Spacecraft elliptical orbit real-time closed-loop pursuit game method and device

Abstract

The invention discloses a real-time closed-loop pursuit game method and device for an elliptical orbit of a spacecraft, belongs to the crossing field of spacecraft orbit dynamics and intelligent game control, and particularly relates to the real-time closed-loop pursuit game method for the elliptical orbit of the spacecraft based on a convex optimization theory. The problems that a traditional orbit game control method is difficult in equilibrium solution, poor in strategy convergence and difficult in on-orbit application are solved. The method comprises the following steps: solving an equivalent discount unilateral minimum time transfer problem to obtain an open-loop optimal strategy pair; according to the optimal control strategy, the state of the spacecraft is subjected to recursion, the state of the escape spacecraft under unknown control is subjected to recursion, and a target point is updated. The real-time closed-loop pursuit game method and device for the elliptical orbit of the spacecraft are suitable for the real-time pursuit game of the elliptical orbit of the spacecraft.

Description

Technical Field

[0001] The present invention relates to the cross - field of spacecraft orbital dynamics and intelligent game control, and particularly to a real - time closed - loop pursuit - evasion game method for spacecraft elliptical orbits based on convex optimization theory. Background Art

[0002] In the prior art, the saddle - point equilibrium solution method based on the maximum principle is often used for the spacecraft pursuit - evasion game problem. Its core is to construct a Hamiltonian function and solve the boundary - value problem of the adjoint differential equation, and finally derive the optimal control strategies of both sides of the game. Such methods rely on the high - precision mathematical expression of the orbital dynamics model and need to jointly iterate and solve the state equation and the co - state equation in the continuous - time domain. However, this technical solution has the following inherent defects:

[0003] (1) In the non - linear dynamics scenario of elliptical orbits, the time - varying characteristics of the state equation and the co - state equation lead to an increased difficulty in solving the boundary - value problem, and the computational complexity exceeds the real - time processing ability of the spacecraft on - board computer;

[0004] (2) In the existing improved schemes, numerical optimization methods such as heuristic search can search for the solution of the boundary - value problem, but they face problems such as poor strategy convergence and sensitivity to initial - value guessing. Especially under multiple constraints with free terminal time, they are prone to falling into local optimal solutions;

[0005] (3) The existing methods lack a dynamic environment perception and closed - loop strategy adjustment mechanism, and the solution process depends on the offline pre - calculation mode, making it difficult to meet the real - time requirements such as sudden changes in target maneuvering strategies and orbital perturbation interference in space confrontation scenarios.

[0006] The above defects lead to a calculation delay of more than a minute when the traditional game - solving method is applied on - orbit, and the strategy stability cannot meet the rigid requirements of the millisecond - level response of the spacecraft attitude and orbit control system. Summary of the Invention

[0007] The present invention proposes a real - time closed - loop pursuit - evasion game method and device for spacecraft elliptical orbits, which solves the problems of difficult equilibrium solution, poor strategy convergence, and difficulty in on - orbit application of traditional orbital game control methods.

[0008] The real - time closed - loop pursuit - evasion game method for spacecraft elliptical orbits according to the present invention includes the following steps:

[0009] Step S1: Given the initial conditions x p (θ0), x e (θ0) and control constraints

[0010] where: θ0 represents the initial true anomaly of the spacecraft; x p(θ0) represents the initial state of the tracking spacecraft; x e (θ0) represents the initial state of the escaping spacecraft; represents the set of feasible control inputs for the tracking spacecraft; represents the set of feasible control inputs for the escaping spacecraft;

[0011] Step S2: Iteratively obtain the closed-loop control strategy; where the iterative process in the s-th stage includes the following steps:

[0012] Step S2.1: At the moment corresponding to θ s input the complete states of both spacecrafts in the pursuit-evasion game, (x p (s), x e (s)), where θ s is the true anomaly angle corresponding to the s-th stage;

[0013] where: x p (s) represents the state of the tracking spacecraft in the s-th stage; x e (s) represents the state of the escaping spacecraft in the s-th stage;

[0014] Step S2.2: Solve the equivalent discounted unilateral minimum-time transfer problem to obtain the open-loop optimal strategy pair and

[0015] where: represents the optimal control strategy of the tracking spacecraft; represents the optimal control strategy of the escaping spacecraft; represents the terminal true anomaly angle corresponding to the game problem solved in the s-th stage;

[0016] Step S2.3: Recursively calculate according to the optimal control strategy Recursively calculate the unknown control u For the escaping spacecraft x e under the condition of e (θ s ), update the target point

[0017] where: represents the state of the tracking spacecraft in the s-th stage according to the optimal control strategy; x e (θ s ) represents the state of the escaping spacecraft in the s-th stage according to the optimal control strategy; represents the relative state target point corresponding to the terminal true anomaly angle of the game problem solution;

[0018] Step S2.3: Determine whether ||φ|| ≤ ε is satisfied:

[0019] If so, the iteration ends, the final closed-loop control game strategy is obtained, the interception of the target is achieved, and the game ends;

[0020] Otherwise, obtain θ s+1 , and continue the iteration in the (s + 1)-th stage:

[0021] θ s+1 = θ s + Δθ;

[0022] where: φ represents the terminal constraint condition; ε represents the error threshold end condition; Δθ represents the difference in the true anomaly angle between two adjacent stages.

[0023] Furthermore, a preferred implementation manner is provided, and the equivalent discounted unilateral minimum-time transfer problem is:

[0024] Solve the minimum-time transfer problem according to the control inputs and current states of the tracking spacecraft and the escaping spacecraft:

[0025]

[0026] x pe (θ s ) = x p (θ s ) - x e (θ s )

[0027] x pe (θ f ) = 0

[0028] where, x pe is the relative state difference between the tracking spacecraft and the escaping spacecraft; u pe is the equivalent discounted control input; u pe is the maximum value of the equivalent control input set; θ f is the optimal true anomaly angle; x p (θ s ) is the initial state of the tracking spacecraft in the s-th stage; x e (θ s ) is the initial state of the escaping spacecraft in the s-th stage; x pe (θ f ) is the terminal state constraint of the relative motion state difference; x pe (θ s ) is the initial state constraint of the relative motion state difference.

[0029] Furthermore, a preferred implementation manner is provided, and the step S2.2 is:

[0030] Repeatedly solve the feasibility problem by solving different given terminal times θ f Solve the feasibility problem:

[0031]

[0032] x pe (θ s ) = x p (θ s ) - x e (θ s )

[0033] where φ(θ f ) is the terminal error at the moment corresponding to the true anomaly; u pe is the equivalent discounted control input; is the boundary of.

