Low-orbit constellation in-plane relative phase maneuvering time optimal control method

Abstract

The invention discloses a low-orbit constellation in-plane relative phase maneuvering time optimal control method, and belongs to the technical field of spacecraft dynamics control. The invention aims to solve the problems that the influence of the orbit height change in the relative phase maneuvering process is not considered and the maneuvering control time cannot be shortest in the existing atmospheric differential towing control strategy optimization method. Comprising the following steps: obtaining a true near angle velocity variable quantity of a control time step according to a satellite true near angle kinetic equation; setting a satellite command matrix in combination with the corresponding relationship between the satellite windward area and the attitude control command; according to an optimization objective of shortest control time and a characteristic that time required by control should be shortened along with optimization, a method for performing control strategy optimization by using a variable length genetic algorithm is designed, and a sequence optimization algorithm for performing single-point optimization in a solution space based on a simulated annealing algorithm is designed at the same time; and nesting and coupling sequence optimization and control strategy optimization to obtain a time optimal command matrix. The method is used for controlling the satellites in the low-orbit constellation.

Description

Technical Field

[0001] The invention relates to an optimal control method for relative phase maneuvering time within a low-orbit constellation plane, and belongs to the technical field of spacecraft dynamics control. Background Art

[0002] With the development of micro-satellites, low-orbit micro-satellite constellations have become a trend of development. Continuously promoting the development of satellite Internet can meet the needs of the space infrastructure system. In the phase control of low-orbit micro-satellite constellations, considering quality, cost, propulsion consumption and atmospheric resistance of low-orbit spacecraft have become the main problems.

[0003] At the current technological level, considering the adaptability of launch vehicles and the feasibility of mass production projects, constellation deployment is generally implemented using the same type of launch vehicle and the same launch site. The launch cycle constraints of the launch site affect the rhythm of constellation deployment. At the same time, considering the reliability of satellites in orbit and the need to enter the working orbit as soon as possible after entering orbit to save their in-orbit life, the deployment method of directly sending them to the predetermined orbital plane is generally adopted, without long-term and large-scale orbital plane drift; in addition, for low-Earth orbit satellite systems, considering that the direction of phase adjustment before and after entering orbit may change with the launch strategy, in order to avoid frequent changes in launch parameters, launch vehicles usually directly aim at the predetermined orbital altitude of the satellite for deployment. After entering orbit, the satellite relies on its own orbital control to carry out orbit transfer process accompanied by a large number of remote control operations, which will also consume manpower and time costs. In addition, due to the orbital characteristics of low-orbit satellites, during the constellation deployment process, the spacecraft is greatly affected by atmospheric perturbations. In order to eliminate this effect, additional propellant is required.

[0004] In 1986, Leonard et al. proposed using atmospheric differential drag to control satellite motion. Since then, researchers have improved the control model, optimized the control method, and conducted research in different fields. These studies have shown that atmospheric differential drag control technology is an effective method for achieving formation control for the relative phase maneuvering control of constellations in the orbital plane. The US Dove satellite constellation has proved its engineering feasibility through in-orbit tests.

[0005] In the paper "Constellation Phasing with Differential Drag on Planet Labs Satellites", Foster et al. proposed an atmospheric differential drag control strategy optimization method based on simulated annealing algorithm for the constellation's in-plane relative phase maneuver control, using the Dove constellation as the project background. Although this method aims to minimize the relative phase maneuver time, the strategy optimization adopts a solution of first performing process trajectory planning and then optimizing the control strategy to approach the target trajectory. It does not specifically consider the impact of orbital altitude changes during the relative phase maneuver process, and cannot ensure that a set of control strategies that minimize the maneuver time is obtained. Summary of the invention

[0006] In view of the problem that the existing atmospheric differential drag control strategy optimization method does not consider the influence of orbital altitude change during relative phase maneuvering and cannot achieve the shortest maneuvering control time, the present invention provides an optimal control method for relative phase maneuvering time within the low-orbit constellation plane.

