A method, device and equipment for generating optimal strategy for spacecraft impulse game

Abstract

A method, device, and apparatus for generating an optimal strategy for a spacecraft pulse game involves constructing a multi-point boundary value configuration expression based on the boundary conditions of the tracker's Hamiltonian function, the boundary conditions of the escaper's Hamiltonian function, the boundary conditions of the covariates in the Hamiltonian function, a sequential pulse differential game model, and the Hamiltonian function and interior point function sequence of the tracker and the escaper's Hamiltonian function and interior point function sequence. The method then solves the initial game strategies corresponding to the tracker and escaper, iteratively solving the initial game strategies based on the iterative design variables, multi-point boundary value configuration expression, pulse interval, pulse amplitude, and situational awareness delay constructed from the initial game strategies to obtain the optimal pulse maneuver strategy. When designing a spacecraft strategy based on pulse maneuvers during orbital adjustments, an optimal pulse game interception strategy suitable for discontinuous spacecraft maneuvers is proposed.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft technology, and in particular to a method, device and equipment for generating an optimal strategy for a spacecraft impulse game. Background Art

[0002] When studying multifaceted political, economic, and military issues, differential game methods are often used to model them as bilateral or multilateral optimal control problems. All participants form a multi-player differential system, which incorporates concepts such as constraints, objective functions, and equilibrium solutions, ultimately aiming to find the optimal or equilibrium strategy outcome for all parties involved. However, previous differential game models have often been continuously differentiable. However, many existing spacecraft are equipped only with chemical propulsion systems, requiring pulsed maneuvers for orbital adjustments. The use of pulse maneuvers makes modeling the spacecraft's game process difficult, primarily for the following reasons: 1) The spacecraft's state undergoes sudden changes, resulting in the non-differentiable dynamic equations at discontinuities in the state, thus failing to satisfy the continuous differentiability conditions of differential game theory; 2) Under the continuous maneuvering assumption, the spacecraft only needs to control the direction of the engine's constant thrust, but under the pulse maneuvering assumption, the number, timing, magnitude, and direction of the pulses become decision variables for the spacecraft, significantly increasing the decision space; 3) When both sides employ pulse maneuvers, the order in which the pulse sequences are applied also affects the outcome of the pursuit-escape game. Therefore, a differential game model for pulse thrust has not yet been developed, nor has the optimal pulse maneuvering strategy for this condition been determined. Summary of the Invention

[0003] The main technical problem solved by the present invention is to propose an optimal pulse game interception strategy suitable for discontinuous maneuvers of spacecraft when designing a strategy for the spacecraft according to the pulse maneuvering method during orbit change adjustment.

[0004] According to the first aspect, an embodiment provides a method for generating an optimal strategy for a spacecraft impulse game, comprising:

[0005] Obtain the pulse interval, pulse amplitude, and situational awareness delay of the pursuer, as well as the pulse interval, pulse amplitude, and situational awareness delay of the evader, in a pursuit-escape pulse maneuver game scenario; wherein the pulse interval refers to the time interval between two adjacent pulses;

[0006] Constructing a sequence pulse differential game model, and constructing the Hamiltonian function and interior point function sequence of the tracker and the Hamiltonian function and interior point function sequence of the escaper; wherein the sequence pulse differential game model includes constraint equations constructed according to the pulse interval and the pulse amplitude;

[0007] Constructing a multi-point boundary value configuration expression based on the boundary conditions of the Hamiltonian function of the tracker, the boundary conditions of the Hamiltonian function of the escaper, the boundary conditions of the co-state variables in the Hamiltonian function, the sequential pulse differential game model, the Hamiltonian function and interior point function sequence of the tracker, and the Hamiltonian function and interior point function sequence of the escaper;

[0008] The initial game strategies corresponding to the pursuer and the evader are solved, and corresponding iterative design variables are constructed according to the initial game strategies. The initial game strategies are iteratively solved based on the iterative design variables, the multi-point boundary value configuration expression, the pulse interval, the pulse amplitude, and the situational awareness delay to obtain an optimal pulse maneuvering strategy.

