A spacecraft orbit pursuit and escape game method based on pulse thrust

Abstract

The present invention provides a spacecraft orbit pursuit and escape game method based on pulse thrust. By establishing a spacecraft pulse orbit pursuit and escape game model, the original minimax optimization problem is transformed into a two-level optimization problem, and then a genetic algorithm with global optimization capability and a pattern search algorithm with fast convergence characteristics are adopted to jointly solve the problem, which significantly improves the problem-solving efficiency. The problem of aerospace game is effectively solved by combining the pulse control method with the spacecraft pulse orbit pursuit and escape game model, thereby laying a theoretical foundation for the realization of engineering applications such as taking over space fault spacecraft and clearing space failed spacecraft.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and specifically to a spacecraft orbit pursuit and escape game method based on pulse thrust, which is used to complete space non-cooperative target pursuit and threat avoidance tasks with game confrontation characteristics under pulse thrust. Background Art

[0002] Spacecraft orbital pursuit is a mathematical problem with a wide range of applications. It is a crucial implementation step in typical scenarios such as rendezvous with non-cooperative targets in space, safe approach to tumbling targets in space, and on-orbit servicing of faulty spacecraft. Classical orbital pursuit problems are generally modeled using continuous force control and then solved using differential game methods. However, during the on-orbit motion of a spacecraft, existing continuous control cannot be applied to impulse control problems. While impulse control is common in aerospace problems, it is not widely used in aerospace game problems. There are very few orbital pursuit models based on impulse velocity increment control, and their corresponding solutions are unclear. Therefore, the development of aerospace game problems under impulse control has greatly limited the development of non-cooperative space missions based on impulse control. Summary of the Invention

[0003] In view of the problem in the prior art that aerospace game cannot be solved by pulse control, the present invention provides a spacecraft orbit pursuit and escape game method based on pulse thrust.

[0004] The present invention is achieved through the following technical solutions:

[0005] A spacecraft orbit pursuit and escape game method based on pulse thrust includes the following steps:

[0006] Step 1: Establish a spacecraft pulse orbit pursuit and escape game model under the action of pulse thrust;

[0007] Step 2: Obtain the parameter information of the spacecraft pursuit and escape, and input the parameter information into the spacecraft pulse orbit pursuit and escape game model, and perform internal and external double-layer optimization on the spacecraft pulse orbit pursuit and escape game model to complete the spacecraft orbit pursuit and escape game.

[0008] Preferably, the calculation formula of the spacecraft pulse orbit pursuit and escape game model is as follows:

[0009]

[0010] Where J represents the bilateral optimization index of the pursuit-escape game; P represents the subscript of the pursuit star; E represents the subscript of the escape star; N represents the total number of pulse velocity increment control; X P Represents the state vector of the tracking star, specifically X P =[x P ,y P ,zP ,v Px ,v Py ,v Pz ] T ;X E represents the state vector of the escape star, specifically X E =[x E ,y E ,z E ,v Ex ,v Ey ,v Ez ] T ; t0 represents the initial moment of pursuit; t f Indicates the terminal moment of pursuit; t i represents the moment when each satellite applies pulse velocity increment control, i = 1, 2, ..., 5; x represents the position component of the orbital radial direction in the relative coordinate system (LVLH system); y represents the position component of the flight direction in the relative coordinate system (LVLH system); z represents the position component of the orbital angular momentum direction in the relative coordinate system (LVLH system); v x represents the velocity component of the orbital radial direction in the relative coordinate system (LVLH system); v y represents the velocity component of the orbital flight direction in the relative coordinate system (LVLH system); v z represents the velocity component of the orbital angular momentum in the relative coordinate system (LVLH system); Δv P (t i ) The specific form is Δv P (t i )=[Δv Px (t i ),Δv Py (t i ),Δv Pz (t i )] T , indicating that the tracking star is at t i Pulse speed increment control applied at every moment; Δv E (t i ) is in the form of Δv E (t i )=[Δv Ex (t i ),Δv Ey (t i ),Δv Ez (t i )] T , indicating that the escape star is at t i Pulse speed increment control applied at all times; ΔV P Represents the column vector of the pulse velocity increment control of the tracking star at all times; ΔV Erepresents the column vector composed of the pulse velocity increment control of the escape star at all times; ψ P (ΔV P ) represents the constraint function of the tracking star pulse velocity increment control; ψ E (ΔV E ) represents the constraint function for the escape star pulse velocity increment control; ||S||2 represents a three-dimensional real vector The 2-norm of

[0011] Furthermore, the constraint function ψ of the tracking star pulse velocity increment control is P (ΔV P ) and the constraint function ψ for the escape star pulse velocity increment control E (ΔV E ) is modeled based on the actual maneuverability of the spacecraft, wherein the actual maneuverability of the spacecraft includes the upper limit constraint on the control component of a single pulse velocity increment, the upper limit constraint on the control size of a single pulse velocity increment, the same size of a single pulse velocity increment, freedom of direction, and an upper limit on the total consumption of the pulse velocity increment.