[0007] A method for optimal control of relative phase maneuvering time within a low-orbit constellation plane of the present invention comprises:

[0008] According to the satellite true near angle dynamics equation, the satellite true near angle θ at the kth time point is obtained. k The expected true satellite near angle θ at the k+1th time point k+1 The corresponding true near-angle angular velocity The true near-angle angular velocity change within the control time step Δt

[0009] According to the true near-angle angular velocity change The corresponding relationship between the satellite frontal area S and the attitude control command u is set to set the satellite command matrix, with the number of rows representing the number of satellites in the constellation, and the elements of each row are the sequential attitude control command strategies for a satellite;

[0010] Satellite No. 1 in the low-orbit constellation is selected as the reference satellite, and all other satellites are sorted; all satellites in the current sorting are controlled separately based on the timing attitude control command strategy, and according to the relative motion state of the reference satellite and other satellites, the timing attitude control command strategy is optimized by a variable-length genetic algorithm with the goal of optimizing the relative phase maneuvering time, and the optimal timing attitude control command strategy for each satellite in the current sorting is determined; the optimal satellite sorting of the currently optimized satellite sorting is determined based on the simulated annealing algorithm; the timing attitude control command strategy under the next satellite sorting is optimized until the current optimal timing attitude control command strategy meets the set termination condition, and the optimal satellite sorting and the corresponding optimal satellite command matrix are obtained, and the optimal control of the relative phase maneuvering time of the low-orbit constellation is achieved according to the optimal satellite command matrix.

[0011] According to the method for optimal control of relative phase maneuvering time within the LEO constellation plane of the present invention, the true near-angle dynamic equation of the satellite is:

[0012]

[0013] According to the method for optimal control of relative phase maneuvering time within the LEO constellation plane of the present invention, the true near-angle angular velocity change for:

[0014]

[0015] Where ρ is the atmospheric density, v is the satellite speed, C D is the satellite drag coefficient, m is the satellite mass, and r is the satellite distance from the Earth’s center.

[0016] According to the method for optimal control of relative phase maneuvering time within the LEO constellation plane of the present invention, the change Δr of the satellite's geocentric distance is affected by the atmospheric force F:

[0017]

[0018] Where μ is the gravitational constant;

[0019]

[0020] The current satellite-to-earth center distance r is determined based on the change in the satellite-to-earth center distance Δr.

[0021] According to the optimal control method of the relative phase maneuvering time within the low-orbit constellation plane of the present invention, the corresponding relationship between the satellite frontal area S and the attitude control command u is:

[0022] S=uS max +(1-u)S min ,

[0023] Where S minis the minimum satellite projection area, S max is the maximum projection area of ​​the satellite.

[0024] According to the optimal control method of relative phase maneuvering time in the LEO constellation plane of the present invention, the timing attitude control command strategy of each row in the satellite command matrix is ​​set to be marked by the effective gene length d sat , effective gene u sat,1 arrive and null genes to u sat,end The effective gene length is d sat The first column is occupied by genes, and each subsequent column represents a posture control command corresponding to the control time step Δt. The effective gene length identifier d is determined by optimizing the sequential posture control command strategy. sat , sat represents the satellite sequence.

[0025] According to the method for optimal control of relative phase maneuvering time within the LEO constellation plane of the present invention, the method for determining the optimal satellite sequence of the currently optimized satellite sequence based on the simulated annealing algorithm is:

[0026] Establish the relative phase correspondence sequence relationship between the initial true near angles of all satellites and the true near angles of the targets. The relative phases of all target true near angles are evenly distributed, and the angular velocity of the target relative true near angle is 0.

[0027] The target true near angle is numbered according to the position, and all satellites in the low-orbit constellation are numbered, and a corresponding sequence relationship between the satellite and the target true near angle is formed; the change of the corresponding sequence relationship is achieved by changing the satellite number;

[0028] Initialize the corresponding sequence relationship: set the initial annealing temperature T 0 and the maximum number of iterations k max ; Set the maximum time t for relative phase maneuvering within the plane max and control time step Δt, the shortest in-plane relative phase maneuvering time l min Initialize to set the maximum value t max ; Randomly generate the initial corresponding sequence relationship;

[0029] According to the optimal timing attitude control command strategy for each satellite obtained under the current sorting, the effective gene length mark d in the corresponding satellite command matrix is sat The maximum value of is recorded as l, and the Metropolis criterion is used to determine whether l is assigned to the shortest in-plane relative phase maneuvering time l min If so, perform the shortest in-plane relative phase maneuver time l minWhen assigning values, the corresponding satellite command matrix and the current corresponding sequence relationship are used as the current optimal satellite command matrix and the current optimal satellite sequence; otherwise, it is determined whether the current optimal timing attitude control command strategy meets the set termination condition. If so, the current optimal satellite command matrix and the current optimal satellite sequence are used as the final optimal satellite sequence and the corresponding final optimal satellite command matrix. Otherwise, the optimization of the timing attitude control command strategy under the next satellite sequence is continued until the end.