[0009] In some embodiments, solving the initial game strategies corresponding to the tracker and the escaper includes:

[0010] Starting from the first pulse phase of a preset multiple pulse phases:

[0011] Acquire the initial orbital positions of the tracker and the escaper in the current pulse phase, wherein the initial orbital position of the tracker and the initial orbital position of the escaper are preset for each pulse phase;

[0012] When there is a pulse thrust on the pursuer and the escaper, solving the pursuer's pulse maneuver strategy and the escaper's pulse maneuver strategy based on the pursuer's initial orbital position and the escaper's initial orbital position, wherein the pursuer's pulse maneuver strategy includes a plurality of pursuit strategies and the escaper's pulse maneuver strategy includes a plurality of escape strategies;

[0013] Selecting the optimal tracking strategy among the pulse maneuver strategies of the pursuer, and selecting the optimal escape strategy among the pulse maneuver strategies of the escaper;

[0014] If the tracker satisfies the preset game conditions when using the optimal tracking strategy and the escaper satisfies the optimal escaping strategy in the pursuit-escape game, or the number of pulse phases experienced is greater than a preset pulse phase threshold, the optimal tracking strategy and the optimal escaping strategy are used as the initial game strategies;

[0015] Otherwise, the next pulse phase is entered to calculate the updated optimal tracking strategy and optimal escape strategy until the preset game conditions are met when the tracker uses the optimal tracking strategy and the escaper uses the optimal escape strategy to play the pursuit and escape game, or the number of pulse phases experienced is greater than the preset game phase threshold, and the updated optimal tracking strategy and optimal escape strategy are used as the initial game strategy; wherein, the game condition is that the remaining interception time is less than the pulse interval of the tracker or less than the pulse interval of the escaper, and the remaining interception time represents the time required for the tracker to intercept the escaper.

[0016] In some embodiments, the initial game strategy includes the pulse maneuver sequence of the pursuer, the pulse maneuver sequence of the escaper, and the game deadline. The pulse maneuver sequence of the pursuer includes Δv P1 ,...,Δv PN , where Δv P1 ,...,Δv PN represent the speed of the pursuer under the action of the 1st... to the Nth pulse respectively. The pulse maneuver sequence of the escaper includes Δv E1 ,...,Δv EN , Δv E1 ,...,Δv EN represent the speed of the escaper under the action of the 1st... to Nth pulses respectively, P represents the pursuer, E represents the escaper, and N represents the number of pulses;

[0017] The iterative design variables include:

[0018] X=[Δv P1 ,...,Δv PN ,Δv E1 ,...,Δv EN ,κ P1 ,...,κ PN ,κ E1 ,...,κ EN ,λ Pr0, λ Er0 ,λ Pv0, t f ] T

[0019] Wherein, X represents the iterative design variable, t f represents the game deadline in the initial game strategy, i.e., the interception time, κ P1 ,...,κ PN Denotes the Lagrange multiplier corresponding to different trackers, κ E1 ,...,k ENDenotes the Lagrange multiplier corresponding to the different escapers, λ Pr0, λ Er0, λ Pv0 They represent the position co-state of the tracker at the initial moment, the position co-state of the escaper at the initial moment, and the velocity co-state of the tracker at the initial moment respectively.

[0020] In some embodiments, the interior point function sequence of the tracer and the interior point function sequence of the escaper include:

[0021] Φ ik =γ ik χ ik +κ ik σ ik ,i=P,E

[0022] Among them, Φ ik represents the interior point function sequence of the spacecraft, γ ik and κ ik represents the Lagrange multiplier of the spacecraft, χ ik represents the position difference of the spacecraft, σ ik represents the velocity impulse inequality of the spacecraft, P represents the tracker, E represents the escaper, k represents the time node, k=1,2,...,N, N represents the number of pulses, wherein when i=P, the spacecraft refers to the tracker, and when i=E, the spacecraft refers to the escaper.

[0023] In some embodiments, the Hamiltonian function of the tracker and the Hamiltonian function of the escaper include:

[0024]

[0025] Among them, H i represents the Hamiltonian function of the spacecraft, P represents the pursuer, E represents the escaper, T represents the transposed symbol, represents the position co-state of the spacecraft, v i represents the speed of the spacecraft, represents the velocity co-state of the spacecraft, g i represents the gravitational acceleration of the spacecraft, wherein when i=P, the spacecraft is the pursuer, and when i=E, the spacecraft is the escaper.