[0034] The present invention also proposes a real-time closed-loop pursuit-evasion game device for a spacecraft in an elliptical orbit, and the device includes the following modules:

[0035] Module S1: Given the initial conditions x p (θ0), x e (θ0) and the control constraints

[0036] where: θ0 represents the initial true anomaly of the spacecraft; x p (θ0) represents the initial state of the tracking spacecraft; x e (θ0) represents the initial state of the escaping spacecraft; represents the set of feasible control inputs of the tracking spacecraft; represents the set of feasible control inputs of the escaping spacecraft;

[0037] Module S2: Iteratively obtain the closed-loop control strategy; among them, the iterative process in the s-th stage includes the following sub-modules:

[0038] Sub-module S2.1: Input the complete states (x s (s), x p (s)) of both sides of the spacecraft in the pursuit-evasion game at the moment corresponding to θ e (s), where θ s is the true anomaly angle corresponding to the s-th stage;

[0039] where: x p (s) represents the state of the tracking spacecraft in the s-th stage; x e (s) represents the state of the escaping spacecraft in the s-th stage;

[0040] Sub-module S2.2: Solve the equivalent discounted unilateral minimum-time transfer problem to obtain the open-loop optimal strategy pair and

[0041] where: Represents the optimal control strategy of the tracking spacecraft; Represents the optimal control strategy of the escaping spacecraft; Represents the true anomaly corresponding to the solution of the game problem at stage s;

[0042] Sub-module S2.3: According to the optimal control strategy Recursively Recursively calculate the unknown control u e The state of the escaping spacecraft x at the next step e (θ s ), update the target point

[0043] Where: Represents the state of the tracking spacecraft according to the optimal control strategy at stage s; x e (θ s ) represents the state of the escaping spacecraft according to the optimal control strategy at stage s; Represents the relative state target point corresponding to the true anomaly at the end of solving the game problem;

[0044] Sub-module S2.3: Judge whether ||φ||≤ε is satisfied:

[0045] If so, the iteration ends, the final closed-loop control game strategy is obtained, the interception of the target is achieved, and the game ends;

[0046] Otherwise, obtain θ s+1 , and continue the iteration in the (s + 1)-th stage:

[0047] θ s+1 = θ s +Δθ;

[0048] Where: φ represents the terminal constraint condition; ε represents the error threshold end condition; Δθ represents the difference in true anomaly between two adjacent stages.

[0049] The present invention also proposes a computer device, including: a processor and a memory, the memory is used to store the executable instructions of the processor, and the processor is configured to execute the real-time closed-loop pursuit-evasion game of the spacecraft elliptical orbit described in any one of the above by executing the executable instructions.

[0050] The present invention also proposes a computer storage medium, in which a computer program is stored, and when the computer program runs, it executes the real-time closed-loop pursuit-evasion game of the spacecraft elliptical orbit described in any one of the above.

[0051] The present invention also proposes a computer program product, including computer programs / instructions, and when the computer programs / instructions are executed by a processor, the steps of the real-time closed-loop pursuit-evasion game of the spacecraft elliptical orbit described in any one of the above are implemented.

[0052] The present invention has the following beneficial effects:

[0053] 1. The real-time closed-loop pursuit-evasion game method for spacecraft on an elliptical orbit according to the present invention does not require manual parameter setting, can solve the closed-loop optimal strategy, and makes the closed-loop strategy optimized based on game theory feasible, which is crucial for the actual in-orbit application of spacecraft.

[0054] 2. The real-time closed-loop pursuit-evasion game method for spacecraft on an elliptical orbit according to the present invention does not require hyperparameter adjustment, its output is deterministic, and it guarantees convergence, making it suitable for airborne applications, especially on resource-constrained spaceborne embedded platforms.

[0055] 3. The real-time closed-loop pursuit-evasion game method for spacecraft on an elliptical orbit according to the present invention is directly used for the autonomous pursuit-evasion confrontation tasks of spacecraft in an elliptical orbit environment, including scenarios such as space target interception, non-cooperative target avoidance, and multi-spacecraft cooperative envelopment; its application fields cover aerospace offensive and defensive confrontation, in-orbit service safety control, space debris active avoidance, etc. By solving high-speed strategies and real-time iteration of game strategies, it solves the problems of traditional orbital game control methods in difficult equilibrium solving, poor strategy convergence, and difficulty in in-orbit application, and provides an autonomous decision-making ability with millisecond-level response for complex space confrontation tasks.

[0056] The real-time closed-loop pursuit-evasion game method and device for spacecraft on an elliptical orbit according to the present invention are applicable to the real-time pursuit-evasion game of spacecraft on an elliptical orbit. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0058] Figure 1 It is a schematic diagram of the rolling time domain of the closed-loop pursuit-evasion game in an embodiment of the present invention;

[0059] Figure 2 It is a schematic diagram of the equivalence conversion condition between the bilateral problem and the unilateral problem in an embodiment of the present invention;

[0060] Figure 3 It is a schematic diagram of the feasibility determination of the convex optimization sub-problem in an embodiment of the present invention;

[0061] Figure 4 It is a schematic diagram of the comparison of the closed-loop terminal time using the trivial strategy and the expected strategy in an embodiment of the present invention;

[0062] Figure 5 In an embodiment of the present invention, it is a schematic diagram of time consistency analysis;

[0063] Figure 6 In an embodiment of the present invention, it is a schematic diagram of unilateral and bilateral trajectories of the short-term interception problem; wherein, (a) is the unilateral trajectory; (b) is the bilateral trajectory;

[0064] Figure 7 In an embodiment of the present invention, it is a schematic diagram of the optimal control input for the short-term interception problem; wherein, (a) is trapezoidal discretization; (b) is pseudospectral discretization;

[0065] Figure 8 In an embodiment of the present invention, it is a schematic diagram of the optimal trajectory for the short-term rendezvous problem; wherein, (a) is the unilateral transfer result; (b) is the bilateral rendezvous result;

[0066] Figure 9 In an embodiment of the present invention, it is a schematic diagram of the verification of the optimality of the closed-loop game; wherein, (a) is the closed-loop interception game; (b) is the closed-loop rendezvous game. Detailed implementation manners

[0067] To make the technical solutions and advantages of the present invention more clearly expressed, the following will further describe the detailed and complete description of the specific implementation manners of the present invention in conjunction with the accompanying drawings. The following described various implementation manners are only a part of the preferred solutions of the present invention, rather than all implementation solutions; the following described various implementation manners are intended to explain the present invention and cannot be understood as a limitation to the present invention; the reasonable combination of the technical features defined in each implementation manner of the present invention, and all other implementation manners obtained by those of ordinary skill in the art based on the implementation manners of the present invention without creative efforts all fall within the scope of protection of the present invention.