[0030] According to the method for optimal control of relative phase maneuvering time within the LEO constellation plane of the present invention, a method for determining the optimal timing attitude control command strategy for each satellite under the current sorting by using a variable length genetic algorithm is as follows:

[0031] Step A1: Identify the effective gene length of the reference satellite as d 1 Set to maximum value:

[0032] d 1 =t max / Δt,

[0033] And set the value of all genes to 0.5;

[0034] Step A2: Optimize the optimal timing attitude control command strategy for each satellite according to the satellite number sequence: Set the maximum iteration number of the variable length genetic algorithm to g max , the mutation probability is p, the number of individuals in the population is n, where the number of individuals in the population is the number of satellites in the low-orbit constellation; the shortest in-plane relative phase maneuvering time w of the current satellite min Initialize to set the maximum value w max ;

[0035] Step A3: Generate the initial control command population: mark the effective gene length of all individuals in the population as d sat Both are set to the maximum value t max / Δt; the gene value of each individual is obtained through a random function;

[0036] Step A4: Calculate the effective gene length of each individual in the population based on the current optimization result: According to the satellite true near angle dynamics equation, take the attitude control command as input, change the satellite frontal area S, and obtain the satellite true near angle at each discrete time point through discrete calculation; calculate whether the relative phase between the current satellite true near angle and the reference satellite true near angle meets the control accuracy requirement:

[0037]

[0038] Where θ sat is the current satellite true near angle, θ ref is the true near angle of the reference satellite, θ f is the target relative phase, ε1 is the relative phase accuracy threshold, is the current true near-angle angular velocity of the satellite, is the true near-angular velocity of the reference satellite, is the target relative angular velocity, ε 2 is the relative angular velocity accuracy threshold;

[0039] In the issue of changing the configuration of low-orbit constellations, In the track change problem,

[0040] If the relative phase of the current satellite true near angle and the reference satellite true near angle meets the control accuracy requirement, the optimization of the current timing attitude control command strategy is terminated; the used genes are regarded as valid genes, and the unused genes are regarded as invalid genes; the valid gene length flag d is modified sat ;

[0041] Step A5: Identify d according to effective gene length sat Arrange the population from small to large, and take the first half of the population as the parents, and discard the second half from the population;

[0042] Step A6: Identify the minimum effective gene length d in the current population sat Denote it as w, and determine whether w<w min , if so, assign w to w min , determine the corresponding timing attitude control command strategy;

[0043] Step A7: Determine whether the maximum number of iterations g has been reached max or in a set number of iterations w min No change, if yes, go to step A11: Otherwise, go to step A8:

[0044] Step A8: Identify the effective gene length identifier d in the current population sat The maximum value d max , and cut off each individual d max All genes after the +1 position;

[0045] Step A9: Perform mutation operation on the current population and randomly change the single gene of the individual based on the mutation probability p;

[0046] Step A10: Perform a crossover operation on the current population, divide the parent population into two groups, namely the paternal population and the maternal population; randomly select a paternal parent and a maternal parent, perform random gene point crossover, and generate offspring individuals; form a new population with all offspring individuals and the paternal individuals, and return to step A4;

[0047] Step A11: Use the current w minThe corresponding sequential attitude control command strategy replaces the corresponding row in the satellite command matrix;

[0048] Step A12: Determine whether w is satisfied min >l min +L, where L is the set threshold; if so, based on the currently obtained optimal timing posture control command strategy, a new timing posture control command strategy is generated in the neighborhood, and the process returns to step A1; otherwise, step A13 is executed;

[0049] Step A13: Based on the number of individuals n in the population, determine whether the timing attitude control command strategies of all satellites in the low-orbit constellation have been optimized. If so, use the currently optimized timing attitude control command strategy as the current optimal timing attitude control command strategy; otherwise, return to step A2 to continue the optimization until the end.

[0050] According to the method for optimal control of relative phase maneuvering time within the LEO constellation plane of the present invention, the set termination condition is: reaching the maximum number of iterations k max Or the optimization results of the sequential attitude control command strategy under different satellite sequences do not change within the set number of times.

[0051] The beneficial effects of the present invention are as follows: the method of the present invention aims at the problem of relative phase maneuvers within the orbital plane during the constellation deployment process, and adopts an atmospheric differential drag control method without additional consumption of propulsion fluid for control; during the whole process of relative phase maneuvers, the influence of the orbital altitude change of low earth orbit satellites on the atmospheric environment and satellite motion is considered; with the shortest control time of the relative phase maneuver within the plane as the optimization goal, the constellation control strategy is optimized based on a variable-length genetic algorithm and a simulated annealing algorithm, and the optimal control strategy with the shortest maneuvering time is obtained.