[0026] In some embodiments, the constraint equation includes:

[0027]

[0028] N f :=r P (t f )-r E (t f)=0

[0029] Wherein, P represents the tracker, E represents the escaper, represents the instant after the pulse acts on the spacecraft, represents the instant before the pulse acts on the spacecraft, χ ik represents the position difference of the spacecraft, represents the position of the spacecraft immediately after the pulse, represents the position of the spacecraft immediately before the pulse, σ ik The velocity impulse inequality for the spacecraft, Δv ik represents the velocity difference of the spacecraft, represents the velocity of the spacecraft immediately after the pulse, The velocity of the spacecraft immediately before the pulse, ΔV i max represents the maximum pulse amplitude of the spacecraft, k represents the time node, N i represents the number of pulses of the spacecraft, N f represents the intercept constraint at the terminal position, t f represents the interception time, r P (t f ) represents the position of the tracker at the moment of interception, r E (t f ) represents the position of the escape vehicle at the moment of interception, wherein when i=P, the spacecraft refers to the pursuer, and when i=E, the spacecraft refers to the escape vehicle.

[0030] In some embodiments, the sequential pulse differential game model further includes a state equation and a payoff function, wherein the state equation is constructed based on the orbital positions and velocities of the pursuer and the escaper.

[0031] In some embodiments, the iteratively solving the initial game strategy based on the iterative design variables, the multi-point boundary value configuration expression, the pulse interval, the pulse amplitude, and the situational awareness delay to obtain the optimal pulse maneuver strategy includes:

[0032] Constructing the trajectory of the tracker at different pulse phases and the trajectory of the escaper at different pulse phases;

[0033] Generate a trajectory end error expression according to the trajectory of the tracker at different pulse phases and the trajectory of the escaper at different pulse phases;

[0034] The target shooting method is used as the iterative algorithm, the iterative design variable is used as the iterative correction value, the multi-point boundary value configuration expression is used as the constraint condition, the pulse interval, the pulse amplitude, and the situation awareness delay are used as input parameters, and the initial game strategy is iteratively solved according to the trajectory end error expression to obtain the optimal pulse maneuvering strategy.

[0035] According to the second aspect, an embodiment provides an optimal strategy generation device for a spacecraft impulse game, comprising:

[0036] A data preparation module is used to obtain the pulse interval, pulse amplitude, and situational awareness delay of the pursuer in a pursuit-and-escape pulse maneuver game scenario, as well as the pulse interval, pulse amplitude, and situational awareness delay of the escaper; wherein the pulse interval refers to the time interval between two adjacent pulses;

[0037] a model construction module for constructing a sequence pulse differential game model, and constructing a Hamiltonian function and an interior point function sequence of the tracker and a Hamiltonian function and an interior point function sequence of the escaper; wherein the sequence pulse differential game model includes a constraint equation constructed according to the pulse interval and the pulse amplitude;

[0038] a multi-point boundary value conversion module, configured to construct a multi-point boundary value configuration expression based on the boundary conditions of the Hamiltonian function of the tracker, the boundary conditions of the Hamiltonian function of the escaper, the boundary conditions of the co-state variables in the Hamiltonian function, the sequential pulse differential game model, the Hamiltonian function and interior point function sequence of the tracker, and the Hamiltonian function and interior point function sequence of the escaper;

[0039] A game strategy generation module is used to solve the initial game strategies corresponding to the tracker and the evader, and construct corresponding iterative design variables based on the initial game strategies. The initial game strategies are iteratively solved based on the iterative design variables, the multi-point boundary value configuration expression, the pulse interval, the pulse amplitude and the situational awareness delay to obtain the optimal pulse maneuver strategy.

[0040] According to a third aspect, an embodiment provides an optimal strategy generation device for a spacecraft impulse game, comprising:

[0041] Memory, used to store programs;

[0042] The processor is configured to implement a game strategy generation method by executing a program stored in the memory.

