A spacecraft escort problem solving method based on policy switching

Abstract

The application discloses a spacecraft escort problem solving method based on strategy switching and belongs to the technical field of spaceflight. Complex performance indexes are decomposed according to distance on a time scale, and are divided into two stages according to the distance between an attacking star and a defending star and the size of a safety distance. At a certain time, the attacking star is only in one stage, and only one of the two goals of pursuing a main star or avoiding a defending star is considered. The above method converts the escort problem into a pursuit and evasion game problem and a trajectory planning problem, greatly simplifies the solving process, and achieves good results in simulation. Application of the model and the method can provide an effective defense threat solution for on-orbit spacecraft adopting main and slave star cooperation.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a method for solving spacecraft escort problems based on strategy switching. Background Technology

[0002] Spacecraft orbital pursuit is a mathematical problem with a wide range of applications. In classic orbital pursuit problems, the participants generally share the same goal: a struggle for distance. However, some spacecraft in orbit, due to their high-value fuel requirements for on-orbit operations, cannot autonomously evade attacks from attacking satellites. They need to release microsatellites or nanosatellites as defensive satellites to coordinate counterattacks, while the spacecraft itself, as the primary satellite, is mainly responsible for information transmission. The struggle between the defensive and attacking satellites for the primary satellite is called the spacecraft escort problem. The attacking satellite's goal is to make every effort to get as close to the primary satellite as possible while ensuring it is not intercepted or destroyed by the defensive satellites; the defensive satellite's goal is to intercept and destroy the attacking satellite before it gets too close to the primary satellite.

[0003] Currently, most modeling and solutions for spacecraft escort problems use differential game methods. However, since it is a non-zero-sum game in the game theory category, the performance indicators of the attacking and defending stars are not the same, so solving for its optimal control strategy is often very complex. Summary of the Invention

[0004] In order to overcome the shortcomings of the prior art, the purpose of this invention is to provide a solution method for the spacecraft escort problem based on strategy switching, so as to solve the problem that the modeling and solution of the spacecraft escort problem in the prior art uses the differential game method, and the solution of the optimal control strategy is very complicated.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A method for solving the spacecraft escort problem based on strategy switching includes:

[0007] Obtain parameters for the spacecraft escort problem of the primary, attacking, and defending stars;

[0008] A spacecraft escort problem model is established based on the spacecraft escort problem parameters of the primary star, attacking star, and defending star;

[0009] Substituting the initial parameters from the spacecraft escort problem parameters of the primary star, attacking star, and defending star into the spacecraft escort problem model, we obtain the control strategies of the attacking and defending stars in the two stages.

[0010] The corresponding control strategy is switched by determining the stage of the attacking and defending stars in real time.

[0011] Preferably, the problem parameters include: the semi-major axis of the reference satellite orbit, the initial state of the attacking satellite, the initial state of the defending satellite, the position of the primary satellite, the upper limit of the magnitude of the acceleration of the attacking satellite, the upper limit of the magnitude of the acceleration of the defending satellite, and the safe distance between the attacking and defending satellites.

[0012] Preferably, the establishment of the spacecraft escort problem model based on the spacecraft escort problem parameters of the primary star, attacking star, and defending star is as follows:

[0013] when hour,

[0014]

[0015] when hour,

[0016]

[0017]

[0018] Where a is the subscript of the attacking star; d is the subscript of the defending star; m is the subscript of the primary star; X a X is the state vector of the attacking star; d Here, x represents the state vector of the defense star; x is the radial position component of the orbit in the relative coordinate system; y is the directional position component of the flight in the relative coordinate system; z is the directional position component of the orbital angular momentum in the relative coordinate system; v x The radial velocity component of the orbit in the relative coordinate system; v y The velocity component in the orbital flight direction in the relative coordinate system; v z The velocity component in the direction of the orbital angular momentum in the relative coordinate system; u a The continuous control amount applied to the attacking star; u d B is the continuous control input applied to the defensive satellite; A is the control matrix for both the attacking and defensive satellites; B is the dynamic constraint matrix for the relative motion of the spacecraft; d safe The safe distance between the attacking and defensive stars is set; J a J is the performance index of the attacking satellite when the distance between the attacking and defending satellites is greater than the safe distance; d J represents the performance index of the defensive satellite when the distance between the attacking and defensive satellites is greater than the safe distance; J represents the performance index of both satellites when the distance between the attacking and defensive satellites is less than the safe distance; u amax The maximum acceleration that can be applied to an attacking star; u dmax The maximum acceleration applied by the defensive star; ‖S‖ represents the acceleration applied to a three-dimensional real vector. 2-norm; Q, R d and R a All are symmetric positive semi-definite matrices.