[0052] The method of the present invention uses the atmospheric differential drag control principle to perform constellation phase control, actively uses atmospheric forces for constellation plane control, and can save orbital control fuel consumption; a simplified dynamic model involving the atmospheric differential drag principle is given, and the influence of orbital altitude on atmospheric forces is considered. According to the optimization goal of shortest control time, the time required for control has the characteristic that it should be shortened with optimization, and a method of using a variable-length genetic algorithm to perform control strategy is designed to gradually shorten the length of the timing control command during the optimization process; considering the different initial motion states of each satellite in the satellite constellation, a sequence optimization algorithm based on a simulated annealing algorithm is designed to perform single-point optimization in the solution space; the method of the present invention nests and couples sequence optimization with control strategy optimization to obtain a time-optimal command matrix, which can reduce the amount of calculation and speed up calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the method for optimal control of relative phase maneuvering time within the LEO constellation plane of the present invention;

[0054] Figure 2 It is a schematic diagram of the sequential attitude control command strategy for each row in the satellite command matrix;

[0055] Figure 3 It is a schematic diagram of generating a new timing attitude control command strategy in a neighborhood based on the current timing attitude control command strategy. DETAILED DESCRIPTION

[0056] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0058] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0059] Specific implementation method 1. Combination Figures 1 to 3 As shown, the present invention provides a method for optimal control of relative phase maneuvering time within a low-orbit constellation plane, comprising:

[0060] The atmospheric differential drag dynamics equations are established for a constellation of co-orbital satellites operating in low earth orbit;

[0061] According to the satellite true near angle dynamics equation, the satellite true near angle θ at the kth time point is obtained. k The expected true satellite near angle θ at the k+1th time point k+1 The corresponding true near-angle angular velocity The true near-angle angular velocity change within the control time step Δt

[0062] According to the true near-angle angular velocity change The corresponding relationship between the satellite frontal area S and the attitude control command u is set to set the satellite command matrix, with the number of rows representing the number of satellites in the constellation, and the elements of each row are the sequential attitude control command strategy for a satellite; the sequential attitude control command strategy is implemented by coding to control the satellite attitude change, and then perform relative phase maneuver control;

[0063] Satellite No. 1 in the low-orbit constellation is selected as the reference satellite, and all other satellites are sorted; all satellites in the current sorting are controlled separately based on the timing attitude control command strategy, and according to the relative motion state of the reference satellite and other satellites, the timing attitude control command strategy is optimized by using a variable-length genetic algorithm with the goal of optimizing the relative phase maneuvering time, and the optimal timing attitude control command strategy for each satellite in the current sorting is determined; the optimal satellite sorting of the currently optimized satellite sorting is determined based on the simulated annealing algorithm; the timing attitude control command strategy under the next satellite sorting is optimized until the current optimal timing attitude control command strategy meets the set termination condition, the optimal satellite sorting and the corresponding optimal satellite command matrix are determined, and the optimal control of the relative phase maneuvering time of the low-orbit constellation is achieved according to the optimal satellite command matrix.

[0064] This implementation method takes into account that the initial in-plane relative phase and initial relative speed of each satellite in the constellation composed of homogeneous satellites are different, faces a set of determined target in-plane relative phase and target relative speed, establishes a corresponding sequence relationship between the satellite and the target motion state, takes the shortest in-plane relative phase maneuver control time as the optimization goal, and optimizes the corresponding sequence relationship based on the genetic algorithm; as the inner layer of the loop optimized by the genetic algorithm, this implementation method is based on the variable-length genetic algorithm, combined with the idea of ​​the existing hidden gene genetic algorithm, takes the shortest in-plane relative phase maneuver control time as the optimization goal, and optimizes to obtain the optimal command matrix for the in-plane relative phase maneuver control time;

[0065] Finally, the optimal control process of the relative phase maneuvering time within the plane can be simulated according to the optimal corresponding sequence relationship and the corresponding optimal command matrix.

[0066] Furthermore, to perform atmospheric differential drag control on the same-orbit constellation, a low earth orbit satellite dynamics model must first be established. There are many studies on the existing low earth orbit satellite dynamics model. Considering the optimization algorithm search capability and calculation speed, this implementation adopts a simplified dynamics model that only considers the two-body gravity and atmospheric force.