[0012] Furthermore, there is an upper limit constraint on the control component of the single pulse velocity increment, which is in the form of:

[0013]

[0014] Where Δv Pxmax ——The maximum value of the tracking star's single pulse velocity increment in the x-direction;

[0015] Δv Pymax ——The maximum value of the tracking star's single pulse velocity increment in the y direction;

[0016] Δv Pzmax ——The maximum value of the tracking star's single pulse velocity increment in the z direction;

[0017] Δv Exmax ——The maximum value of the velocity increment of a single pulse of the escape star in the x-direction;

[0018] Δv Eymax ——The maximum value of the velocity increment of a single pulse of the escape star in the y direction;

[0019] Δv Ezmax ——The maximum value of the velocity increment of a single pulse of the escape star in the z direction;

[0020] There is an upper limit constraint on the control size of a single pulse speed increment, which is in the form of:

[0021]

[0022] Where: Δv Pmax ——The maximum value of the velocity increment of a single pulse of the tracking star;

[0023] Δv Emax ——The maximum value of the velocity increment of a single pulse of the escaping star;

[0024] The speed increment of a single pulse is the same in size and free in direction. The specific form is:

[0025]

[0026] Where: Δv Pmax ——The maximum value of the velocity increment of a single pulse of the tracking star;

[0027] Δv Emax ——The maximum value of the velocity increment of a single pulse of the escaping star;

[0028] α P (t i )——the pitch angle of the tracking satellite’s single pulse velocity increment;

[0029] β P (t i )——yaw angle of the tracking satellite’s single pulse velocity increment;

[0030] α E (t i ) — the pitch angle of the velocity increment of a single pulse of the escape star;

[0031] β E (t i ) — the yaw angle of the escape star’s single pulse velocity increment;

[0032] There is an upper limit on the total consumption of pulse speed increments, which is as follows:

[0033] or

[0034]

[0035] Where: ΔV Pmax ΔV is the total reserve of the tracking star pulse velocity increment; Emax ——The total reserve of the runaway star's pulse velocity increment.

[0036] Preferably, the parameter information of the pursuit-escape game includes the pursuit-escape starting time t0 and the end time t f ; N pulse application times t1, t2,…, t N ; Reference satellite orbit semi-major axis a; Tracking star initial state X P (t0); initial state of the escape star X E(t0); the upper limit of the pulse velocity increment of the tracking star Δv Pmax ; The upper limit of the pulse velocity increment of the escape star Δv Emax .

[0037] Preferably, the calculation formula for the inner and outer double-layer optimization of the spacecraft pulse orbit pursuit game model is as follows:

[0038]

[0039] stG(ΔV P ,ΔV E )≤0

[0040] in, represents the outer optimization problem, represents the inner optimization problem; G(ΔV P ,ΔV E )≤0 is to integrate all the constraints in the spacecraft pulse orbit pursuit game model into a formal expression.

[0041] Furthermore, the spacecraft pulse orbit pursuit and escape game model is optimized using the genetic algorithm GA for the outer layer, and the genetic algorithm hybrid mode search algorithm PG for the inner layer.

[0042] Furthermore, the specific steps for internal and external double-layer optimization are as follows:

[0043] S1. Determine the specific parameters of the genetic algorithm GA solver, where the specific parameters include determining the population size L, evolutionary generations D, crossover coefficient C and variation coefficient K; and set the objective function As a fitness function;

[0044] S2, for the independent variable ΔV P Corresponding genetic algorithm chromosome Initialize

[0045] S3. For each given chromosome Solve the inner layer optimization problem based on the PGA algorithm and obtain the optimal ΔV E Record Then calculate its objective function value, that is,

[0046] S4. Use the objective function value to evaluate chromosome individuals The pros and cons of all chromosomes Perform selection, crossover, and mutation operations to generate new populations and the current optimal results

[0047] S5. Judge the output result. If the output result does not reach the evolutionary generation or other conditions for GA algorithm termination do not appear, return to S3 to solve the inner optimization problem according to the PGA algorithm and recalculate its objective function value; otherwise, output the individual with the maximum fitness in the current result as the optimal solution. At the same time, mark the corresponding inner optimization optimal solution Will It is output as the Nash equilibrium solution of the pursuit-escape game to complete the spacecraft orbit pursuit-escape game.