[0068] Brief description of the prior art:

[0069] The existing research on the spacecraft pursuit-evasion problem usually has a huge amount of calculation and usually relies on heuristic search methods or nonlinear programming techniques to derive open-loop strategies. These methods hinder their on-orbit implementation, especially on platforms with limited computing resources. The present invention proposes a real-time closed-loop method to solve the spacecraft pursuit-evasion problem for two games of interception and rendezvous docking with time-varying thrust profiles in elliptical orbits. This method is based on convex optimization methods, and the specific steps are summarized as follows:

[0070] 1. Problem transformation: Transform the bilateral optimal control problem into an equivalent discounted minimum-time transfer problem.

[0071] 2. Determine the optimal terminal time: Determine the optimal terminal time by iteratively solving a series of convex sub-problems through the bisection method.

[0072] 3. Extended to a receding - horizon pursuit - evasion scheme: The proposed open - loop strategy is extended to a receding - horizon pursuit - evasion scheme and its victory is ensured.

[0073] The numerical results show that the proposed method can solve the pursuit - evasion game problem in real - time within nearly 100 milliseconds. Compared with existing methods, the computational time is significantly reduced and no manual parameter adjustment is required. In addition, Monte Carlo simulations show that the proposed closed - loop strategy is robust against evaders with unknown actions and provides empirical evidence for guaranteed performance.

[0074] When a spacecraft performs a close - range operation (such as an interception mission) around a non - cooperative target, it is reasonable to assume that the target will take actions to mitigate potential threats or attempt to escape (if the target is rational and well - informed). However, even if the player adopts an optimal strategy derived from static trajectory optimization, there is still a risk of misjudging the opponent's actions. This is because the response of the agent invalidates the initial assumptions before the game starts. Therefore, the traditional single - sided trajectory optimization problem evolves into a more complex problem involving two agents making optimal decisions dynamically.

[0075] Game theory is used to model and analyze the dynamic interactions among multiple players and the process of making optimal decisions. When the state evolution of the players is controlled by differential equations, this game is called a differential game.

[0076] The optimal interception or close - range guidance of a spacecraft towards a potentially maneuvering target can be formulated as a pursuit - evasion game, which is a variant of dynamic non - cooperative differential games. Here, the pursuer aims to capture the evader, while the evader tries to avoid being captured. A basic assumption is that the maneuverability of the pursuer exceeds that of the evader, ensuring that the game ends within an unknown but finite time. Therefore, the goal of the pursuer is to minimize the terminal time, while the evader tries to maximize the terminal time. This situation constitutes a zero - sum game, which is of great significance in the aerospace field.

[0077] The main challenge in pursuit - evasion games lies in constructing an efficient and reliable method to find saddle - point strategies, especially for real - time applications in practical scenarios. Currently, the methods for solving pursuit - evasion games are mainly divided into indirect methods, semi - direct nonlinear programming methods, and reachability - based methods.

[0078] 1. Existing methods and their limitations:

[0079] Indirect method: Based on the Pontryagin's Minimum Principle (PMP), it is the main method in the existing literature to solve the spacecraft pursuit-evasion game. However, it faces significant difficulties in solving the resulting boundary value problem, especially in cases where reliable convergence on-board equipment is required. Due to the presence of disturbances and uncertainties as well as the unpredictable responses of opponents, the utility of the PMP open-loop strategy is limited. These factors require a closed-loop strategy, which requires efficient repeated computational guidance. The pursuit-evasion game leads to high-dimensional boundary value problems, which are particularly challenging even for problems involving linear dynamics with limited resources.

[0080] Reachability-based method: The terminal time is determined based on the forward reachable set inclusion criterion and provides intuitive insights. Those skilled in the art have studied the pursuit-evasion game with impulsive maneuvers using reachability and also solved the continuous game with multiple pursuers and evaders using the Hamilton-Jacobi-Isaacs (HJI) reachability method. Although the HJI method provides a comprehensive framework for obtaining closed-loop solutions, it is far from real-time implementation, especially in time-varying scenarios. It is mainly used for simple motions; typically, only kinematics on a plane is used. Analytic solutions and closed-loop strategies can be obtained. However, for the spacecraft pursuit-evasion game, it is difficult to obtain explicit analytic solutions even for linear relative dynamics. In addition, due to the need to traverse the approximate reachable surface, the reachability-based method has a high computational cost. Moreover, due to the difficulty in handling the exact reachable set, the error in the terminal time is large, and the optimal control strategy is usually suboptimal because it usually comes from the grid.

[0081] 2. Advantages of the method of the present invention:

[0082] Real-time guidance and trajectory optimization are crucial for online pursuit-evasion games. As far as those skilled in the art know, there is currently no method to calculate the solution of the pursuit-evasion differential game in real time. However, with the advancement of hardware computing power, the method of the present invention based on convex optimization solves the problem of real-time calculation of the pursuit-evasion differential game. The main advantage of convex optimization is its ability to provide a globally optimal solution and fast convergence speed, which is crucial for autonomous decision-making. Through the state-of-the-art interior point method, a customized convex optimization algorithm can be implemented on an embedded system.

[0083] Spacecraft pursuit-evasion is a typical minimum-time problem, while the free-time problem is a typical non-linear programming problem. The optimal time is usually determined by PMP and depends on the initial co-state. Usually, approximate estimation is carried out to guess and then provided to solve the exact optimal value. However, it is difficult to generate a reasonable initial guess of the co-state and obtain a convergent solution. Sequential convex optimization is also a mature method to solve the free-time problem, treating the free time as an optimization variable to handle the unknown time. However, for a linear free-time problem, it can be solved losslessly through a series of convex (optimization) sub-problems to obtain the optimal time, and the present invention adopts this method.

[0084] 3. The main contributions of the method of the present invention can be summarized as follows:

[0085] (1) Proposing the equivalent discounted minimum time (transfer) problem: A fully equivalent discounted minimum time problem is proposed, and its optimal solution is almost everywhere consistent with the original two-sided pursuit-evasion game. This is applicable to interception and rendezvous-docking games with time-varying thrust.

[0086] (2) Determining the minimum feasible time by the bisection method: The bisection search method is adopted. By using the minimum transfer convex sub-problem as the feasibility criterion for game termination, the minimum feasible time is determined within a finite number of iterations. The proposed rolling horizon closed-loop strategy is verified to be able to handle the control of unknown evaders. Numerical empirical evidence shows that compared with the open-loop equilibrium solution, the performance of the proposed method is guaranteed.