[0067] The satellite true near-angle dynamic equation is:

[0068]

[0069] Take Δt as the control time step, take the true near angle as the control change in the orbital plane, and the true near angle angular velocity change for:

[0070]

[0071] Where ρ is the atmospheric density, obtained from the atmospheric model; v is the incoming flow velocity, which can be approximately regarded as the satellite motion velocity, C Dis the satellite drag coefficient, which is usually an empirical value; m is the satellite mass, and r is the satellite distance from the Earth’s center.

[0072] When the orbital eccentricity e≠0, Δt is required to be much smaller than the orbital period to ensure that the changes in the satellite's distance from the Earth's center and the atmospheric density in the environment within the range of Δt are small, thus guaranteeing the reliability of the simplified dynamic model to a certain extent.

[0073] The satellite acceleration a along the track direction is calculated based on the satellite's frontal area S:

[0074]

[0075] The change in the satellite's distance from the Earth's center Δr is affected by the atmospheric force F:

[0076]

[0077] Where μ is the gravitational constant;

[0078]

[0079] The current satellite-to-earth center distance r is determined based on the change in the satellite-to-earth center distance Δr, and the corresponding atmospheric density is obtained through the atmospheric model for the dynamic calculation of the next Δt.

[0080] The higher the accuracy of the dynamics model, the more comprehensive the environmental force perturbations considered, and the optimal command matrix control effect obtained by the final optimization will be closer to the actual situation; at the same time, the high-precision dynamics model has some restrictions on the orbit recursion step size, requiring a corresponding calculation time cost. During use, perturbation items can be added according to actual needs to improve the dynamics accuracy.

[0081] The corresponding relationship between the satellite frontal area S and the attitude control command u is:

[0082] S=uS max +(1-u)S min ,

[0083] Where S min is the minimum satellite projection area, S max The maximum projection area of ​​the satellite. The windward area can be changed through attitude control.

[0084] Further, if Figure 2 As shown in Figure 1, a set of control strategy encoding methods is designed, and the command matrix is ​​used to represent the timing attitude control command. The number of rows in the command matrix represents the number of satellites in the constellation. The timing attitude control command strategy of each row in the satellite command matrix is ​​set by the effective gene length d sat , effective gene u sat,1 arrive and null genes to u sat,endThe effective gene length is d sat The first column is occupied by genes, and each subsequent column represents a posture control command corresponding to the control time step Δt. The effective gene length identifier d is determined by optimizing the sequential posture control command strategy. sat , sat represents the satellite sequence.

[0085] Furthermore, the method for determining the optimal satellite order of the currently optimized satellite order based on the simulated annealing algorithm is:

[0086] For satellite constellations with similar structures and homogeneous on-orbit missions, the relative phase correspondence sequence relationship between the initial true near angles and the target true near angles of all satellites is established. Taking the target relative motion state as the uniform distribution in the plane and stable operation as an example, the relative phase of all target true near angles is uniformly distributed, and the target relative true near angle angular velocity is 0;

[0087] The target true near angle is numbered according to the position, and all satellites in the low-orbit constellation are numbered, and a corresponding sequence relationship between the satellite and the target true near angle is formed; the change of the corresponding sequence relationship is achieved by changing the satellite number;

[0088] Initialize the corresponding sequence relationship: set the initial annealing temperature T 0 and the maximum number of iterations k max ; Set the maximum time t for relative phase maneuvering within the plane max and control time step Δt, the shortest in-plane relative phase maneuvering time l min Initialize to set the maximum value t max ; Randomly generate the initial corresponding sequence relationship;

[0089] According to the optimal timing attitude control command strategy for each satellite obtained under the current sorting, the effective gene length mark d in the corresponding satellite command matrix is sat The maximum value of is recorded as l, and the Metropolis criterion is used to determine whether l is assigned to the shortest in-plane relative phase maneuvering time l min If so, perform the shortest in-plane relative phase maneuver time l min When assigning values, the corresponding satellite command matrix and the current corresponding sequence relationship are used as the current optimal satellite command matrix and the current optimal satellite sequence; otherwise, it is determined whether the current optimal timing attitude control command strategy meets the set termination condition. If so, the current optimal satellite command matrix and the current optimal satellite sequence are used as the final optimal satellite sequence and the corresponding final optimal satellite command matrix. Otherwise, the optimization of the timing attitude control command strategy under the next satellite sequence is continued until the end.