[0048] Furthermore, the specific steps of the PGA algorithm to solve the inner optimization problem are as follows:

[0049] S31, ΔV is obtained by searching with the genetic algorithm GA E An approximate optimal value of

[0050] S32, with As the initial value, the pattern search algorithm PA is used to obtain a better optimal value And calculate its objective function value, that is

[0051] Compared with the prior art, the present invention has the following beneficial technical effects:

[0052] The present invention provides a spacecraft orbit pursuit and escape game method based on pulse thrust. By establishing a spacecraft pulse orbit pursuit and escape game model, the original minimax optimization problem is transformed into a two-level optimization problem, and then a genetic algorithm with global optimization capability and a pattern search algorithm with fast convergence characteristics are adopted to jointly solve the problem, which significantly improves the problem-solving efficiency. The problem of aerospace game is effectively solved by combining the pulse control method with the spacecraft pulse orbit pursuit and escape game model, thereby laying a theoretical foundation for the realization of engineering applications such as taking over space fault spacecraft and clearing space failed spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a flow chart of the spacecraft orbit pursuit and escape game method based on pulse thrust in the present invention;

[0054] Figure 2 This is a spacecraft orbit pursuit scenario based on pulse velocity increment control to which the present invention is applicable;

[0055] Figure 3 Schematic diagram of the three-dimensional trajectory of the spacecraft chasing and escaping under the 5-pulse velocity increment control of the present invention;

[0056] Figure 4 Schematic diagram of the two-dimensional trajectory of the spacecraft chasing and escaping under the 5-pulse velocity increment control of the present invention;

[0057] Figure 5 Schematic diagram of the relative distance change of the spacecraft chasing and escaping under the 5-pulse velocity increment control of the present invention;

[0058] Figure 6 Schematic diagram of a two-dimensional motion trajectory of the pursuing party gradually approaching the escaping party assuming that the escaping party is stationary in the present invention;

[0059] Figure 7 Schematic diagram of the change in relative distance between the pursuing party and the escaping party assuming that the escaping party is stationary in the present invention; DETAILED DESCRIPTION

[0060] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0061] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0062] The present invention is described in further detail below with reference to the accompanying drawings:

[0063] The present invention provides a spacecraft orbit pursuit and escape game method based on pulse thrust, which can effectively solve the spacecraft pursuit and escape problem under the action of pulse thrust. It is an effective extension of the continuous thrust pursuit and escape game model and method in the existing technology.

[0064] Specifically, such as Figure 1 As shown, the spacecraft orbit pursuit and escape game method based on pulse thrust includes the following steps:

[0065] Step 1: Establish a spacecraft pulse orbit pursuit and escape game model;

[0066] Specifically, the calculation formula of the spacecraft pulse orbit pursuit and escape game model is as follows:

[0067]

[0068] Where J represents the bilateral optimization index of the pursuit-escape game; P represents the subscript of the pursuit star; E represents the subscript of the escape star; N represents the total number of pulse velocity increment control; X P Represents the state vector of the tracking star, specifically X P =[x P ,y P ,z P ,v Px ,v Py ,v Pz ] T ;X E represents the state vector of the escape star, specifically X E =[x E ,y E ,z E ,v Ex ,v Ey ,v Ez ] T ; t0 represents the initial moment of pursuit; t f Indicates the terminal moment of pursuit; t i represents the moment when each satellite applies pulse velocity increment control, i = 1, 2, ..., 5; x represents the position component of the orbital radial direction in the relative coordinate system (LVLH system); y represents the position component of the flight direction in the relative coordinate system (LVLH system); z represents the position component of the orbital angular momentum direction in the relative coordinate system (LVLH system); v x represents the velocity component of the orbital radial direction in the relative coordinate system (LVLH system); v y represents the velocity component of the orbital flight direction in the relative coordinate system (LVLH system); v z represents the velocity component of the orbital angular momentum in the relative coordinate system (LVLH system); Δv P (t i ) The specific form is Δv P (t i )=[Δv Px (t i ),Δv Py (t i ),Δv Pz (t i )] T , indicating that the tracking star is at t i Pulse speed increment control applied at every moment; Δv E (t i ) is in the form of Δv E (t i )=[Δv Ex (t i),Δv Ey (t i ),Δv Ez (t i )] T , indicating that the escape star is at t i Pulse speed increment control applied at all times; ΔV P Represents the column vector of the pulse velocity increment control of the tracking star at all times; ΔV E represents the column vector composed of the pulse velocity increment control of the escape star at all times; ψ P (ΔV P ) represents the constraint function of the tracking star pulse velocity increment control; ψ E (ΔV E ) represents the constraint function for the escape star pulse velocity increment control; ||S||2 represents a three-dimensional real vector The 2-norm of

[0069] Among them: matrix satisfy:

[0070] M=[I 3×3 ,0 3×3 ]; B = [0 3×3 ,I 3×3 ] T (2)

[0071] Where:

[0072]

[0073] The state transfer matrix Φ(t j ,t i ) is used to implement the i Time to t j The specific form of the state transition at the moment is constructed through the CW equation in orbital dynamics, namely:

[0074]

[0075] where Δt = t j -t i , represents the orbital angular velocity of the reference satellite, μ is the Earth's gravitational field coefficient, and a is the semi-major axis of the reference satellite's orbit.