[0043] According to the above-described embodiment, the optimal strategy generation method, device, and apparatus for spacecraft pulse games are applicable to the discontinuous maneuvers of spacecraft when subjected to pulse thrust, due to the construction of a sequential pulse differential game model. Multi-point boundary value configuration expressions are constructed based on the sequential pulse differential game model, the Hamiltonian function and interior point function sequence of the tracker, and the Hamiltonian function and interior point function sequence of the escaper. The interior point function sequence of the tracker and the interior point function sequence of the escaper take into account the sequence situation when pulse maneuvers are used as discontinuous points and are converted into a multi-point boundary value problem. In the process of solving the pulse maneuver strategy, iterative design variables are constructed based on the solved initial game strategy, and an iterative solution is performed, thereby improving the accuracy of the strategy solution. As a result, a precise optimal pulse maneuver strategy can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of a method for generating an optimal strategy for a spacecraft impulse game according to an embodiment of the present application;

[0045] Figure 2 A flowchart of solving the initial game strategies corresponding to the tracker and the escaper according to an embodiment;

[0046] Figure 3 A flowchart of an embodiment of an optimal pulse maneuver strategy obtained by iteratively solving the initial game strategy based on iterative design variables, multi-point boundary value configuration expressions, pulse intervals, pulse amplitudes, and situational awareness delays;

[0047] Figure 4a 、 Figure 4b 、 Figure 4c and Figure 4d are respectively the game results in one embodiment;

[0048] Figure 5a 、 Figure 5b 、 Figure 5c and Figure 5d are respectively the game results in one embodiment;

[0049] Figure 6 A schematic structural diagram of an optimal strategy generation device for a spacecraft impulse game according to an embodiment. DETAILED DESCRIPTION

[0050] The present invention will be further described in detail below by means of specific embodiments in conjunction with the accompanying drawings. Similar elements in different embodiments are numbered with associated similar elements. In the following embodiments, many detailed descriptions are provided to enable the present application to be better understood. However, those skilled in the art will readily appreciate that some of the features may be omitted in different circumstances, or may be replaced by other elements, materials, or methods. In some cases, some operations related to the present application are not shown or described in the specification. This is to avoid the core portion of the present application being overwhelmed by excessive descriptions, and for those skilled in the art, it is not necessary to describe these related operations in detail. They will fully understand the related operations based on the description in the specification and the general technical knowledge in the art.

[0051] In addition, the features, operations, or characteristics described in the specification may be combined in any appropriate manner to form various embodiments. Furthermore, the steps or actions in the method description may be reordered or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various sequences in the specification and drawings are provided solely for the purpose of clearly describing a particular embodiment and are not intended to be mandatory, unless otherwise specified.

[0052] The serial numbers assigned to components herein, such as "first," "second," etc., are used solely to distinguish the objects being described and do not convey any sequential or technical meaning. References to "connection" and "coupling" herein, unless otherwise specified, include both direct and indirect connections (couplings).

[0053] In this game, it is assumed that both the pursuer and the evader have perfect state observation. The pursuer will only maneuver after observing the evader's escape pulse maneuver. The amplitude of each party's pulse maneuver is capped but the direction is free. The goal of each game is interception / counter-interception, and the game duration is free. If the pursuer can intercept the evader within a single escape-pursuit pulse maneuver, the game is a single-pulse interception game. If the pursuer fails to intercept the evader within a single pulse maneuver, and both parties can perform multiple pulse maneuvers at equal intervals, the game becomes a multi-pulse interception game. Since both parties can observe the other party's latest state before making decisions on the next maneuver, this game becomes a multi-pulse sequence decision game. The use of pulse maneuvers makes modeling the spacecraft's game process difficult, primarily due to the following: 1) The spacecraft's state undergoes sudden changes, resulting in the non-differentiable dynamic equations at discontinuities in the state, thus failing to satisfy the continuous differentiability conditions of differential game theory; 2) Under the continuous maneuvering assumption, the spacecraft only needs to control the direction of the engine's constant thrust, but under the pulse maneuvering assumption, the number, timing, magnitude, and direction of the pulses become decision variables for the spacecraft, significantly increasing the decision space; 3) When both sides employ pulse maneuvers, the order in which the pulse sequences are applied also affects the outcome of the pursuit-escape game. Therefore, a differential game model for pulse thrust has not yet been developed, nor has the optimal pulse maneuvering strategy for this condition been determined.

[0054] Please refer to Figure 1 In an embodiment of the present invention, a method for generating an optimal strategy for a spacecraft impulse game is proposed, including steps S1 to S4, which are described in detail below.