[0019] Preferably, the symmetric positive semi-definite matrix satisfy:

[0020] Q = k1I 6×6 R d =k2I 3×3 R a =k3I 3×3 (4)

[0021] In the formula:

[0022]

[0023] k1 = 10 -5 k2 = 1, k3 = 0.8

[0024] A is specifically constructed using the CW equations in orbital dynamics, namely:

[0025]

[0026]

[0027] Where n is the orbital angular velocity of the reference satellite; μ is the Earth's gravitational field coefficient; a0 is the semi-major axis of the reference satellite's orbit; and k1, k2, and k3 are weighting coefficients.

[0028] Preferably, the initial parameters obtained from the spacecraft escort problem parameters of the primary star, attacking star, and defending star are substituted into the spacecraft escort problem model to obtain the control strategies of the attacking and defending stars in the two stages, as follows:

[0029] S1: Substitute the initial parameters from the spacecraft escort problem parameters of the primary star, attacking star, and defending star into the spacecraft escort problem model;

[0030] S2: When The time is stage α.

[0031] when The time is stage β;

[0032] S3: Use dynamic programming to solve the bilateral optimization problem of stage α in S2, and obtain the control strategies of the attacking star and the defending star in stage α;

[0033] S4: Determine the control strategy for the attacking and defensive stars in phase β.

[0034] Preferably, in S3, the specific steps are as follows:

[0035] S301, the Hamiltonian function is defined as follows:

[0036]

[0037] S302, List the optimality conditions for the bilateral optimization problem:

[0038]

[0039] S303, Substituting the Hamiltonian function into the above optimality conditions yields the formal solution of the optimal control strategy for both parties:

[0040]

[0041] S304, Substituting the optimal control strategy solutions of both parties into the Hamiltonian function yields the Hamilton-Jacobi equation:

[0042]

[0043] S305, In order to obtain the feedback control strategy, assume that the costate variables have the following form under optimal conditions:

[0044]

[0045] S306, Substituting the above equation into the formal solution yields the optimal feedback control strategy for both the attacker and defender:

[0046]

[0047] S307, the Hamilton-Jacobi equation is rewritten accordingly, as follows:

[0048]

[0049] Summarized as follows:

[0050]

[0051] S308. The Lyapunov iterative method is used to solve for the unknown matrix P, that is, to solve the rewritten and simplified Hamilton-Jacobi equation, also known as the Riccati equation. The iterative algorithm is as follows:

[0052]

[0053] The initial value is selected as:

[0054]

[0055] Obtain the matrix

[0056] S309, the final control strategies for the attacking and defensive stars in phase α are as follows:

[0057]

[0058] Where X is the relative state vector between the defensive and offensive stars, and λ is the costate variable used to construct the Hamiltonian function; u a The continuous control amount applied to the attacking star; u d B is the continuous control input applied to the defensive satellite; A is the control matrix for both the attacking and defensive satellites; Q and R are the dynamic constraint matrices for the relative motion of the spacecraft. d and R a All are symmetric positive semi-definite matrices.