[0087] (3) Comprehensive numerical verification and comparison: The effectiveness and reliability of the proposed method are demonstrated. This method avoids obtaining initial guesses and solves the unreliable convergence situations encountered in long-term games. It utilizes an efficient convex optimization algorithm and is very suitable for real-time applications in pursuit-evasion games.

[0088] In one embodiment, the basic concepts of the pursuit-evasion differential game and the equivalent formula of the discounted minimum time transfer problem are described:

[0089] 1. Regarding the two-sided pursuit-evasion game:

[0090] For the pursuit-evasion game carried out on an elliptical reference orbit, the relative dynamics are described by the following Tschauner-Hempel (T-H) equations, where the true anomaly θ is used as the independent variable:

[0091]

[0092] In the formula:

[0093]

[0094]

[0095] Where:

[0096] represents the position (r i ) and velocity (v i ) of player (or participant, spacecraft) i in the LVLH (Local Vertical and Local Horizontal) coordinate system, and the subscript i ∈ {p, e} represents the pursuer (p, or pursuit spacecraft) and the evader (e, or evasion spacecraft, fleeing spacecraft) respectively.

[0097] Equation (1) represents a linear time-varying system and is also a control-affine (dynamics) system.

[0098] u i is the unit control vector; ρ is the introduced intermediate variable, ρ = 1 / (e + cosθ), where e is the eccentricity of the reference orbit; is the instantaneous angular velocity, μ is the Earth's gravitational constant, and h is the orbital angular momentum.

[0099] The initial state of the player at θ0 is given by:

[0100] x i (θ0) = x i，0 (2)

[0101] Without loss of generality, assume that the mass of the spacecraft varies during the maneuver.

[0102] Without loss of generality, assume that the spacecraft has a varying mass during the maneuver. Introduce the scalar function to represent the time-varying thrust profile of the player. For a specific fixed thrust magnitude case, this function degenerates to a constant function. Specifically defined as

[0103]

[0104] where:

[0105] u i，max represents the initial maximum control velocity of player i; c i is its effective exhaust velocity; t represents the time;

[0106] The alternative control quantity of player i is composed of all feasible control quantities, denoted as:

[0107]

[0108] where, is the optimal terminal true anomaly at the end of the game.

[0109] Generally speaking, the pursuit-evasion problem is modeled as a zero-sum game, where the goal of the pursuer is to minimize the terminal time, and the goal of the evader is to maximize the terminal time. The corresponding payoff function is the amount of time θ that satisfies the following terminal condition f :

[0110] φ(x p , x e ) = 0 (5)

[0111] Specifically, it is given by:

[0112] J(u p , u e ) = θf (6)

[0113] Consider two pursuit-evasion games: the interception game and the rendezvous-docking game. The terminal conditions are expressed as follows respectively:

[0114] Interception game:

[0115] Rendezvous-docking game:

[0116] The optimal strategy pair of the game is described by the Nash equilibrium, which is also called the saddle point in a zero-sum game, and it satisfies the following inequalities:

[0117]

[0118] The core advantage of the Nash equilibrium is that no participant can improve their own payoff by unilaterally changing their strategy. The information structure of the pursuit-evasion game is assumed to be complete information, that is, both the pursuer and the evader are fully aware of all relevant information, including the strategy set

[0119] Therefore, the zero-sum pursuit-evasion game problem can be formulated as an optimization problem

[0120]

[0121] where: s.t. (1), (2), (4), (5), (6), (7) represent the constraints based on the above formulas (1), (2), (4), (5), (6), (7).

[0122] The necessary conditions for the bilateral optimal control solution are obtained from the Pontryagin minimum principle, and the bilateral Hamiltonian function is constructed as follows:

[0123] H = H p + H e = λ p ·(Ax p + Bu p g p ) + λ e ·(Ax e + Bu ege )

[0124] 49P

[0125] where is the co-state variable of player i.

[0126] Note that the Hamiltonian function is separable, then the optimal controls for the pursuer and the evader are given by:

[0127]

[0128] The specific expression is:

[0129]

[0130] Among them, the co-state variables are solved through the following equations:

[0131]

[0132] The terminal value of the co-state variable is determined by the Lagrange multiplier τ:

[0133]

[0134] Rendezvous game With full state constraints While the interception game Only has position constraints And the terminal co-state variable λ i Needs to expand the zero component, that is, λ v，i = 0. The transversality condition of the terminal Hamiltonian function is:

[0135] H(θ f ) + 1 = 0 (13)

[0136] Obviously, λ p (θ f ) + λ e (θ f ) = 0, and considering the linear co-state equation, then the optimal controls of the pursuer and the evader are almost the same everywhere, except that the control singularity appears at the terminal time in the interception game.

[0137] Therefore, the derived boundary value problem Is formulated as:

[0138]

[0139] That is, to find the parameters τ, θ f , such that equations (12) and (13) hold.

[0140] Obviously, the rendezvous and docking game is more challenging than the interception problem because the terminal constraints are more complex.

[0141] 2. Regarding the discounted minimum time transfer problem:

[0142] To reduce the complexity, the control-affine dynamics of equation (1) are expressed in the reduced state space:

[0143]

[0144] where x pe = x p - x e is the state difference. Based on the necessary conditions, the optimal control directions of the two players are the same. Assume that the control input of the evader is always the same as that of the pursuer, effectively making the evader an imitation agent. This assumption is a relaxation of the original problem and will be equivalent when taking the optimal solution. Therefore, Equation (15) is reformulated as:

[0145]

[0146] where g pe = g p - g e is the difference in control magnitude, u pe represents the thrust direction and is the same as u p and u e . The discounted feasible control is:

[0147]

[0148] Then, the reduced-order initial state is:

[0149] x pe (θ0) = x pe，0 (18)

[0150] The corresponding terminal conditions for the interception game and the rendezvous and docking game are respectively:

[0151]

[0152] Therefore, an equivalent (equivalent) discounted minimum-time (transfer) problem is derived, denoted as This problem involves transferring the system from the initial state x pe (θ0) to the origin 0, i.e.:

[0153]

[0154] Similar to the bilateral Pontryagin's minimum principle (PMP), the Hamiltonian function of

[0155]

[0156] is defined as:

[0157]

[0158] where the co-state variable satisfies:

[0159]

[0160] and

[0161]

[0162] To reduce the terminal Hamiltonian constraint, the transversality condition requires satisfaction of:

[0163] H pe (θ f ) + 1 = 0 (24)

[0164] where: τ pe is the unknown Lagrange multiplier of the original transfer problem; for an intercept game, there is For a rendezvous game, there is

[0165] Express the discounted boundary value problem of as

[0166]

[0167] That is, find the parameters τ pe , θ f such that equations (23) and (24) hold.