[0076] Constraint function ψ for tracking star pulse velocity increment control P (ΔV P ) and the constraint function ψ for the escape star pulse velocity increment control E (ΔV E) Modeling is performed based on the actual maneuverability of the spacecraft, wherein the actual maneuverability of the spacecraft includes upper constraints on the control component of a single pulse velocity increment, upper constraints on the control size of a single pulse velocity increment, and upper limits on the total consumption of the same size, freedom of direction, and pulse velocity increments;

[0077] Among them, the control component of the single pulse velocity increment has an upper limit constraint, which is in the form of:

[0078]

[0079] Where Δv Pxmax ——The maximum value of the tracking star's single pulse velocity increment in the x-direction;

[0080] Δv Pymax ——The maximum value of the tracking star's single pulse velocity increment in the y direction;

[0081] Δv Pzmax ——The maximum value of the tracking star's single pulse velocity increment in the z direction;

[0082] Δv Exmax ——The maximum value of the velocity increment of a single pulse of the escape star in the x-direction;

[0083] Δv Eymax ——The maximum value of the velocity increment of a single pulse of the escape star in the y direction;

[0084] Δv Ezmax ——The maximum value of the velocity increment of a single pulse of the escape star in the z direction;

[0085] There is an upper limit constraint on the control size of a single pulse speed increment, which is in the form of:

[0086]

[0087] Where: Δv Pmax ——The maximum value of the velocity increment of a single pulse of the tracking star;

[0088] Δv Emax ——The maximum value of the velocity increment of a single pulse of the escaping star;

[0089] The speed increment of a single pulse is the same in size and free in direction. The specific form is:

[0090]

[0091] Where: Δv Pmax ——The maximum value of the velocity increment of a single pulse of the tracking star;

[0092] Δv Emax——The maximum value of the velocity increment of a single pulse of the escaping star;

[0093] α P (t i )——the pitch angle of the tracking satellite’s single pulse velocity increment;

[0094] β P (t i )——yaw angle of the tracking satellite’s single pulse velocity increment;

[0095] α E (t i ) — the pitch angle of the velocity increment of a single pulse of the escape star;

[0096] β E (t i ) — the yaw angle of the escape star’s single pulse velocity increment;

[0097] There is an upper limit on the total consumption of pulse speed increments, which is as follows:

[0098]

[0099] or:

[0100] Where: ΔV Pmax ΔV is the total reserve of the tracking star pulse velocity increment; Emax ——The total reserve of the runaway star's pulse velocity increment.

[0101] Formula (8) addresses the same situation as Formula (5), indicating that there are limits on the pulse velocity increments of the spacecraft's thrusters in three directions. The difference is that Formula (5) limits the size of the single thrust output, while Formula (8) limits the size of the total thrust output. Note that Formula (5) and Formula (8) can also be used together to indicate that there are constraints on both the single output and the total output.

[0102] Similarly, formula (9) addresses the same situation as formula (6), indicating that there is a limit on the pulse velocity increment of the spacecraft's thruster in the vector direction. The difference is that formula (6) limits the size of the single thrust output, while formula (9) limits the size of the total thrust output. Formula (6) and formula (9) can also be used together to indicate that there are constraints on both the single output and the total output.

[0103] Step 2: Obtain the parameter information of the pursuit-escape game, input the parameter information into the spacecraft pulse orbit pursuit-escape game model, and perform internal and external double-layer optimization on the spacecraft pulse orbit pursuit-escape game model to complete the spacecraft orbit pursuit-escape game.

[0104] Specifically, the parameter information of the pursuit game includes the pursuit start time t0 and the end time tf ; N pulse application times t1, t2,…, t N ; Reference satellite orbit semi-major axis a; Tracking star initial state X P (t0); initial state of the escape star X E (t0); the upper limit of the pulse velocity increment of the tracking star Δv Pmax ; The upper limit of the pulse velocity increment of the escape star Δv Emax .

[0105] Specifically, the calculation formula for the inner and outer double-layer optimization based on the spacecraft pulse orbit pursuit and escape game model is as follows:

[0106]

[0107] in, represents the outer optimization problem, represents the inner optimization problem; G(ΔV P ,ΔV E )≤0 is to integrate all the constraints in the spacecraft pulse orbit pursuit game model into a formal expression.