[0059] Preferably, the specific steps in S4 are as follows:

[0060] S401, since the performance indicators of the defense satellite are the same in phase α and phase β, its control strategy is designed to be the same in phase α and phase β, that is, the following feedback control law is also adopted:

[0061] Stage β

[0062] S402, design the control strategy for the attacking star in phase β, its control law is as follows:

[0063] u a * =-K p [x a -x m ,y a -y m ,z a -z m ] T -K d [v ax ,v ay ,v az ] T Stage β

[0064] Among them, K p and K d denoted as PD control coefficient; a is the subscript of the attacking star; d is the subscript of the defending star; m is the subscript of the primary star; x is the radial position component of the orbit in the relative coordinate system; y is the directional position component of the flight in the relative coordinate system; z is the directional position component of the orbit in the relative coordinate system; v x The radial velocity component of the orbit in the relative coordinate system; v y The velocity component in the orbital flight direction in the relative coordinate system; v z X represents the velocity component in the direction of orbital angular momentum in the relative coordinate system; X is the relative state vector between the defending and attacking stars; B is the control matrix between the attacking and defending stars.

[0065] Preferably, the stage of attacking and defending satellites is determined in real time by using the attacking and defending satellites in real time. With d safeDetermining the size relationship,

[0066] when The time is stage α.

[0067] when The time is stage β;

[0068] Where a is the subscript of the attacking star; d is the subscript of the defending star; m is the subscript of the principal star; x is the radial position component of the orbit in the relative coordinate system; y is the directional position component of the flight in the relative coordinate system; z is the directional position component of the orbit in the relative coordinate system; d safe The safe distance between the attacking star and the defending star.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] This invention provides a method for modeling and solving spacecraft escort problems based on strategy switching. It decomposes complex performance indicators over time according to distance, dividing the problem into two stages based on the distance between the attacking and defending satellites and the safe distance. At any given moment, the attacking satellite is only in one stage, considering only one of the two targets: chasing the host satellite or evading the defending satellite. This method transforms the escort problem into a pursuit-escape game and trajectory planning problem, greatly simplifying the solution process and achieving good results in simulations. The application of this model and method can provide an effective threat defense solution for on-orbit spacecraft employing master-slave satellite cooperation. Attached Figure Description

[0071] Figure 1 This is the game-theoretic scenario of spacecraft protection to which this invention applies;

[0072] Figure 2 This is a flowchart illustrating the specific implementation of the spacecraft protection problem in this invention;

[0073] Figure 3 This is a simulation trajectory diagram of the present invention;

[0074] Figure 4 The simulation acceleration variation diagram of the present invention. Detailed Implementation

[0075] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0076] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0077] The present invention will now be described in further detail with reference to the accompanying drawings:

[0078] A method for solving the spacecraft escort problem based on strategy switching includes:

[0079] Obtain parameters for the spacecraft escort problem of the primary, attacking, and defending stars;

[0080] The parameters in question include: the semi-major axis of the reference satellite orbit, the initial state of the attacking satellite, the initial state of the defending satellite, the position of the primary satellite, the upper limit of the magnitude of the acceleration of the attacking satellite, the upper limit of the magnitude of the acceleration of the defending satellite, and the safe distance between the attacking and defending satellites.

[0081] A spacecraft escort problem model is established based on the spacecraft escort problem parameters of the primary star, attacking star, and defending star;

[0082] Specifically as follows:

[0083] when hour,

[0084]

[0085] when hour,

[0086]

[0087]

[0088] Where a is the subscript of the attacking star; d is the subscript of the defending star; m is the subscript of the primary star; X a X is the state vector of the attacking star; d Here, x represents the state vector of the defense star; x is the radial position component of the orbit in the relative coordinate system; y is the directional position component of the flight in the relative coordinate system; z is the directional position component of the orbital angular momentum in the relative coordinate system; v x The radial velocity component of the orbit in the relative coordinate system; v yThe velocity component in the orbital flight direction in the relative coordinate system; v z The velocity component in the direction of the orbital angular momentum in the relative coordinate system; u a The continuous control amount applied to the attacking star; u d B is the continuous control input applied to the defensive satellite; A is the control matrix for both the attacking and defensive satellites; B is the dynamic constraint matrix for the relative motion of the spacecraft; d safe The safe distance between the attacking and defensive stars is set; J a J is the performance index of the attacking satellite when the distance between the attacking and defending satellites is greater than the safe distance; d J represents the performance index of the defensive satellite when the distance between the attacking and defensive satellites is greater than the safe distance; J represents the performance index of both satellites when the distance between the attacking and defensive satellites is less than the safe distance; u amax The maximum acceleration that can be applied to an attacking star; u dmax The maximum acceleration applied by the defensive star; ‖S‖ represents the acceleration applied to a three-dimensional real vector. 2-norm; Q, R d and R a All are symmetric positive semi-definite matrices.