[0168] The optimal solution of the original bilateral optimal control problem is the same as that of the discounted unilateral minimum-time transfer problem, and the two are equivalent almost everywhere.

[0169] Analyze the sufficient conditions. Since the adjoint equations and the optimal controls of the bilateral and discounted unilateral problems have the same structure, the corresponding optimal controls can be determined by assigning the terminal values of the adjoint states.

[0170] Let τ = τ pe , then λ p = λ pe , λ e = -λ pe = -λ p , so equation (24) is the same as the bilateral Hamiltonian function (13). Then the bilateral optimal control can be constructed from the discounted optimal solution:

[0171]

[0172] This is the same as the bilateral optimal control (10). And all the conditions of problem are satisfied from the solution of . By the same operation, the necessary conditions can also be obtained by replacing τ in with .

[0173] For the pursuit-evasion game problem with a complete information structure (or full information structure), there is no difference between the original bilateral optimal control problem and the discounted unilateral minimum-time transfer problem, and the conversion roadmap is as Figure 2 shown. This equivalence can be explained from two perspectives:

[0174] First, the game only depends on the difference between the initial state and the control input. Therefore, due to the linear terminal condition and the linear co-state, when the player adopts the saddle-point strategy, the player's optimal control is almost the same everywhere.

[0175] Second, with a complete information structure, the existence of the control of the escaping spacecraft (or evader) can be eliminated in advance for the pursuer. The control effect of the evader acts as a discount factor applied to the control amplitude of the pursuer. This property benefits from the separable Hamiltonian function, linear dynamics, and linear terminal conditions (applicable to interception and rendezvous games).

[0176] In one embodiment, a convex-optimization-based method for the minimum-time problem in interception and rendezvous (docking) games is proposed, and its convergence is analyzed:

[0177] 1. Regarding the feasibility sub-problem of the minimum-time game based on convex optimization:

[0178] The minimum-time transfer problem can be solved losslessly through a series of feasible convex sub-problems. This method uses the direct method rather than the indirect method of BMP. For the optimization problem with a free terminal time and linear dynamics, assuming that (A, B) is controllable, a linear search method (such as the golden section method or the bisection method) can be used to determine the optimal terminal time

[0179] The discounted minimum-time transfer problem can be solved losslessly through a series of fixed-time feasible convex sub-problems, considering the minimum final error problem and formulating the terminal constraint φ as a cost under the given θ f :

[0180]

[0181] For the problem if ‖φ‖ > 0, then the sub-problem is infeasible unless In addition, for the infeasible sub-problem, the control amplitude lies on the boundary of the feasible set . The entire interval is divided into two parts, namely the capture region and the escape region, corresponding to the feasible sub-problem and the infeasible solution respectively, as Figure 3In fact, the feasibility of the subproblem provides a qualitative criterion for determining the outcome of the game, win or lose. If given θ f If the subproblem is feasible, the pursuer wins, otherwise, from the pursuer's perspective, the game fails. If the subproblem is not feasible, the escaper wins. Considering the maximum maneuverability assumption g e ≤g p , the game is guaranteed to be played in a finite time θ f ≤∞. Therefore, the problem The optimal value of is equivalent to the minimum feasible solution.

[0182] The numerical solution of the convex subproblem is discussed. To simplify the expression, the state quantity x is omitted without loss of generality. pe , control quantity u pe And the constraint condition g pe Two discretization methods are proposed: trapezoidal discretization method and pseudo-spectral discretization method to solve the subproblems caused by time-varying dynamics.

[0183] Given a fixed terminal time θ f , the interval [θ0, θ f The control quantity and state quantity in ] are discretized into N nodes:

[0184] [u0;…;u N-1 ] and [x0; ...; x N-1 ].

[0185] For each discrete moment θ k ∈[θ0,θ f ], k = 0, 1, ..., N-1, the trapezoidal discretization of formula (16) constitutes a local approximate expression:

[0186]

[0187] The step size is defined as:

[0188] Δθ=(θ f -θ0) / (N-1).

[0189] Pseudospectral discretization is a global approximation method that converges exponentially when the solution is smooth. A temporal affine transformation is required to fit the Chebyshev-Gauss-Lobatto (CGL) collocation interval:

[0190] θ=w1l+w2,

[0191] Where: parameter l∈[-1, 1].

[0192]

[0193] where: differential matrix D ki is defined by the CGL method.

[0194] Finally, stack the feasible subproblems into a second-order cone program (SOCP), whose formula is:

[0195]

[0196] where: decision variables matrix M is composed of sparse coefficient matrices.

[0197] Use the binary search method to find the minimum feasible time, which is reliable and has the advantage of output prediction. Assume that there is an optimal equilibrium solution in the given search interval [θ f，min , θ f，max . Given the tolerance ∈, the maximum number of iterations can be determined in advance, and is bounded by . If there is an optimal terminal time within the given interval, this method guarantees convergence. If the output optimal final time is θ f，max , then the problem is infeasible; in other words, the pursuer cannot capture the evader within the given search interval.

[0198] Since is a convex optimization problem, it can ensure that a lossless solution is obtained at any precision without considering numerical errors. Under the assumption that the maneuverability g p > g e > 0, it can be considered that there is always a saddle point. In addition, by appropriately selecting the search interval for the bisection method, this algorithm guarantees to terminate within a finite number of iterations, thus ensuring the acquisition of the optimal equilibrium solution.

[0199] 2. Regarding the rolling horizon closed-loop minimum-time pursuit-evasion strategy:

[0200] The saddle point strategy obtained based on the Pontryagin's minimum principle (PMP) belongs to open-loop control, and its practical applicability is limited. In fact, the evader may take any feasible but irrational action, even if it is not an optimal strategy. If the pursuer continuously follows the initially obtained "optimal strategy", the expected result cannot be achieved. In addition, considering the uncertainty of irrational evaders, a closed-loop strategy must be implemented. However, the global closed-loop pursuit-evasion strategy u * (x pe ) described by the HJI provides the closed-loop optimal equilibrium solution for all states, and there are implementation obstacles: the partial differential equation solution method based on the grid method is only applicable to problems with four dimensions or less, which is time-consuming and impractical for on-orbit applications.

[0201] As is known to those skilled in the art, there is currently no existing method to analytically obtain the closed-loop equilibrium of the spacecraft pursuit-evasion game. Constructing a closed-loop strategy is inevitable, especially in terms of real-time applicability. Here, for the first time, the requirements for a closed-loop pursuit strategy are proposed. First, the closed-loop strategy should ensure that the escapee is captured under a given maneuverability assumption. This condition is met because the state space is unconstrained in the spacecraft pursuit game. Second, the closed-loop capture time It should be close to the global closed-loop equilibrium u obtained by HJI theory * (x pe ,θ) generated time and is less than the open-loop equilibrium strategy u * (θ) The optimal time obtained like Figure 4 In contrast, even a bad trivial strategy will achieve capture, but the payoff will be worse than the ideal equilibrium strategy.