[0055] Step S1: Obtain the pulse interval, pulse amplitude, and situational awareness delay of the pursuer, as well as the pulse interval, pulse amplitude, and situational awareness delay of the evader in the pursuit-escape pulse maneuver game scenario.

[0056] In some embodiments, in the pursuit-escape pulse maneuver game scenario, both the tracker and the escaper are initially operating in low Earth orbit or near geostationary orbit. The orbital position of the tracker or the escaper is expressed using classical orbital elements, semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, and argument of latitude. Therefore, the tracker's orbital position can be expressed as [a P ,e P ,i P ,Ω P ,θ uP ]=[6778.137km,0,0°,0°,0°], the orbital position of the escape vehicle can be expressed as [a E ,e E ,i E ,Ω E ,θ uE]=[6878.137km,0,0°,0°,1.5°], where a P represents the semi-major axis of the tracker, e P represents the eccentricity of the tracker, i P represents the tracker's orbital inclination, Ω P represents the right ascension of the tracker's ascending node, θ uP Indicates the latitude argument of the tracker. The pulse interval of the tracker is T P is 1000s, the pulse interval of the escaper is T E is 1000s, and the pulse amplitude of the tracker is ΔV P max =150m / s, the pulse amplitude of the escaper is ΔV E max =50m / s, tracker's situational awareness delay τ P is 0s, the situational awareness delay τ of the escape device E The pulse interval of the pursuer and the pulse interval of the escaper refer to the time interval between two adjacent pulses.

[0057] Step S2: Construct a sequential pulse differential game model, and construct the Hamiltonian function and interior point function sequence of the tracker and the Hamiltonian function and interior point function sequence of the escaper.

[0058] In some embodiments, the sequential pulse differential game model includes constraint equations constructed based on pulse intervals and pulse amplitudes. At the same time, the sequential pulse differential game model also includes state equations and payoff functions, wherein the state equations are constructed based on the orbital positions and velocities of the pursuer and the escaper.

[0059] In some embodiments, the constraint equations include:

[0060]

[0061] N f :=r P (t f )-r E (t f )=0

[0062] Among them, P represents the tracker, E represents the escaper, represents the instant after the pulse acts on the spacecraft, represents the instant before the pulse acts on the spacecraft, χ ik represents the position difference of the spacecraft, represents the position of the spacecraft immediately after the pulse, represents the position of the spacecraft immediately before the pulse, σ ik The velocity impulse inequality for the spacecraft, Δv ik represents the velocity difference of the spacecraft, represents the velocity of the spacecraft immediately after the pulse, The velocity of the spacecraft immediately before the pulse, ΔV i max represents the maximum pulse amplitude of the spacecraft, k represents the time node, N i Represents the number of spacecraft pulses, N f represents the intercept constraint at the terminal position, t f represents the interception time, r P (t f ) represents the position of the tracker at the moment of interception, r E (t f ) represents the position of the escape vehicle at the moment of interception, where when i = P, the spacecraft refers to the pursuer, and when i = E, the spacecraft refers to the escape vehicle.

[0063] In some embodiments, if the tracker can complete the interception as early as possible, the interception time satisfies t f ≤T E , then the game ends in a single pulse phase. If the escaper maximizes the interception time so that t f >T E , then the escaper will be able to apply a second pulse, and the game will enter a multi-stage multi-pulse game. E represents the pulse interval of the escaper. Assume that the number of pulses of the chaser and escaper is N P and N E , the pulse maneuver sequence of the tracker is Δv P1 ,Δv P2 ,..., The escape vehicle's impulse maneuver sequence is Δv E1 ,Δv E2 ,..., The time of the first pulse of both parties is recorded as t P1 and t E1 , then the tracker's action time of the k+1th pulse is t Pk+1 =t E1 +τ P +k·T P ,k=1,2,3,...,N P -1, the time of action of the escaper at the k+1th pulse is t Ek+1 =t E1 +k·T E ,k=1,2,3,...,N E -1, where τ P Represents the situational awareness latency of the tracker.