[0089] The symmetric positive semidefinite matrix satisfy:

[0090] Q = k1I 6×6 R d =k2I 3×3 R a =k3I 3×3 (4)

[0091] In the formula:

[0092]

[0093] k1 = 10 -5 k2 = 1, k3 = 0.8

[0094] A is specifically constructed using the CW equations in orbital dynamics, namely:

[0095]

[0096]

[0097] Where n is the orbital angular velocity of the reference satellite; μ is the Earth's gravitational field coefficient; a0 is the semi-major axis of the reference satellite's orbit; and k1, k2, and k3 are weighting coefficients.

[0098] Substituting the initial parameters from the spacecraft escort problem parameters of the primary star, attacking star, and defending star into the spacecraft escort problem model, we obtain the control strategies of the attacking and defending stars in the two stages.

[0099] S1: Substitute the initial parameters from the spacecraft escort problem parameters of the primary star, attacking star, and defending star into the spacecraft escort problem model;

[0100] S2: When The time is stage α.

[0101] when The time is stage β;

[0102] S3: Use dynamic programming to solve the bilateral optimization problem of stage α in S2, and obtain the control strategies of the attacking star and the defending star in stage α;

[0103] S301, the Hamiltonian function is defined as follows:

[0104]

[0105] S302, List the optimality conditions for the bilateral optimization problem:

[0106]

[0107] S303, Substituting the Hamiltonian function into the above optimality conditions yields the formal solution of the optimal control strategy for both parties:

[0108]

[0109] S304, Substituting the optimal control strategy solutions of both parties into the Hamiltonian function yields the Hamilton-Jacobi equation:

[0110]

[0111] S305, In order to obtain the feedback control strategy, assume that the costate variables have the following form under optimal conditions:

[0112]

[0113] S306, Substituting the above equation into the formal solution yields the optimal feedback control strategy for both the attacker and defender:

[0114]

[0115] S307, the Hamilton-Jacobi equation is rewritten accordingly, as follows:

[0116]

[0117] Summarized as follows:

[0118]

[0119] S308. The Lyapunov iterative method is used to solve for the unknown matrix P, that is, to solve the rewritten and simplified Hamilton-Jacobi equation, also known as the Riccati equation. The iterative algorithm is as follows:

[0120]

[0121] The initial value is selected as:

[0122]

[0123] Obtain the matrix

[0124] S309, the final control strategies for the attacking and defensive stars in phase α are as follows:

[0125]

[0126] Where X is the relative state vector between the defensive and offensive stars, and λ is the costate variable used to construct the Hamiltonian function; u a The continuous control amount applied to the attacking star; u d B is the continuous control input applied to the defensive satellite; A is the control matrix for both the attacking and defensive satellites; Q and R are the dynamic constraint matrices for the relative motion of the spacecraft. d and R a All are symmetric positive semi-definite matrices.

[0127] S4: Determine the control strategies for the attacking and defending stars in phase β;

[0128] S401, since the performance indicators of the defense satellite are the same in phase α and phase β, its control strategy is designed to be the same in phase α and phase β, that is, the following feedback control law is also adopted:

[0129] Stage β

[0130] S402, design the control strategy for the attacking star in phase β, its control law is as follows:

[0131] u a * =-K p [x a -x m ,y a -y m ,z a -z m ] T -K d [v ax ,v ay ,v az ] T Stage β

[0132] Among them, K p and K d denoted as PD control coefficient; a is the subscript of the attacking star; d is the subscript of the defending star; m is the subscript of the primary star; x is the radial position component of the orbit in the relative coordinate system; y is the directional position component of the flight in the relative coordinate system; z is the directional position component of the orbit in the relative coordinate system; v x The radial velocity component of the orbit in the relative coordinate system; v y The velocity component in the orbital flight direction in the relative coordinate system; v z X represents the velocity component in the direction of orbital angular momentum in the relative coordinate system; X is the relative state vector between the defending and attacking stars; B is the control matrix between the attacking and defending stars.