[0202] For a given initial parameter or game setting, iteratively solve the quantitative problem It is a reasonable and feasible solution to build a closed-loop update decision. Assume that the exact state of the player is known. When the game starts, the optimal terminal time is determined by the initial state and the control profile: Corresponding to the open-loop strategy pair:

[0203]

[0204] However, considering that player i makes a reaction decision and observes the states of other players, a minimum observation time delay ΔT is taken into account. Following the rolling horizon strategy:

[0205]

[0206] in:

[0207] is the value of the game; i (s) is the strategy of player i at stage s;

[0208] The values ​​of the game sequence {V(0), ..., V(s-1), V(s), V(s+1), ..., Vcl} correspond to

[0209] use Indicates the terminal time of the closed-loop strategy.

[0210] Next, we analyze the properties of the closed-loop strategy. In general, if it exists, the global closed-loop equilibrium terminal time It is the best performance that can be expected.

[0211] like Figure 5 As shown, where x p (s), x e(s) is from x p (s - 1), x e (s - 1) and the equilibrium obtained balanced state.

[0212] x′ e (s) is the updated state of player e, where u′ e (s - 1) is unknown. If the strong time consistency of the open-loop strategy is satisfied, then the following inequality holds:

[0213] V(s - 1) = V(x p (s - 1), x e (s - 1)) ≥ V(xp(s), x e (s)) ≥ V(x p (s), x′ e (s)) = V(s)

[0214] Then V(s - 1) ≥ V(s) is satisfied, the sequence is monotonically decreasing, and:

[0215]

[0216] Unfortunately, the open-loop equilibrium strategy is not strongly time-consistent and does not satisfy the subgame equilibrium property. Therefore, the decreasing property of the sequence of V(s) cannot be guaranteed. Since the open-loop equilibrium strategy is only weakly time-consistent, it turns out that it only maintains the equilibrium for the states along the equilibrium path. Note that the receding horizon method is not an equilibrium strategy but a normal solution. However, in the subsequent numerical simulations, it is shown that the proposed receding horizon method behaves like a time-consistent strategy and guarantees the performance in both short-term and long-term games.

[0217] Figure 1 Shows the receding horizon schematic of the closed-loop pursuit-evasion game. Since the opponent's strategy is unknown, the only available information includes the observed state x s at time t -i and the control profile g -i , where -i represents the opponent of player i. At any stage s at θ s , player i solves the pursuit-evasion game by the proposed discounted unilateral problem while deriving a pair of optimal strategies and the unilateral is propagated. After the minimum ΔT, a refreshed decision is made with the updated state; this process is repeated until the terminal tolerance ||φ|| ≤ ε is satisfied.

[0218] In one embodiment, a numerical simulation comparison experiment is provided. The method of the present invention is compared with existing indirect methods. According to the comparison results, weak time consistency is verified, and it is proved by Monte Carlo simulation that the proposed rolling horizon closed-loop strategy can ensure victory:

[0219] For the existing indirect methods used for comparison, see the following documents: "Research on Optimal Tracking / Evasion Trajectories of SpaceX Spacecraft in the Hill Reference Frame", "Research on Differential Games for Close Proximity Operations in Elliptical Orbits", and "Solving Elliptical Orbit Pursuit-Evasion Games by Exact Gradients".

[0220] To verify the effectiveness of the proposed method, the proposed method (the convex optimization-based method LCVX) will be compared with existing numerical methods (the indirect heuristic method IHM, the direct pseudospectral method PSM). The indirect heuristic method (IHM) is used to solve the two-point boundary value problem. The direct pseudospectral method (PSM) is used to solve the one-sided optimal effectiveness problem.

[0221] Both the interception game and the rendezvous game are considered using two discretization methods.

[0222] The initial parameters of the GEO reference orbit are as follows:

[0223] The escaping spacecraft is located at the coordinate origin;

[0224] The orbital period is T = 86400 s, u p,max = 0.0686 m / s 2 , u e,max = 0.0343 m / s 2 .

[0225] Table 1 Initial State Parameters of the Spacecraft

[0226] <![CDATA[r x (t0)m]]> <![CDATA[r y (t0)m]]> <![CDATA[r z (t0)m]]> <![CDATA[v x (t0) m / s]]> <![CDATA[v y (t0) m / s]]> <![CDATA[v z (t0)m / s]]> <![CDATA[x p (t0)]]> <![CDATA[-3.89328×10 4 > <![CDATA[-1×10 5 > <![CDATA[1×10 4 > 0 0 0 <![CDATA[x e (t0)]]> 0 0 0 0 0 0

[0227] To discretely solve the minimum-time transfer problem, pseudospectral discretization and the trapezoidal method are used for discretization at 50 collocation points.

[0228] The indirect heuristic method is implemented using the particle swarm method, and the population size is set to 80 to ensure comparable computational time.

[0229] The minimum-time nonlinear programming problem is solved by GPOPS-II.

[0230] The average results shown in Table 2 are obtained through 100 simulations. It can be found that the three methods have consistent results, but the convex optimization-based method has the highest computational efficiency.

[0231] The optimal trajectory and control are respectively at Figure 6 and Figure 7Depicted. The proposed LCVX method is much faster than both the indirect heuristic method and the nonlinear programming method. The results based on pseudospectral discretization and trapezoidal discretization are consistent.

[0232] Table 2 Comparison of Results for Short-Term Interception Problems

[0233]

[0234] Compared with the interception game problem, the rendezvous game problem has a greater computational difficulty due to the increase in terminal constraints. To verify the effectiveness of the proposed method in the rendezvous game problem, it is verified for short-term rendezvous game problems and long-term rendezvous game problems.

[0235] The rendezvous game problem contains 7 free parameters, almost twice that of the four parameters in the interception game. The increase in parameters makes it more difficult for the indirect heuristic method to find the optimal solution, thus significantly increasing the running time. In contrast, compared with the interception game problem, the method based on (lossless) convex optimization only adds three additional equality constraints. Therefore, regardless of the terminal, the computational complexity of this problem is almost the same and the performance remains consistent.

[0236] The results of the same short-term rendezvous problem are shown in Table 3. It can be found that in the rendezvous game, the IHM method using PSO fails to find the optimal solution even through manual parameter adjustment.