[0064] In some embodiments, the sequential pulse differential game model further includes a state equation, wherein the state equation is constructed based on the orbital position and velocity of the pursuer and the escaper. The position vectors of the two spacecraft in the geocentric inertial system are r P and r E , when the perturbation force is neglected, the motion of the two obeys Kepler orbital dynamics, or in other words, presents the state equation in the game:

[0065]

[0066] Among them, μ represents the gravitational constant of the central celestial body, r P and r E are the position vectors of the pursuer and escaper in the Earth-centered inertial system, r P0 represents the tracker's orbital position at the initial moment, v P0 represents the speed of the tracker at the initial moment, r E0 represents the orbital position of the escaper at the initial moment, v E0 represents the speed of the escaper at the initial moment, and t0 represents the initial moment of the game.

[0067] In some embodiments, the sequential pulse differential game model includes a payoff function where, in a multi-pulse game, each pulse of the evader is not only a response to the preceding pursuer pulse maneuver, but also takes into account future pursuer maneuvers to continuously maximize interception time:

[0068]

[0069] Among them, J represents the payment function, N P and N E represents the number of pulses of the chaser and escaper, t f Indicates the interception moment.

[0070] In some embodiments, the solution that satisfies the above formula is called a multi-stage Steinberg equilibrium. The game behavior of each decision-making step of both parties is reflected in that not only the local optimality of the action for the current time is considered, but also the global optimality for subsequent actions is considered in a forward-looking manner.

[0071] In some embodiments, since the pulse interruption times of the tracker and the escaper are inconsistent, the Hamiltonian function of the tracker and the Hamiltonian function of the escaper are constructed separately, including:

[0072]

[0073] Among them, H i represents the Hamiltonian function of the spacecraft, P represents the pursuer, E represents the escaper, T represents the transposed symbol, represents the position co-state of the spacecraft, v irepresents the speed of the spacecraft, represents the velocity co-state of the spacecraft, g i represents the gravitational acceleration of the spacecraft, where when i=P, the spacecraft refers to the pursuer, and when i=E, the spacecraft refers to the escaper.

[0074] In some embodiments, at the discontinuous points of the pulse action, i.e., the interior points, a tracker interior point function sequence and an escaper interior point function sequence are constructed respectively, including:

[0075] Φ ik =γ ik χ ik +κ ik σ ik ,i=P,E

[0076] Among them, Φ ik represents the interior point function sequence of the spacecraft, γ ik and κ ik represents the Lagrange multiplier of the spacecraft, χ ik represents the position difference of the spacecraft, σ ik represents the velocity impulse inequality of the spacecraft, P represents the pursuer, E represents the escaper, k represents the time node, k=1,2,…,N, N represents the number of pulses, among which, when i=P, the spacecraft refers to the pursuer, and when i=E, the spacecraft refers to the escaper.

[0077] In some embodiments, a terminal function Φ is constructed at the terminal moment f Including the constraints on the terminal moment and the terms related to the terminal moment in the payment function, it is expressed as: Φ f =t f .

[0078] Step S3: Construct a multi-point boundary value configuration expression based on the boundary conditions of the Hamiltonian function of the tracker, the boundary conditions of the Hamiltonian function of the escaper, the boundary conditions of the co-state variables in the Hamiltonian function, the sequential pulse differential game model, the Hamiltonian function and interior point function sequence of the tracker, and the Hamiltonian function and interior point function sequence of the escaper.

[0079] In some embodiments, based on the transversal condition of the Hamiltonian function, the boundary conditions of the Hamiltonian function of the tracker and the boundary conditions of the Hamiltonian function of the escaper can be obtained as follows: i (t f )=-1.

[0080] In some embodiments, the boundary conditions of the co-state variables in the Hamiltonian function can be obtained based on the transversal conditions of the co-state variables:

[0081]

[0082]

[0083] in, represents the position co-state of the tracker at the instant before the pulse, represents the position co-state of the tracker at the instant after the pulse is applied, Φ k represents the interior point function sequence of the spacecraft, Indicates the position of the tracker at the moment before the pulse is applied. represents the position co-state of the escaper at the instant before the pulse acts, represents the position co-state of the escaper at the instant after the pulse acts on it, Indicates the position of the escaper at the instant before the pulse acts, represents the velocity co-state at the instant after the pulse acts on the tracker, represents the velocity of the tracker at the instant after the pulse is applied, κ Pk represents the Lagrange multiplier of the tracker at time k, Δv Pk represents the speed of the tracker under the action of the kth pulse.