[0133] The corresponding control strategy is switched by determining the stage of the attacking and defending stars in real time.

[0134]

Example

[0135] To obtain the spacecraft escort problem parameters for the primary, attacking, and defending stars, see [link to relevant documentation]. Figure 1 Assume that at an initial time t0 = 0, there are three satellites near a circular orbit with an altitude of 2000 km (corresponding to a semi-major axis a0 = 8731 km): the primary satellite m, the attacking satellite a, and the defending satellite d. An LVLH coordinate system is established with the primary satellite as the origin, and its initial state is shown in Table 1. Assume that there are upper limits on the acceleration control values ​​of the attacking and defending satellites, with the attacking satellite's acceleration not exceeding 6 m / s² and the defending satellite's acceleration not exceeding 5 m / s².

[0136] Table 1. Initial relative position and velocity (m, m / s) between attacking star a and defending star d

[0137] 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)]]> a 2728.4 1234.2 0 175.94 53.10 0 d 2435.5 1357.7 0 -86.47 21.25 0

[0138] Based on the above conditions, specific embodiments of the present invention are given below, see [link to specific embodiments]. Figure 2 .

[0139] A spacecraft escort problem model is established based on the parameters of the primary star, attacking star, and defending star. The model is as follows:

[0140] when hour,

[0141]

[0142] when hour,

[0143]

[0144]

[0145] Where: symmetric positive semi-definite matrix satisfy:

[0146] Q = k1I 6×6 R d =k2I 3×3 R a =k3I 3×3 (4)

[0147] In the formula:

[0148] k1 = 10 -5 k2 = 1, k3 = 0.8 are the weighting coefficients.

[0149] Where matrix A represents the spacecraft's relative motion dynamics constraint matrix, its specific form is constructed using the CW equations in orbital dynamics, namely:

[0150]

[0151] in The value represents the orbital angular velocity of the reference satellite, μ is the Earth's gravitational field coefficient, and a0 = 8731 km is the semi-major axis of the reference satellite's orbit.

[0152] The meanings of the other symbols in equations (1) to (3) are as follows:

[0153] a — the subscript of the attacking star;

[0154] d — the subscript of the defense star;

[0155] m — the subscript of the primary star;

[0156] X a —The state vector of the attacking star, specifically X a =x a ,y a ,z a ,v ax ,v ay ,v az ] T ;

[0157] X d —The state vector of the defense star, specifically X d =x d ,y d ,z d ,v dx ,v dy ,v dz ] T ;

[0158] x — the radial position component of the orbit relative to the coordinate system (LVLH system);

[0159] y — the position component of the flight direction in a relative coordinate system (LVLH system);

[0160] z — Position component of the orbital angular momentum direction relative to the coordinate system (LVLH system);

[0161] v x —The radial velocity component of the orbit in the relative coordinate system (LVLH system);

[0162] v y —The velocity components in the orbital flight direction under the relative coordinate system (LVLH system);

[0163] v z —The velocity component in the direction of the orbital angular momentum in a relative coordinate system (LVLH system);

[0164] u a —The continuous control quantity applied by the attacking star, specifically in the form of u a =[u ax ,u ay ,u az ] T ;

[0165] u d —The continuous control quantity applied by the defensive star, specifically in the form of u d =[u dx ,u dy ,u dz ] T ;

[0166] B—The control matrix for the attacking and defending stars, specifically in the form B = [0 3×3 ,I 3×3 ] T ;

[0167] d safe —The safe distance between the attacking star and the defending star, d safe =200m;

[0168] J a —Performance indicators of the attacking satellite when the distance between the attacking and defending satellites is greater than the safe distance;

[0169] J d —Performance indicators of the defensive satellite when the distance between the attacking and defensive satellites is greater than the safe distance;

[0170] J—Performance index of both the attacking and defending stars when the distance between them is less than the safe distance;

[0171] uamax —The maximum acceleration that the attacking star can exert, u = amax ;

[0172] u dmax —The maximum acceleration that the defensive star can apply, u dmax ;

[0173] ‖s‖ — represents a three-dimensional real vector The 2-norm, i.e.