[0237] Figure 8 Depicts the unilateral trajectories (unilateral transfer results) and bilateral optimal trajectories (bilateral rendezvous results) of short and long line games. For long-term games, the relative motion is more complex compared to short games. Both trapezoidal and pseudospectral discretizations produce the same solution, but trapezoidal discretization is more efficient. Compared with the interception problem, the convex optimization-based game solution method does not significantly increase the time.

[0238] Table 3 Results of Short-Term Rendezvous Problems

[0239]

[0240] Closed-Loop Game Verification:

[0241] Both sides of the pursuit-evasion game adopt optimal control strategies and then roll forward until the game ends, and the results are as Figure 9 shown. The results of the closed-loop game show that even if the opponent adopts an optimal strategy, the obtained results are consistent with the open-loop predicted results. In other words, the results of the closed-loop game strategy are not worse than the open-loop results and are risk-free strategies. No matter what strategy the opponent adopts, it cannot escape being intercepted or captured.

[0242] In summary, the present invention proposes a new method for solving the pursuit-evasion differential game. Under the assumptions of complete information and three conventional conditions, the bilateral optimal control problem corresponding to the pursuit-evasion game is transformed into an equivalent discounted minimum-time switching problem. This transformation effectively cancels out the influence of the opponent, regarding the control input of the other player (or game participant) as a completely known disturbance that can be pre-eliminated. Utilizing the computational advantages of convex optimization, a method for binary-searching the optimal capture time is proposed. This method is implemented in real-time using the state-of-the-art interior-point method, enabling the game to be solved efficiently and reliably in approximately 100 milliseconds.

[0243] In one embodiment, according to the above embodiment, the real-time closed-loop pursuit-evasion game method for a spacecraft in an elliptical orbit is summarized as follows:

[0244] A real-time closed-loop pursuit-evasion game method for a spacecraft in an elliptical orbit, the method comprising the following steps:

[0245] Step S1: Given the initial conditions x p (θ0), x e (θ0) and control constraints

[0246] where: θ0 represents the initial true anomaly of the spacecraft; x p (θ0) represents the initial state of the pursuing spacecraft; x e (θ0) represents the initial state of the escaping spacecraft; represents the set of feasible control inputs for the pursuing spacecraft; represents the set of feasible control inputs for the escaping spacecraft;

[0247] Step S2: Iteratively obtain the closed-loop control strategy; wherein, the iterative process in the s-th stage includes the following steps:

[0248] Step S2.1: Input the complete states (x s (s), x p (s)) of both sides of the spacecraft in the pursuit-evasion game at the moment corresponding to θ e , where θ s is the true anomaly angle corresponding to the s-th stage;

[0249] where: x p (s) represents the state of the pursuing spacecraft at the s-th stage; x e (s) represents the state of the escaping spacecraft at the s-th stage;

[0250] Step S2.2: Solve the equivalent discounted unilateral minimum-time transfer problem to obtain the open-loop optimal strategy pair and

[0251] where: Represents the optimal control strategy of the tracking spacecraft; Represents the optimal control strategy of the escaping spacecraft; Represents the true anomaly at the terminal corresponding to solving the game problem in the s stage;

[0252] Step S2.3: According to the optimal control strategy Recursively Recursively calculate the unknown control u e The escaping spacecraft x in the next step e (θ s ), update the target point

[0253] Where: Represents the state of the tracking spacecraft in the s stage according to the optimal control strategy; x e (θ s ) represents the state of the escaping spacecraft in the s stage according to the optimal control strategy; Represents the relative state target point corresponding to the true anomaly at the terminal of solving the game problem;

[0254] Step S2.3: Determine whether ||φ||≤ε is satisfied:

[0255] If so, the iteration ends, and the final closed-loop control game strategy is obtained to achieve the interception of the target, and the game ends;

[0256] Otherwise, obtain θ s+1 , and continue the iteration in the s + 1 stage:

[0257] θ s+1 = θ s + Δθ;

[0258] Where: φ represents the terminal constraint condition; ε represents the error threshold end condition; Δθ represents the difference in true anomaly angles between two adjacent stages.

[0259] In this embodiment, the equivalent discounted unilateral minimum-time transfer problem is:

[0260] Solve the minimum-time transfer problem based on the control inputs and current states of the tracking spacecraft and the escaping spacecraft:

[0261]

[0262] x pe (θ s ) = x p (θ s ) - x e (θ s )

[0263] x pe (θ f ) = 0

[0264] where x pe is the relative state difference between the tracking spacecraft and the escaping spacecraft; u pe is the equivalent discounted control input; is the maximum value of the equivalent control input set; θ f is the optimal true anomaly; x p (θ s ) is the initial state of the tracking spacecraft in the s stage; x e (θ s ) is the initial state of the escaping spacecraft in the s stage; x pe (θ f ) is the terminal state constraint of the relative motion state difference; x pe (θ s ) is the initial state constraint of the relative motion state difference.

[0265] In this embodiment, the step S2.2 is as follows:

[0266] Repeatedly solve for different given terminal times θ f Solve the feasibility problem:

[0267]

[0268] x pe (θ s ) = x p (θ s ) - x e (θ s )

[0269] where φ(θ f ) is the terminal error at the time corresponding to the given true anomaly; u pe is the equivalent discounted control input; is the boundary of.

[0270] In this embodiment, the true anomaly angle at each moment and each stage is in one-to-one correspondence and can be mutually converted.

[0271] In this embodiment, by constructing a unilateral equivalent model of orbital game dynamics and combining a model predictive closed-loop feedback mechanism, real-time strategy generation and dynamic trajectory optimization in a high-speed orbital game scenario are realized.

[0272] In this embodiment, the method is directly used for the autonomous pursuit-evasion confrontation mission of a spacecraft in an elliptical orbit environment, including scenarios such as space target interception, non-cooperative target avoidance, and multi-spacecraft cooperative encirclement. Its application fields cover aerospace attack and defense confrontation, on-orbit service safety control, active space debris avoidance, etc. By solving high-speed strategies and iteratively updating game strategies in real time, it solves the problems of traditional orbit game control methods, such as difficult equilibrium solution, poor strategy convergence, and difficulty in on-orbit application, and provides an autonomous decision-making ability with millisecond-level response for complex space confrontation missions.

[0273] It should be noted that the traditional open-loop game strategy of a spacecraft is essentially a static decision-making process. Its control instructions cannot be updated online after being determined at the initial stage of the mission, resulting in the inability to cope with the sudden maneuvers of an escaping spacecraft. The optimal strategy obtained under the assumption of complete information is unilateral, resulting in potential mismatches with unknown opponents in practical applications. The method described in this embodiment adopts a closed-loop game strategy, which can offset the influence of the uncertainty of the opponent's strategy, thus meeting the requirements of practical applications.