[0108] Specifically, the spacecraft pulse orbit pursuit and escape game model uses the genetic algorithm GA for outer layer optimization and the genetic algorithm hybrid mode search algorithm PG for inner layer optimization. The specific steps are as follows:

[0109] S1. Determine the specific parameters of the genetic algorithm GA solver, where the specific parameters include determining the population size L, evolutionary generations D, crossover coefficient C and variation coefficient K; and set the objective function As a fitness function;

[0110] S2, for the independent variable ΔV P Corresponding genetic algorithm chromosome Initialize

[0111] S3. For each given chromosome Solve the inner layer optimization problem based on the PGA algorithm and obtain the optimal ΔV E Record Then calculate its objective function value, that is,

[0112] S4. Use the objective function value to evaluate chromosome individuals The pros and cons of all chromosomes Perform selection, crossover, and mutation operations to generate new populations and the current optimal results

[0113] S5. Judge the output result. If the output result does not reach the evolutionary generation or other conditions for GA algorithm termination do not appear, return to S3 to solve the inner optimization problem according to the PGA algorithm and recalculate its objective function value; otherwise, output the individual with the maximum fitness in the current result as the optimal solution. At the same time, mark the corresponding inner optimization optimal solution Will It is output as the Nash equilibrium solution of the pursuit-escape game to complete the spacecraft orbit pursuit-escape game.

[0114] Among them, the specific steps of the PGA algorithm to solve the inner layer optimization problem are as follows:

[0115] S31, ΔV is obtained by searching with the genetic algorithm GA E An approximate optimal value of

[0116] S32, with As the initial value, the pattern search algorithm PA is used to obtain a better optimal value And calculate its objective function value, that is

[0117] Example

[0118] Assume that at an initial time t0 = 0, there are two satellites near a circular orbit with an orbital altitude of 500 km (corresponding to the semi-major axis of the orbit a = 6878.137 km), namely the pursuer P and the escaper E. Their initial states are shown in Table 1. The process of the two parties chasing and escaping in the form of pulse thrust is as follows: Figure 2 As shown. Now the pursuit mission requires the pursuit star to be in t f = 1 hour later, the pursuer star is as close as possible to the escape star. Assume that both parties apply N = 5 pulse velocity increments, and that the pulse application times are evenly distributed, i.e., t1 = 0, t2 = 12 minutes, ..., t5 = 48 minutes. Assume that the control component of a single pulse velocity increment is subject to upper constraints, with the pursuer star's velocity not exceeding 10 m / s and the escape star's velocity not exceeding 1 m / s.

[0119] j <![CDATA[x j (t0)]]> <![CDATA[y j (t0)]]> <![CDATA[z j (t0)]]> <![CDATA[v xj (t0)]]> <![CDATA[v yj (t0)]]> <![CDATA[v zj (t0)]]> P 0 100 0 0 0 0 E 0 0 0 0 0 0

[0120] Table 1 Initial relative position and velocity of the pursuing star P and the escaping star E (km, km / s)

[0121] Based on the above conditions, the specific application steps of the present invention are given below.

[0122] 1. First, according to step 1 of the invention, the spacecraft pulse orbit pursuit and escape game model under the above problem parameters is established as follows:

[0123]

[0124] Among them: matrix satisfy:

[0125] M=[I 3×3 ,0 3×3 ],B=[0 3×3 ,I 3×3 ] T

[0126] Where:

[0127]

[0128] The state transfer matrix Φ(t j ,t i ) is used to implement the i Time to t j The specific form of the state transition at the moment is constructed through the CW equation in orbital dynamics, namely:

[0129]

[0130] where Δt = t j -t i , represents the orbital angular velocity of the reference satellite, μ is the Earth’s gravitational field coefficient, and a=6878.137 km is the semi-major axis of the reference satellite’s orbit.

[0131] Where J represents the bilateral optimization index of the pursuit-escape game; P represents the subscript of the pursuit star; E represents the subscript of the escape star; N represents the total number of pulse velocity increment control, which is 5 in this example; X P Represents the state vector of the tracking star, specifically X P =[x P ,y P ,z P ,v Px ,v Py ,v Pz ] T ;X E represents the state vector of the escape star, specifically X E =[x E ,y E ,z E ,v Ex ,v Ey ,v Ez ] T ; t0 represents the initial moment of pursuit; t f Indicates the terminal moment of pursuit; t irepresents the moment when each satellite applies pulse velocity increment control, i = 1, 2, ..., 5; x represents the position component of the orbital radial direction in the relative coordinate system (LVLH system); y represents the position component of the flight direction in the relative coordinate system (LVLH system); z represents the position component of the orbital angular momentum direction in the relative coordinate system (LVLH system); v x represents the velocity component of the orbital radial direction in the relative coordinate system (LVLH system); v y represents the velocity component of the orbital flight direction in the relative coordinate system (LVLH system); v z represents the velocity component of the orbital angular momentum in the relative coordinate system (LVLH system); Δv P (t i ) The specific form is Δv P (t i )=[Δv Px (t i ),Δv Py (t i ),Δv Pz (t i )] T , indicating that the tracking star is at t i Pulse speed increment control applied at every moment; Δv E (t i ) is in the form of Δv E (t i )=[Δv Ex (t i ),Δv Ey (t i ),Δv Ez (t i )] T , indicating that the escape star is at t i Pulse speed increment control applied at all times; ΔV P Represents the column vector of the pulse velocity increment control of the tracking star at all times; ΔV E represents the column vector composed of the pulse velocity increment control of the escape star at all times; ψ P (ΔV P ) represents the constraint function of the tracking star pulse velocity increment control; ψ E (ΔV E ) represents the constraint function for the escape star pulse velocity increment control; ||S||2 represents a three-dimensional real vector The 2-norm of