[0174] Substituting the initial parameters from the spacecraft escort problem parameters (primary, attacking, and defending satellites) into the spacecraft escort problem model, we obtain the control strategies for the attacking and defending satellites in two phases. The solution steps are as follows:

[0175] S1, Input parameters for the spacecraft escort problem, including the semi-major axis of the reference satellite orbit a0 = 8731 km; the initial state of the attacking satellite X. a (t0)=[2728.4m,1234.2m,0,175.94m / s,53.10m / s,0] T Defense Star Initial State X d (t0)=[2435.5m,1357.7m,0,-86.47m / s,21.25m / s,0] T The position of the primary star [x] m ,y m ,z m ] T =[0,0,0] T The upper limit of the acceleration magnitude of the attacking star, u amax =6m / s; the upper limit of the magnitude of the acceleration of the defense star, u dmax = 5m / s; the safe distance d between the attacking and defending stars safe =200m;

[0176] S2, the spacecraft escort problem model, i.e., formulas (1) to (3), is used to solve the phased optimal control strategies for the attacking and defending satellites respectively: when This is called stage α, and when The time is called stage β, and it is obvious that at any given time the system can only be in one stage;

[0177] S3, the dynamic programming method is used to solve the bilateral optimization problem of stage α above. The specific steps are as follows:

[0178] S301, the Hamiltonian function is defined as follows:

[0179]

[0180] Where X is the relative state vector between the defensive and offensive stars, denoted as X = X a -X d λ is the costate variable used to construct the Hamiltonian function.

[0181] S302, List the optimality conditions for the bilateral optimization problem:

[0182]

[0183] S303, Substituting the Hamiltonian function into the above optimality conditions yields the formal solution of the optimal control strategy for both parties:

[0184]

[0185] S304, Substituting the optimal control strategy solutions of both parties into the Hamiltonian function yields the Hamilton-Jacobi equation (HJ equation):

[0186]

[0187] S305, In order to obtain the feedback control strategy, assume that the costate variables have the following form under optimal conditions:

[0188]

[0189] S306, Substituting the above equation into the formal solution yields the optimal feedback control strategy for both the attacker and defender:

[0190]

[0191] S307, the HJ equation is rewritten accordingly, as follows:

[0192]

[0193] Summarized as follows:

[0194]

[0195] S308. The Lyapunov iterative method is used to solve for the unknown matrix P, that is, to solve the rewritten and simplified HJ equation, also known as the Riccati equation. The iterative algorithm is as follows:

[0196]

[0197] The initial value is selected as:

[0198]

[0199] Obtain the matrix

[0200] S309, the final control strategies for the attacking and defensive stars in phase α are as follows:

[0201]

[0202] S4, design control strategies for the attacking and defensive stars in phase β, with the following specific steps:

[0203] S401, since the performance indicators of the defense satellite are the same in phase α and phase β, its control strategy is designed to be the same in phase α and phase β, that is, the following feedback control law is also adopted:

[0204] Stage β

[0205] S402, the following design outlines the control strategy for the attacking satellite in phase β. Since its performance index is only the distance to the host satellite, and the host satellite is a non-maneuvering spacecraft, the PD control method can be directly used to design the control strategy for the attacking satellite. The control law is as follows:

[0206] u a * =-K p [x a -x m ,y a -y m ,z a -z m ] T -K d [v ax ,v ay ,v az ] T Stage β

[0207] Where K p =5×10 -3 and K d =5×10 -3 This is the PD control coefficient;

[0208] S5 yields the control strategies for the attacking and defending stars in phases α and β, respectively, with the following expressions:

[0209]

[0210]

[0211] When calculating the accelerations of the attacking and defending stars using the above formulas, if the acceleration ||u| of the attacking star at a certain moment is calculated... a ||>u amax =6m / s 2 Then take ||u a ||=u amax=6m / s 2 Furthermore, the direction of acceleration remains constant to ensure that the theoretical acceleration does not exceed the actual acceleration capability of the spacecraft. Similarly, the acceleration of a defense satellite is ||u||. d ||>u dmax =5m / s 2 Then take ||u d ||=u dmax =5m / s 2 And the direction of acceleration remains unchanged.

