function value calculated in S4 is less than the corresponding individual extreme value pbest(i), replace pbest(i) with the calculated fitness function value.

[0087] In this embodiment, the individual extreme value pbest(i) calculated in a certain iteration is updated as follows:

[0088]

[0089] S6. For each particle, if the fitness function value calculated in S4 is less than the global extremum gbest, replace the global extremum gbest with the fitness function value of that particle.

[0090] In this embodiment, the global extreme value gbest calculated in a certain iteration is updated to -60.1709.

[0091] S7. Update particle velocity and particle position, and perform boundary processing of particle position according to the spatial envelope and the selectable range of separation energy.

[0092] In step S7, the particle velocity is updated as follows:

[0093] v i (t+1)=v i (t)+c1r1[pbest i -x i (t)]+c2r2(t)[gbest i -x i (t)];

[0094] The method for updating particle positions is: x i (t+1)=x i (t)+v i (t+1);

[0095] Among them, v i (t+1) represents the velocity update of the i-th particle at the next moment, x i (t+1) represents the position of the i-th particle at the next time step, c1 and c2 are learning factors set by the user according to the model, and r1 and r2 are uniformly distributed random numbers between 0 and 1.

[0096] The particle positions are processed at the boundary, specifically as follows:

[0097] The boundary conditions are processed based on the satellite's installation position envelope on the payload support and the adjustable capability of the separation energy. The constraints of x(1)~x(14) and y(1)~y(14) are the installation position envelope on the payload support, and the constraints of power1(1)~power14(k) are the adjustable capability of the separation energy. If the particle position exceeds the constraint conditions, the particle position takes a random value within the constraint conditions.

[0098] S8. Repeat S4 to S7 until the preset termination condition is met, and output the optimized layout result of one arrow for multiple satellites.

[0099] In this embodiment, the preset termination condition may include one of the following forms:

[0100] 1) The fitness function value is less than the set value, 2) It satisfies 5000 iterations.

[0101] This embodiment uses a 14-satellite layout with a central support cylinder for a certain mission, and the initial calculation results are shown in Figure 6(a). The outer border represents the available envelope of the central support cylinder column segment, and each internal rectangle represents the envelope of each satellite (including 100mm of operating space). Running the particle swarm optimization algorithm, after 14 iterations in one calculation, the satellites can achieve mutual non-interference with sufficient operating space, and the far-field distance must be no less than 500m. The multi-satellite layout optimization process is as follows: Figures 6(a) to 6(d) As shown.

[0102] Example 2

[0103] Based on the one-rocket-multiple-satellite deployment method based on separation safety design proposed in Embodiment 1, a one-rocket-multiple-satellite deployment system based on separation safety design is provided, including a payload adapter selection module, a satellite-rocket separation deviation acquisition module, and an intelligent deployment module;

[0104] The payload adapter selection module is used to select the appropriate fairing and satellite adapter based on the satellite envelope size, separation requirements, and available operational space.

[0105] The satellite-rocket separation deviation acquisition module is used to acquire the orbital attitude deviation at the moment of satellite-rocket separation and to set the initial separation state.

[0106] The intelligent layout module executes an algorithm that includes the following steps:

[0107] T1. Set the M groups of "the centroid coordinates of each satellite relative to the rocket body and the separation energy of each satellite" in the initial separation state as the initial particle positions, initialize the initial particle velocities, initialize the individual extreme value pbest(i) of each particle and the global extreme value gbest of the entire particle swarm, i = 1, 2, ..., M, where M is the number of particles;

[0108] T2. Based on the near-field and far-field safety analysis of satellite separation, a fitness function is established with the minimum far-field distance between the two satellites within half to five cycles after separation and the sum of the attitude angular velocities of each satellite after separation as optimization indicators.

[0109] T3. Calculate the fitness function value of each particle based on its current position;

[0110] T4. For each particle, if the calculated fitness function value is less than the corresponding individual extreme value pbest(i), replace pbest(i) with the calculated fitness function value.

[0111] T5. For each particle, if the calculated fitness function value is less than the global optimum gbest, replace the global optimum gbest with the fitness function value of that particle.

[0112] T6. Update particle velocity and particle position, and perform boundary processing of particle position according to the spatial envelope and the selectable range of separation energy.

[0113] T7. Repeat T3 to T6 until the preset termination condition is met, and output the optimized layout result of one rocket launching multiple satellites.

[0114] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for deploying multiple satellites in a single launcher based on a separation security design, characterized in that, Includes the following steps: S1. Obtain the orbital attitude deviation at the moment of separation of the satellite and rocket, and set the initial separation state; S2. Set the M groups of "the centroid coordinates of each satellite relative to the rocket body and the separation energy of each satellite" in the initial separation state as the initial particle positions, initialize the particle velocities, initialize the individual extreme value pbest(i) of each particle and the global extreme value gbest of the entire particle swarm, i = 1, 2, ..., M, where M is the number of particles; S3. Based on the near-field and far-field safety analysis of satellite separation, a fitness function is established with the minimum far-field distance between the two satellites within half to five cycles after separation and the sum of the attitude angular velocities of each satellite after separation as optimization indicators. S4. Calculate the fitness function value of each particle based on its current position; S5. For each particle, if the fitness function value calculated in S4 is less than the corresponding individual extreme value pbest(i), replace pbest(i) with the calculated fitness function value. S6. For each particle, if the fitness function value calculated in S4 is less than the global extremum gbest, replace the global extremum gbest with the fitness function value of that particle. S7. Update particle velocity and particle position, and perform boundary processing of particle position according to the spatial envelope and the selectable range of separation energy. S8. Repeat S4 to S7 until the preset termination condition is met, and output the optimized layout result of one arrow for multiple satellites.