[0132] 2. Then according to step 2 of the invention, the pulse velocity increment control constraint ψ in the above pursuit model P (ΔV P ),ψ E (ΔV E), which is consistent with the situation where the control component of the single pulse velocity increment has an upper limit constraint, specifically:

[0133]

[0134] 3. Next, according to step 3 of the invention, the pursuit and escape game problem is solved. The specific solution steps are as follows:

[0135] S1, input the relevant parameters of the pursuit game, including the pursuit start time t0 = 0 and the end time t f = 3600s; 5 pulse application times t1 = 0, t2 = 12min, ..., t5 = 48min; reference satellite orbit semi-major axis a = 6878.137km; tracking satellite initial state X P (t0); initial state of the escape star X E (t0) is shown in Table 1; the maximum value of the single pulse velocity increment component Δv of the chaser Pxmax =Δv Pymax =Δv Pzmax =10m / s, the maximum value of the single pulse velocity increment component of the escape star Δv Exmax =Δv Eymax =Δv Ezmax =1m / s.

[0136] S2, the calculation formula for the spacecraft pulse orbit pursuit game model to perform internal and external double-layer optimization is as follows:

[0137]

[0138] stG(ΔV P ,ΔV E )≤0

[0139] in, represents the outer optimization problem, represents the inner optimization problem; G(ΔV P ,ΔV E )≤0 is to integrate all the constraints in the spacecraft pulse orbit pursuit game model into a formal expression.

[0140] S3, using a genetic algorithm (GA) to solve the above outer layer optimization problem, and using a genetic algorithm hybrid pattern search algorithm (PGA) to solve the above inner layer optimization problem, wherein the specific steps of the GA-based outer layer optimization are:

[0141] S31, determine the specific parameters of the GA solver, such as population size L = 10, evolutionary generation D = 10, cross coefficient C = 0.8, and variation coefficient K = 0.2, and convert the objective function J(ΔV P ,ΔV E ) as the fitness function;

[0142] S32, initialize the independent variable ΔV P Corresponding genetic algorithm chromosome

[0143] S33, for each given chromosome Solve the inner layer optimization problem based on the PGA algorithm and obtain the optimal ΔV E Record Then calculate its objective function value, that is, Specifically, the solution process using the PGA algorithm can be divided into two sub-steps:

[0144] S331, first use the GA algorithm to search and obtain ΔV E An approximate optimal value of

[0145] S332, then As the initial value, the pattern search algorithm (PA) is used to obtain a better optimal value And calculate its objective function value, that is

[0146] S34, use this function value to evaluate chromosome individuals The pros and cons of all chromosomes Perform selection, crossover, and mutation operations to generate a new population (outer optimization) and the current optimal result

[0147] S35: If the evolutionary generation has not been reached or other conditions for the GA algorithm to terminate have not occurred, then return to S33; otherwise, the individual with the maximum fitness in the current result is output as the optimal solution. At the same time, mark the corresponding inner optimization optimal solution Will Output as the Nash equilibrium solution of the pursuit-escape game. The specific calculation results are shown in Table 2 and Table 3.

[0148]

[0149]

[0150] Table 2 Calculation results of the 5-pulse velocity increment of the pursuer P and the escaper E (m / s)

[0151] According to the calculation results of the pulse velocity increment of both parties in Table 2, the motion evolution of the pursuit spacecraft and the escape spacecraft is deduced, and the results are as follows: Figure 3-Figure 5 As shown. Among them, Figure 3The motion trajectories and motion directions of the pursuing and escaping spacecraft in the three-dimensional relative motion space are given; Figure 4 The motion trajectories and directions of the pursuing and escaping spacecraft on the xoy plane are given; Figure 5 A curve showing the distance between the pursuers and fugitives changing with time is given.