[0212] S6, the timing of attacking and defending stars is determined. With d safe The magnitude of the values ​​is used to determine whether the current stage is α or β, and to continuously update the control strategy.

[0213] S7, perform numerical simulation to obtain the trajectory diagrams of both sides in the guarding problem (e.g., Figure 3 ) and acceleration change curves (such as Figure 4 ).

[0214] In summary, this invention discloses a method, system, and device for solving the spacecraft escort problem based on strategy switching. Specifically, it includes: firstly, establishing a spacecraft escort problem model based on strategy switching, comprising optimization indices, optimization variables, dynamic constraints, and acceleration capability constraints; wherein the optimization indices are described by a weighted quadratic function including inter-satellite distance and fuel consumption, the optimization variables are the continuous control force accelerations of both attacking and defending parties, the dynamic constraints are described by the CW equations under a relative motion model, and the acceleration capability constraints are modeled using acceleration amplitude limits. Then, a solution method for the aforementioned optimization problem was established, specifically including the following steps: S1, the optimization problem was divided into a bilateral optimization problem and a trajectory transition problem according to the stages; S2, for the bilateral optimization problem, dynamic programming was used to solve it, transforming the bilateral optimization problem into a two-point boundary value problem, and finally obtaining the optimal feedback control solution by solving the Riccati equation; S3, for the trajectory transition, the proportional-derivative control method was used to design the control law; S4, the control laws of the attacking and defending sides in two different stages were obtained; S5, the stage was determined based on the real-time inter-satellite distance between the attacking and defending sides, and the respective control strategies were switched simultaneously according to the stage transition; S6, the solution to the spacecraft escort problem was output. This solution method for the spacecraft escort problem can effectively solve the spacecraft escort problem under continuous thrust, and is an effective extension of the existing continuous thrust escort problem model and method. This model adopts a strategy switching method, thus simplifying the solution of the difficult-to-solve weighted performance index escort problem and improving the solution efficiency of non-zero-sum game problems.

[0215] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for solving a spacecraft escort problem based on policy switching, characterized in that, include: Obtain parameters for the spacecraft escort problem of the primary, attacking, and defending stars; A spacecraft escort problem model is established based on the parameters of the spacecraft escort problem involving the primary star, the attacking star, and the defending star; the details are as follows: When time, （1） When time, （2） （3） Substituting the initial parameters from the spacecraft escort problem parameters (primary, attacking, and defensive satellites) into the spacecraft escort problem model yields the control strategies for the attacking and defensive satellites in two phases; specifically as follows: S1: Substitute the initial parameters from the spacecraft escort problem parameters of the primary star, attacking star, and defending star into the spacecraft escort problem model; S2: When is the phase , When is a phase ; S3: Solve the phase in S2 using dynamic programming. The bilateral optimization problem yields the results of the offensive and defensive stars at different stages. Control strategy; S4: Determine the control strategy of the attacking star and the defending star in phase S4: Determine the control strategy of the attacking star and the defending star in phase By switching the corresponding control strategy based on the real-time determination of the stage of the attacking and defending stars; Where a is the subscript of the attacking star; d is the subscript of the defending star; and m is the subscript of the master star. The state vector of the attacking star; The state vector of the defense star; The radial position component of the track in the relative coordinate system; The position component of the flight direction in a relative coordinate system; This represents the position component of the orbital angular momentum direction in the relative coordinate system. The radial velocity component of the track in the relative coordinate system; The velocity component in the orbital flight direction in the relative coordinate system; The velocity component in the direction of the orbital angular momentum in the relative coordinate system; The continuous control amount applied to the attacking star; The continuous control quantity applied to the defensive star; The control matrix for offensive and defensive stars; The relative motion dynamics constraint matrix of the spacecraft. The safe distance between the attacking and defensive satellites; This refers to the performance indicators of the attacking satellite when the distance between the attacking and defending satellites is greater than a safe distance. This refers to the performance indicators of the defensive satellite when the distance between the attacking and defensive satellites is greater than the safe distance. This refers to the performance indicators of both the attacking and defending satellites when the distance between them is less than the safe distance. The maximum acceleration applied to the attacking star; The maximum acceleration applied to the defensive star energy; To represent a three-dimensional real vector The 2-norm; ,and All are symmetric positive semi-definite matrices.