[0090] Furthermore, the method of using a variable-length genetic algorithm to determine the optimal timing attitude control command strategy for each satellite under the current order is:

[0091] Step A1: Identify the effective gene length of the reference satellite as d 1 Set to maximum value:

[0092] d 1 =t max / Δt,

[0093] All genes in the reference satellite control command are valid genes. In order to give the non-reference satellite the maximum controllable range, the values ​​of all genes are set to 0.5;

[0094] Step A2: Optimize the optimal timing attitude control command strategy for each satellite according to the satellite number sequence: Set the maximum iteration number of the variable length genetic algorithm to g max , the mutation probability is p, the number of individuals in the population is n, where the number of individuals in the population is the number of satellites in the low-orbit constellation; the shortest in-plane relative phase maneuvering time w of the current satellite min Initialize to set the maximum value w max ;

[0095] Step A3: Generate the initial control command population: mark the effective gene length of all individuals in the population as d sat Both are set to the maximum value t max / Δt; the gene value of each individual is obtained through a random function;

[0096] Step A4: Calculate the effective gene length of each individual in the population based on the current optimization result: According to the satellite true near angle dynamics equation, take the attitude control command as input, change the satellite frontal area S, and obtain the satellite true near angle at each discrete time point through discrete calculation; calculate whether the relative phase between the current satellite true near angle and the reference satellite true near angle meets the control accuracy requirement:

[0097]

[0098] Where θ sat is the current satellite true near angle, θ ref is the true near angle of the reference satellite, θ f is the target relative phase, ε 1 is the relative phase accuracy threshold, is the current true near-angle angular velocity of the satellite, is the true near-angular velocity of the reference satellite, is the target relative angular velocity, ε 2 is the relative angular velocity accuracy threshold;

[0099] In the issue of changing the configuration of low-orbit constellations, In the track change problem,

[0100] If the relative phase of the current satellite true near angle and the reference satellite true near angle meets the control accuracy requirement, the optimization of the current timing attitude control command strategy is terminated; the used genes are regarded as valid genes, and the unused genes are regarded as invalid genes; the valid gene length flag d is modified sat ;

[0101] Step A5: Identify d according to effective gene length sat Arrange the population from small to large, and take the first half of the population as the parents, and discard the second half from the population;

[0102] Step A6: Identify the minimum effective gene length d in the current population sat Denote it as w, and determine whether w<w min , if so, assign w to w min , determine the corresponding timing attitude control command strategy;

[0103] Step A7: Determine whether the maximum number of iterations g has been reached max or in a set number of iterations w min No change, if yes, go to step A11: Otherwise, go to step A8:

[0104] Step A8: Identify the effective gene length identifier d in the current population sat The maximum value d max , and cut off each individual d max + All genes after the 1st position; shorten the length of individual genes and reduce the amount of optimization calculation;

[0105] Step A9: Perform mutation operation on the current population and randomly change the single gene of the individual based on the mutation probability p;

[0106] Step A10: Perform a crossover operation on the current population, divide the parent population into two groups, namely the paternal population and the maternal population; randomly select a paternal parent and a maternal parent, perform random gene point crossover, and generate offspring individuals; form a new population with all offspring individuals and the paternal individuals, and return to step A4;

[0107] Step A11: Use the current w min The corresponding sequential attitude control command strategy replaces the corresponding row in the satellite command matrix;

[0108] Step A12: Determine whether w is satisfied min >l min+L, where L is the set threshold; if so, it proves that the current control sequence is far from the optimal control sequence in the solution space and is a poor solution. There is no need to continue the strategy optimization under this sequence. Immediately jump out of the sequence optimization to reduce the amount of calculation, and based on the current optimal sequential attitude control command strategy, generate a new sequential attitude control command strategy in the neighborhood, such as Figure 3 As shown; return to step A1; otherwise, execute step A13;

[0109] Step A13: Based on the number of individuals n in the population, determine whether the timing attitude control command strategies of all satellites in the low-orbit constellation have been optimized. If so, use the currently optimized timing attitude control command strategy as the current optimal timing attitude control command strategy; otherwise, return to step A2 to continue the optimization until the end.

[0110] In this embodiment, the termination condition is: reaching the maximum number of iterations k max Or the optimization results of the sequential attitude control command strategy under different satellite sequences do not change within the set number of times.

[0111] Finally, based on the established dynamic model, the optimal command matrix control under the optimal sequence is optimized through simulation, the correctness of this solution is verified, and the time-optimal control strategy and simulation results are obtained.