[0274] In this embodiment, the method does not require manual parameter setting and can solve the closed-loop optimal strategy, making the closed-loop strategy optimized based on game theory guidance feasible, which is crucial for the on-orbit application of actual spacecraft.

[0275] In this embodiment, the method does not require hyperparameter adjustment, and its output is deterministic, ensuring convergence, making it suitable for airborne applications, especially on resource-constrained spaceborne embedded platforms.

[0276] The above further describes the technical solutions provided by the present invention through several specific embodiments to highlight the advantages and beneficial effects of the technical solutions provided by the present invention. However, the above several specific embodiments are not used as limitations on the present invention. Any reasonable changes and improvements to the present invention, reasonable combinations of implementation manners, and equivalent replacements within the spirit and principle of the present invention should be included within the protection scope of the present invention.

Claims

1. A real-time closed-loop pursuit-and-escape game method for spacecraft elliptical orbits, characterized in that: The method comprises the following steps: Step S1: Given the initial condition x p (θ0),x e (θ0) and the control constraints Where: θ0 represents the initial true anomaly of the spacecraft; x p (θ0) represents the initial state of the tracking spacecraft; x e (θ0) represents the initial state of the escape spacecraft; represents the set of feasible control inputs for the tracking spacecraft; represents the set of feasible control inputs for the escape spacecraft; Step S2: Iterate to obtain a closed-loop control strategy; wherein the iterative process in the sth stage includes the following steps: Step S2.1: At θ s The complete state of both spacecraft in the pursuit-escape game at the corresponding time (x p (s),x e (s)), where θ s is the true periapsis angle corresponding to the s phase; Where: x p (s) represents the state of the tracking spacecraft in phase s; x e (s) represents the state of the escape spacecraft at stage s; Step S2.2: Solve the equivalent discounted unilateral minimum time transfer problem and obtain the open-loop optimal strategy for and in: represents the optimal control strategy for the tracking spacecraft; represents the optimal control strategy for the escape spacecraft; It represents the true anomaly angle of the terminal corresponding to solving the game problem in stage s; Step S2.3: According to the optimal control strategy Recursion Recursive unknown control u e Next escape spacecraft x e (θ s ), update the target point in: Indicates the state of the spacecraft tracked according to the optimal control strategy in stage s; x e (θ s ) represents the state of the escape spacecraft according to the optimal control strategy in stage s; It represents the relative state target point corresponding to the true anomaly angle of the terminal for solving the game problem; Step S2.3: Determine whether ||φ||≤ε is satisfied: If yes, the iteration ends, and the final closed-loop control game strategy is obtained to intercept the target, and the game ends; Otherwise, get θ s+1 , continue the iteration of the s+1th phase: i s+1 =θ s +△θ; Where: φ represents the terminal constraint condition; ε represents the error threshold end condition; Δθ represents the difference in true periapsis angle between two adjacent stages.

2. The real-time closed-loop pursuit-and-escape game method for spacecraft elliptical orbits according to claim 1 is characterized in that: The equivalent discounted unilateral minimum time transfer problem is: Solve the minimum time transfer problem based on the control input and current state of the pursuit spacecraft and the escape spacecraft: x pe (i s )=x p (i s )-x e (i s ) x pe (i f )=0 Among them, x pe The relative status of the tracking spacecraft and the escaping spacecraft is poor; pe Input for equivalent discount control; is the maximum value of the equivalent control input set; θ f is the optimal true anomaly angle; x p (θ s ) is the initial state of the tracking spacecraft in phase s; x e (θ s ) is the initial state of the escape spacecraft in phase s; x pe (θ f ) is the relative motion state difference terminal state constraint; x pe (θ s ) is the initial state constraint of the relative motion state difference.

3. The real-time closed-loop pursuit-and-escape game method for spacecraft elliptical orbit according to claim 2 is characterized in that: The step S2.2 is: Repeatedly solve for different given terminal times θ f Solve the feasibility problem: x pe (i s )=x p (i s )-x e (i s ) Among them, φ(θ f ) is the terminal error at the corresponding moment of the given true anomaly; u pe Equivalent discount control input; for The border of.

4. A real-time closed-loop pursuit and escape game device for spacecraft elliptical orbits, characterized in that: The device comprises the following modules: Module S1: Given initial conditions x p (θ0), x e (θ0) and the control constraints Where: θ0 represents the initial true anomaly of the spacecraft; x p (θ0) represents the initial state of the tracking spacecraft; x e (θ0) represents the initial state of the escape spacecraft; represents the set of feasible control inputs for the tracking spacecraft; represents the set of feasible control inputs for the escape spacecraft; Module S2: Iteratively obtain closed-loop control strategy; wherein the iterative process in the sth stage includes the following submodules: Submodule S2.1: In θ s The complete state of both spacecraft in the pursuit-escape game at the corresponding time (x p (s),x e (s)), where θ s is the true periapsis angle corresponding to the s phase; Where: x p (s) represents the state of the tracking spacecraft in phase s; x e (s) represents the state of the escape spacecraft at stage s; Submodule S2.2: Solve the equivalent discounted unilateral minimum time transfer problem and obtain the open-loop optimal strategy for and in: represents the optimal control strategy for the tracking spacecraft; represents the optimal control strategy for the escape spacecraft; It represents the true anomaly angle of the terminal corresponding to solving the game problem in stage s; Submodule S2.3: According to the optimal control strategy Recursion Recursive unknown control u e Next escape spacecraft x e (θ s ), update the target point in: Indicates the state of the spacecraft tracked according to the optimal control strategy in stage s; x e (θ s ) represents the state of the escape spacecraft according to the optimal control strategy in stage s; It represents the relative state target point corresponding to the true anomaly angle of the terminal for solving the game problem; Submodule S2.3: Determine whether ||φ||≤ε is satisfied: If yes, the iteration ends, and the final closed-loop control game strategy is obtained to intercept the target, and the game ends; Otherwise, get θ s+1 , continue the iteration of the s+1th phase: i s+1 =θ s +△θ; Where: φ represents the terminal constraint condition; ε represents the error threshold end condition; Δθ represents the difference in true periapsis angle between two adjacent stages.

5. A computer device comprising: A processor and a memory, characterized in that the memory is used to store executable instructions of the processor, and the processor is configured to execute the real-time closed-loop pursuit and escape game of the spacecraft elliptical orbit as described in any one of claims 1 to 3 by executing the executable instructions.

6. A computer storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is run, the real-time closed-loop pursuit and escape game of the spacecraft elliptical orbit described in any one of claims 1 to 3 is executed.

7. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the real-time closed-loop pursuit-and-escape game of a spacecraft in an elliptical orbit as described in any one of claims 1 to 3 are implemented.

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