2. The method according to claim 1, wherein, The parameters in question include: the semi-major axis of the reference satellite orbit, the initial state of the attacking satellite, the initial state of the defending satellite, the position of the primary satellite, the upper limit of the magnitude of the acceleration of the attacking satellite, the upper limit of the magnitude of the acceleration of the defending satellite, and the safe distance between the attacking and defending satellites.

3. The method of claim 1, wherein, the symmetric positive semi-definite matrix , , satisfies: ， ， （4） In the formula: , The specific form is constructed by the CW equation in the orbit dynamics, i.e. wherein, is the orbital angular velocity of the reference satellite; is the Earth gravitational field coefficient, is the orbital semi-major axis of the reference satellite; , and are weight coefficients.

4. The method of claim 1, wherein, In S3, the specific steps are as follows: S301, the Hamiltonian function is defined as follows: ； S302, List the optimality conditions for the bilateral optimization problem: S303, Substituting the Hamiltonian function into the above optimality conditions yields the formal solution of the optimal control strategy for both parties: S304, Substituting the optimal control strategy solutions of both parties into the Hamiltonian function yields the Hamilton-Jacobi equation: S305, In order to obtain the feedback control strategy, assume that the costate variables have the following form under optimal conditions: S306, Substituting the above equation into the formal solution yields the optimal feedback control strategy for both the attacker and defender: S307, the Hamilton-Jacobi equation is rewritten accordingly, as follows: Summarized as follows: S308, using Lyapunov iteration method to solve unknown matrix S308, using Lyapunov iteration method to solve unknown matrix S308, using Lyapunov iteration method to solve unknown matrix The initial value is selected as: matrix ; S309, finally get the attack star and defense star in the stage control strategy as follows: in, This represents the relative state vector between the defensive and offensive stars. To construct the costate variables of the Hamiltonian function; The continuous control amount applied to the attacking star; The continuous control quantity applied to the defensive star; The control matrix for offensive and defensive stars; This represents the dynamic constraint matrix for the relative motion of the spacecraft. ,and All are symmetric positive semi-definite matrices.

5. The method of claim 1, wherein, The specific steps in S4 are as follows: S401, due to the defensive star in phase and stages The performance indicators are the same, so it is designed to perform in the same stage. and stages The control strategy is the same, that is, the following feedback control law is also adopted: S402, the design attack star in stage S401, the control strategy of the defense star in stage in, and denoted as PD control coefficient; a is the subscript of the attacking star; d is the subscript of the defensive star; m is the subscript of the master star; The radial position component of the track in the relative coordinate system; The position component of the flight direction in a relative coordinate system; This represents the position component of the orbital angular momentum direction in the relative coordinate system. The radial velocity component of the track in the relative coordinate system; The velocity component in the orbital flight direction in the relative coordinate system; The velocity component in the direction of the orbital angular momentum in the relative coordinate system; This represents the relative state vector between the defensive and offensive stars; The control matrix for offensive and defensive stars.

6. The method of claim 1, wherein, Real-time determination of the current stage of attacking and defending stars. and Determining the size relationship, When is a phase , When is a phase ; Where a is the subscript of the attacking star; d is the subscript of the defending star; and m is the subscript of the master star. The radial position component of the track in the relative coordinate system; The position component of the flight direction in a relative coordinate system; This represents the position component of the orbital angular momentum direction in the relative coordinate system. The safe distance between the attacking star and the defending star.

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