[0112] In summary, the method of the present invention is based on genetic algorithm and simulated annealing algorithm, and uses the principle of atmospheric differential drag technology to design a set of optimization algorithms for optimizing control strategies for the specific problem of relative phase maneuvering in the plane of co-orbital low earth orbit constellations. According to the optimization goal of shortest control time, the effective gene length is used as the fitness function in the optimization process, and an algorithm combining variable length genetic algorithm for strategy optimization and simulated annealing algorithm for sequence optimization is designed. A control strategy that minimizes the relative phase maneuvering time in the plane is proposed, and its calculation process can reduce the amount of calculation and improve the calculation efficiency.

[0113] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. A method for optimal control of relative phase maneuvering time within a low-orbit constellation plane, characterized in that: include: According to the satellite true near angle dynamics equation, the satellite true near angle θ at the kth time point is obtained. k The expected true satellite near angle θ at the k+1th time point k+1 The corresponding true near-angle angular velocity The true near-angle angular velocity change within the control time step Δt According to the true near-angle angular velocity change The corresponding relationship between the satellite frontal area S and the attitude control command u is set to set the satellite command matrix, with the number of rows representing the number of satellites in the constellation, and the elements of each row are the sequential attitude control command strategies for a satellite; Select satellite No. 1 in the low-orbit constellation as the reference satellite and rank all other satellites; Based on the timing attitude control command strategy, all satellites in the current sequence are controlled separately, and according to the relative motion state of the reference satellite and other satellites, the timing attitude control command strategy is optimized by using a variable-length genetic algorithm with the goal of optimizing the relative phase maneuvering time, and the optimal timing attitude control command strategy for each satellite in the current sequence is determined; based on the simulated annealing algorithm, the optimal satellite sequence of the currently optimized satellite sequence is determined; then the timing attitude control command strategy under the next satellite sequence is optimized until the current optimal timing attitude control command strategy meets the set termination condition, and the optimal satellite sequence and the corresponding optimal satellite command matrix are obtained, and the optimal control of the relative phase maneuvering time of the low-orbit constellation is achieved according to the optimal satellite command matrix.

2. The method for optimal control of relative phase maneuvering time within the LEO constellation plane according to claim 1, characterized in that: The satellite true near-angle dynamic equation is:

3. The method for optimal control of relative phase maneuvering time within the LEO constellation plane according to claim 2, characterized in that: True near-angle angular velocity change for: Where ρ is the atmospheric density, v is the satellite speed, C D is the satellite drag coefficient, m is the satellite mass, and r is the satellite distance from the Earth’s center.

4. The method for optimal control of relative phase maneuvering time within the LEO constellation plane according to claim 3, characterized in that: The change in the satellite's distance from the Earth's center Δr is affected by the atmospheric force F: Where μ is the gravitational constant; The current satellite-to-earth center distance r is determined based on the change in the satellite-to-earth center distance Δr.

5. The method for optimal control of relative phase maneuvering time within the LEO constellation plane according to claim 4, characterized in that: The corresponding relationship between the satellite frontal area S and the attitude control command u is: S=uS max +(1-u)S min , Where S min is the minimum satellite projection area, S max is the maximum projection area of ​​the satellite.

6. The method for optimal control of relative phase maneuvering time within the LEO constellation plane according to claim 5, characterized in that: Set the timing attitude control command strategy of each row in the satellite command matrix to be identified by the effective gene length d sat , effective gene u sat,1 arrive and null genes to u sat,end The effective gene length is d sat The first column is occupied by genes, and each subsequent column represents a posture control command corresponding to the control time step Δt. The effective gene length identifier d is determined by optimizing the sequential posture control command strategy. sat , sat represents the satellite sequence.

7. The method for optimal control of relative phase maneuvering time within the LEO constellation plane according to claim 6, characterized in that: The method for determining the optimal satellite order of the currently optimized satellite order based on the simulated annealing algorithm is: Establish the relative phase correspondence sequence relationship between the initial true near angles of all satellites and the true near angles of the targets. The relative phases of all target true near angles are evenly distributed, and the angular velocity of the target relative true near angle is 0. The target true near angle is numbered according to the position, and all satellites in the low-orbit constellation are numbered, and a corresponding sequence relationship between the satellite and the target true near angle is formed; the change of the corresponding sequence relationship is achieved by changing the satellite number; Initialize the corresponding sequence relationship: set the initial annealing temperature T0 and the maximum number of iterations k max ; Set the maximum time t for relative phase maneuvering within the plane max and control time step Δt, the shortest in-plane relative phase maneuvering time l min Initialize to set the maximum value t max ; Randomly generate the initial corresponding sequence relationship; According to the optimal timing attitude control command strategy for each satellite obtained under the current sorting, the effective gene length mark d in the corresponding satellite command matrix is sat The maximum value of is recorded as l, and the Metropolis criterion is used to determine whether l is assigned to the shortest in-plane relative phase maneuvering time l min If so, perform the shortest in-plane relative phase maneuver time l min While assigning the values, the corresponding satellite command matrix and the current corresponding sequence relationship are used as the current optimal satellite command matrix and the current optimal satellite sequence; Otherwise, determine whether the current optimal timing attitude control command strategy meets the set termination conditions. If so, take the current optimal satellite command matrix and the current optimal satellite order as the final optimal satellite order and the corresponding final optimal satellite command matrix. Otherwise, continue to optimize the timing attitude control command strategy under the next satellite order until the end.