[0152]

[0153]

[0154] Table 3 Calculation results of the 5-pulse velocity increment of the pursuing star when the escaping star E is stationary (m / s)

[0155] According to the calculation results of the pulse velocity increment of both parties in Table 3, the motion evolution of the pursuit spacecraft and the escape spacecraft is deduced, and the results are as follows: Figure 6-Figure 7 As shown. Figure 6 The motion trajectory and motion direction of the tracking spacecraft and the escaping spacecraft on the xoy plane are shown; Figure 7 The evolution of the distance between the pursuers and fugitives over time.

[0156] In summary, the present invention provides a spacecraft orbit pursuit game method based on pulse thrust. By establishing a spacecraft pulse orbit pursuit game model, the original minimax optimization problem is transformed into a two-level optimization problem, and then a genetic algorithm with global optimization capability and a pattern search algorithm with fast convergence characteristics are jointly solved, which significantly improves the efficiency of problem solving. The problem of aerospace game is effectively solved by combining the pulse control method with the spacecraft pulse orbit pursuit game model, thereby laying a theoretical foundation for the realization of engineering applications such as taking over space fault spacecraft and clearing space failure spacecraft. The optimization index is described by the inter-satellite distance of the terminal time, the optimization variable is the pulse velocity increment of the pursuit and escape parties at a fixed time interval, the state transition constraint is described by the state transition matrix under the relative motion model, and the pulse maneuverability constraint is modeled by the pulse velocity increment size, direction and total consumption. Then, a solution method for the above-mentioned min-max optimization problem was established. The model also uses a state transfer matrix, which makes the dynamic evolution calculation relatively simple and convenient. The model solution adopts a two-layer optimization structure, avoiding the difficulty of directly solving the min-max problem. It further combines the genetic algorithm with the pattern search algorithm to improve the problem's global search and rapid convergence capabilities.

[0157] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A spacecraft orbit pursuit and escape game method based on pulse thrust, characterized in that: The steps include: Step 1: Establish a spacecraft pulse orbit pursuit and escape game model under the action of pulse thrust; Step 2: Obtain the parameter information of the spacecraft pursuit and escape, input the parameter information into the spacecraft pulse orbit pursuit and escape game model, and perform internal and external double-layer optimization on the spacecraft pulse orbit pursuit and escape game model to complete the spacecraft orbit pursuit and escape game; The calculation formula of the spacecraft pulse orbit pursuit and escape game model is as follows: Where J represents the bilateral optimization index of the pursuit-escape game; P represents the subscript of the pursuit star; E represents the subscript of the escape star; N represents the total number of pulse velocity increment control; X P Represents the state vector of the tracking star, specifically X P =[x P ,y P ,z P ,v Px ,v Py ,v Pz ] T ;X E represents the state vector of the escape star, specifically X E =[x E ,y E ,z E ,v Ex ,v Ey ,v Ez ] T ; t0 represents the initial moment of pursuit; t f Indicates the terminal moment of pursuit; t i represents the moment when each satellite applies pulse velocity increment control, i = 1, 2, ..., 5; x represents the position component of the orbital radial direction in the relative coordinate system (LVLH system); y represents the position component of the flight direction in the relative coordinate system (LVLH system); z represents the position component of the orbital angular momentum direction in the relative coordinate system (LVLH system); v x represents the velocity component of the orbital radial direction in the relative coordinate system (LVLH system); v y represents the velocity component of the orbital flight direction in the relative coordinate system (LVLH system); v z represents the velocity component of the orbital angular momentum in the relative coordinate system (LVLH system); Δv P (t i ) The specific form is Δv P (t i )=[Δv Px (t i ),Δv Py (t i ),Δv Pz (t i )] T , indicating that the tracking star is at t i Pulse speed increment control applied at every moment; Δv E (t i ) is in the form of Δv E (t i )=[Δv Ex (t i ),Δv Ey (t i ),Δv Ez (t i )] T , indicating that the escaped star is at t i Pulse speed increment control applied at all times; ΔV P Represents the column vector of the pulse velocity increment control of the tracking star at all times; ΔV E represents the column vector composed of the pulse velocity increment control of the escape star at all times; ψ P (ΔV P ) represents the constraint function of tracking star pulse velocity increment control; ψ E (ΔV E ) represents the constraint function for the escape star pulse velocity increment control; ||S||2 represents a three-dimensional real vector The 2-norm of 2. A spacecraft orbit pursuit and escape game method based on pulse thrust according to claim 1, characterized in that: Constraint function ψ for tracking star pulse velocity increment control P (ΔV P ) and the constraint function ψ for the escape star pulse velocity increment control E (ΔV E ) is modeled based on the actual maneuverability of the spacecraft, wherein the actual maneuverability of the spacecraft includes the upper limit constraint on the control component of a single pulse velocity increment, the upper limit constraint on the control size of a single pulse velocity increment, the same size of a single pulse velocity increment, freedom of direction, and an upper limit on the total consumption of the pulse velocity increment.