2. The method for deploying multiple satellites in a single launcher based on a separation security design according to claim 1, characterized in that, The orbital insertion attitude deviation specifically includes: The deviations in the position of the entry point, the velocity of the entry point, the pitch, yaw, and roll angles of the entry point.

3. The method for deploying multiple satellites with a single launcher based on a separation security design according to claim 1, characterized in that, Setting the initial separation state also includes setting the rocket's final stage mass characteristics, payload mass characteristics, and the selectable range of separation energy.

4. The method for deploying multiple satellites with a single launcher based on a separation security design according to claim 1, characterized in that, The particle position is represented by vector X. i i = 1, 2, ..., M; X i ={x(1),……,x(N),y(1),……,y(N),power1(1),……,power1(j),……,powerN(1),……,powerN(k)}; Where x(1), ..., x(N) are the X-axis coordinates of the 1st to Nth satellites in the rocket body coordinate system, y(1), ..., y(N) are the Y-axis coordinates of the 1st to Nth satellites in the rocket body coordinate system, power1(1), ..., power1(j) are the 1st to jth group of separation energy for the 1st satellite, and so on, powerN(1), ..., powerN(k) are the 1st to kth group of separation energy for the Nth satellite; where N is the total number of satellites on the rocket.

5. The method for deploying multiple satellites with a single launcher based on a separation security design according to claim 4, characterized in that, The fitness function is specifically: Where d is the minimum far-field distance between the two satellites within half to five periods after separation, and ω nx ω ny ω nz η represents the attitude angular velocities of the nth satellite in the x, y, and z directions in the body coordinate system after separation, where n = 1, 2, ..., N; and η is the fitness function value.

6. The method for deploying multiple satellites with a single launcher based on a separation security design according to claim 5, characterized in that, Step S4 specifically includes: based on the particle position X i Using the physical quantities in the model as initial conditions, two satellites are randomly selected from N satellites and substituted into the near-field and far-field separation dynamics models for calculation. From the results, the minimum far-field distance d between the two satellites within half to five cycles after separation was selected, and the attitude angular velocities ω of each satellite in the x, y, and z directions in the body coordinate system after separation were calculated. nx ω ny ω n .

7. The method for deploying multiple satellites with a single launcher based on a separation security design according to claim 4, characterized in that, S7 describes the boundary processing of particle positions, specifically including: The constraints of x(1)~x(N) and y(1)~y(N) are the installation position envelope on the load support, and the constraints of power1(1)~powerN(k) are the adjustable capability of the separated energy. If the particle position exceeds the constraint conditions, the particle position takes a random value within the constraint conditions.

8. The method for deploying multiple satellites in a single launcher based on a separation security design according to claim 1, characterized in that, The method for launching multiple satellites in one rocket also includes: selecting appropriate fairings and satellite adapters based on satellite envelope size, separation requirements, and available operational space.

9. A method for deploying multiple satellites in a single launcher based on a separation security design according to claim 1, characterized in that, The preset termination conditions include one of the following: the fitness function value is less than the set value, or the preset maximum number of iterations is reached.

10. A multi-satellite deployment system based on a separation security design, according to any one of claims 1 to 9, characterized in that, This includes a payload adapter selection module, a satellite-rocket separation deviation acquisition module, and an intelligent layout module; The payload adapter selection module is used to select the appropriate fairing and satellite adapter based on the satellite envelope size, separation requirements, and available operational space. The satellite-rocket separation deviation acquisition module is used to acquire the orbital attitude deviation at the moment of satellite-rocket separation and to set the initial separation state. The intelligent layout module executes an algorithm that includes the following steps: T1. Set the M groups of "the center of mass coordinates of each satellite relative to the rocket body and the separation energy of each satellite" in the initial separation state as the initial particle position, initialize the initial particle velocity, initialize the individual extreme value pbest(i) of each particle and the global extreme value gbest of the entire particle swarm, i = 1, 2, ..., M, where M is the number of particles; T2. Based on the near-field and far-field safety analysis of satellite separation, a fitness function is established with the minimum far-field distance between the two satellites within half to five cycles after separation and the sum of the attitude angular velocities of each satellite after separation as optimization indicators. T3. Calculate the fitness function value of each particle based on its current position; T4. For each particle, if the calculated fitness function value is less than the corresponding individual extreme value pbest(i), replace pbest(i) with the calculated fitness function value. T5. For each particle, if the calculated fitness function value is less than the global optimum gbest, replace the global optimum gbest with the fitness function value of that particle. T6. Update particle velocity and particle position, and perform boundary processing of particle position according to the spatial envelope and the selectable range of separation energy. T7. Repeat T3 to T6 until the preset termination condition is met, and output the optimized layout result of one rocket launching multiple satellites.

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