8. The method for optimal control of relative phase maneuvering time within the LEO constellation plane according to claim 7, characterized in that: The method of using variable-length genetic algorithm to determine the optimal timing attitude control command strategy for each satellite under the current sorting is: Step A1: Set the effective gene length indicator d1 of the reference satellite to the maximum value: d1=t max / Δt, And set the value of all genes to 0.5; Step A2: Optimize the optimal timing attitude control command strategy for each satellite according to the satellite number sequence: Set the maximum iteration number of the variable length genetic algorithm to g max , the mutation probability is p, the number of individuals in the population is n, where the number of individuals in the population is the number of satellites in the low-orbit constellation; the shortest in-plane relative phase maneuvering time w of the current satellite min Initialize to set the maximum value w max ; Step A3: Generate the initial control command population: mark the effective gene length of all individuals in the population as d sat Both are set to the maximum value t max / Δt; the gene value of each individual is obtained through a random function; Step A4: Calculate the effective gene length of each individual in the population based on the current optimization result: According to the satellite true near angle dynamics equation, take the attitude control command as input, change the satellite frontal area S, and obtain the satellite true near angle at each discrete time point through discrete calculation; calculate whether the relative phase between the current satellite true near angle and the reference satellite true near angle meets the control accuracy requirement: Where θ sat is the current satellite true near angle, θ ref is the true near angle of the reference satellite, θ f is the target relative phase, ε1 is the relative phase accuracy threshold, is the current true near-angle angular velocity of the satellite, is the true near-angular velocity of the reference satellite, is the target relative angular velocity, ε2 is the relative angular velocity accuracy threshold; In the issue of changing the configuration of low-orbit constellations, In the track change problem, If the relative phase of the current satellite true near angle and the reference satellite true near angle meets the control accuracy requirement, the optimization of the current timing attitude control command strategy is terminated; the used genes are regarded as valid genes, and the unused genes are regarded as invalid genes; the valid gene length flag d is modified sat ; Step A5: Identify d according to effective gene length sat Arrange the population from small to large, and take the first half of the population as the parents, and discard the second half from the population; Step A6: Identify the minimum effective gene length d in the current population sat Denote it as w, and determine whether w<w min , if so, assign w to w min , determine the corresponding timing attitude control command strategy; Step A7: Determine whether the maximum number of iterations g has been reached max or in a set number of iterations w min No change, if yes, go to step A11: Otherwise, go to step A8: Step A8: Identify the effective gene length identifier d in the current population sat The maximum value d max , and cut off each individual d max All genes after the +1 position; Step A9: Perform mutation operation on the current population and randomly change the single gene of the individual based on the mutation probability p; Step A10: Perform a crossover operation on the current population, divide the parent population into two groups, namely the paternal population and the maternal population; randomly select a paternal parent and a maternal parent, perform random gene point crossover, and generate offspring individuals; form a new population with all offspring individuals and the paternal individuals, and return to step A4; Step A11: Use the current w min The corresponding sequential attitude control command strategy replaces the corresponding row in the satellite command matrix; Step A12: Determine whether w is satisfied min >l min +L, where L is the set threshold; if so, based on the currently obtained optimal timing posture control command strategy, a new timing posture control command strategy is generated in the neighborhood, and the process returns to step A1; otherwise, step A13 is executed; Step A13: judging whether the timing attitude control command strategies of all satellites in the low-orbit constellation have been optimized based on the number of individuals n in the population, and if so, taking the timing attitude control command strategy currently optimized as the current optimal timing attitude control command strategy; Otherwise, return to step A2 to continue the optimization until the end.

9. The method for optimal control of relative phase maneuvering time within the LEO constellation plane according to claim 1, characterized in that: The termination condition of the setting is: reaching the maximum number of iterations k max Or the optimization results of the sequential attitude control command strategy under different satellite sequences do not change within the set number of times.

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