3. The spacecraft orbit pursuit and escape game method based on pulse thrust according to claim 2 is characterized in that: The control component of a single pulse velocity increment has an upper limit constraint, which is in the form of: Where Δv Pxmax ——The maximum value of the tracking star's single pulse velocity increment in the x-direction; Δv Py max ——The maximum value of the tracking star's single pulse velocity increment in the y direction; Δv Pz max ——The maximum value of the tracking star's single pulse velocity increment in the z direction; Δv Ex max ——The maximum value of the velocity increment of a single pulse of the escape star in the x direction; Δv Ey max ——The maximum value of the velocity increment of a single pulse of the escape star in the y direction; Δv Ez max ——The maximum value of the velocity increment of a single pulse of the escape star in the z direction; There is an upper limit constraint on the control size of a single pulse speed increment, which is in the form of: Where: Δv P max ——The maximum value of the velocity increment of a single pulse of the tracking star; Δv E max ——The maximum value of the velocity increment of a single pulse of the escaping star; The speed increment of a single pulse is the same in size and free in direction. The specific form is: Where: Δv P max ——The maximum value of the velocity increment of a single pulse of the tracking star; Δv E max ——The maximum value of the velocity increment of a single pulse of the escaping star; α P (t i )——the pitch angle of the tracking satellite’s single pulse velocity increment; β P (t i )——yaw angle of the tracking satellite’s single pulse velocity increment; α E (t i ) — the pitch angle of the velocity increment of a single pulse of the escape star; β E (t i ) — the yaw angle of the escape star’s single pulse velocity increment; There is an upper limit on the total consumption of pulse speed increments, which is as follows: or Where: ΔV Pmax ΔV is the total reserve of the tracking star pulse velocity increment; Emax ——The total reserve of the runaway star's pulse velocity increment.

4. The spacecraft orbit pursuit and escape game method based on pulse thrust according to claim 1 is characterized in that: The parameter information of the pursuit game includes the pursuit start time t0 and the end time t f ; N pulse application times t1, t2,…, t N ; Reference satellite orbit semi-major axis a; Tracking star initial state X P (t0); initial state of the escape star X E (t0); the upper limit of the pulse velocity increment of the tracking star Δv Pmax ; The upper limit of the pulse velocity increment of the escape star Δv Emax .

5. The spacecraft orbit pursuit and escape game method based on pulse thrust according to claim 1 is characterized in that: The calculation formula for the inner and outer double-layer optimization of the spacecraft pulse orbit pursuit game model is as follows: stG(ΔV P ,ΔV E )≤0 in, represents the outer optimization problem, represents the inner optimization problem; G(ΔV P ,ΔV E )≤0 is to integrate all the constraints in the spacecraft pulse orbit pursuit game model into a formal expression.

6. The spacecraft orbit pursuit and escape game method based on pulse thrust according to claim 5 is characterized in that: The genetic algorithm GA is used to optimize the outer layer of the spacecraft pulse orbit pursuit and escape game model, and the genetic algorithm hybrid mode search algorithm PG is used to optimize the inner layer.

7. The spacecraft orbit pursuit and escape game method based on pulse thrust according to claim 6 is characterized in that: The specific steps for internal and external double-layer optimization are as follows: S1. Determine the specific parameters of the genetic algorithm GA solver, where the specific parameters include determining the population size L, evolutionary generations D, crossover coefficient C and variation coefficient K; and set the objective function As a fitness function; S2, for the independent variable ΔV P Corresponding genetic algorithm chromosome Initialize S3. For each given chromosome Solve the inner layer optimization problem based on the PGA algorithm and obtain the optimal ΔV E Record Then calculate its objective function value, that is, S4. Use the objective function value to evaluate chromosome individuals The pros and cons of all chromosomes Perform selection, crossover, and mutation operations to generate new populations and the current optimal results S5. Judge the output result. If the output result does not reach the evolutionary generation or other conditions for GA algorithm termination do not appear, return to S3 to solve the inner optimization problem according to the PGA algorithm and recalculate its objective function value. Otherwise, the individual with the maximum fitness in the current result is output as the optimal solution At the same time, mark the corresponding inner optimization optimal solution Will It is output as the Nash equilibrium solution of the pursuit-escape game to complete the spacecraft orbit pursuit-escape game.

8. The spacecraft orbit pursuit and escape game method based on pulse thrust according to claim 7 is characterized in that: The specific steps of the PGA algorithm to solve the inner optimization problem are as follows: S31, ΔV is obtained by searching with the genetic algorithm GA E An approximate optimal value of S32, with As the initial value, the pattern search algorithm PA is used to obtain a better optimal value And calculate its objective function value, that is

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