[0084] In some embodiments, Δr(t f )=r P (t f )-r E (t f ) represents the terminal position vector difference between the pursuer and the escaper.

[0085] In some embodiments, since the escaper's impulse maneuver is applied at the initial moment, the escaper's trajectory will be divided into N segments by N interior points, and the tracker's trajectory will be divided into N+1 segments by N interior points. Therefore, the multi-point boundary value configuration expression is constructed as follows:

[0086]

[0087] in, represents the position vector of the escaper at the initial moment of the game, r E0 represents the orbital position of the escaper at the initial moment, represents the velocity co-state of the escaper at the initial moment of the game, κ E1 represents the Lagrange multiplier of the escaper when k = 1, Δv E1 represents the speed of the escaper under the action of the first pulse, represents the position co-state of the escaper at the instant before the pulse acts, represents the position co-state of the escaper at the instant after the pulse acts on it, represents the velocity co-state at the instant before the pulse acts on the escaper, represents the velocity co-state at the instant after the pulse acts on the escaper, It represents the position of the escaper at the moment the pulse acts on it. represents the position of the escaper at the instant before the pulse acts, r E (t f ) represents the position vector of the escape vehicle at the moment of interception, r P (t f ) represents the position vector of the tracker at the interception moment, represents the velocity co-state of the escape vehicle at the moment of interception, represents the position co-state of the tracker at the instant before the pulse, represents the position co-state of the tracker at the instant after the pulse is applied, κ Pk represents the Lagrange multiplier of the tracker at time k, Δv Pk represents the speed of the tracker under the action of the kth pulse, It represents the position of the tracker at the moment after the pulse is applied. Indicates the position of the tracker at the moment before the pulse is applied. Represents the velocity co-state at the instant after the pulse is applied to the tracker.

[0088] In some embodiments, the additional N+1 unknown parameters of the tracker correspond to N+1 equations, expressed as:

[0089]

[0090] Among them, κ i1 ,...κ iN represents the Lagrange multiplier of the spacecraft at time nodes k=1,...,N, σ i1 ,...σ iN The velocity impulse inequality of the spacecraft at the time nodes k=1,...,N is expressed as follows: H(t f )=-1 represents the boundary condition of the Hamiltonian function of the spacecraft.

[0091] Step S4: Solve the initial game strategies corresponding to the pursuer and the evader, and construct the corresponding iterative design variables based on the initial game strategies. The initial game strategies are iteratively solved based on the iterative design variables, multi-point boundary value configuration expressions, pulse intervals, pulse amplitudes, and situational awareness delays to obtain the optimal pulse maneuver strategy.

[0092] Please refer to Figure 2 In some embodiments, step S4 solves the initial game strategies corresponding to the tracker and the evader, including steps S41 to S45, wherein steps S41 to S45 are executed starting from the first pulse phase of a preset plurality of pulse phases, as described in detail below.

[0093] Step S41: Obtain the initial orbital positions of the tracker and the escaper in the current pulse phase.

[0094] In some embodiments, each pulse phase is preset with an initial orbital position of the tracker and an initial orbital position of the escaper.

[0095] Step S42: When there is pulse thrust on the tracker and the escaper, the tracker's pulse maneuvering strategy and the escaper's pulse maneuvering strategy are solved based on the tracker's initial orbital position and the escaper's initial orbital position.

[0096] In some embodiments, the pulse maneuver strategy of the pursuer includes multiple pursuit strategies, and the pulse maneuver strategy of the escaper includes multiple escape strategies.

[0097] Step S43: Select the optimal tracking strategy among the pulse maneuver strategies of the tracker, and select the optimal escape strategy among the pulse maneuver strategies of the escaper.

[0098] In some embodiments, the optimal tracking strategy in the pulse maneuver strategy of the tracker is solved The strategy that minimizes the interception time is the optimal tracking strategy Similarly, the optimal escape strategy in the escape device's pulse maneuver strategy is

[0099] Step S44: If the tracker satisfies the preset game conditions when using the optimal tracking strategy and the evader uses the optimal escaping strategy for the pursuit-escape game, or the number of pulse stages experienced is greater than the preset pulse stage threshold, the optimal tracking strategy and the optimal escaping strategy are used as the initial game strategies.

[0100] In some embodiments, the preset pulse phase threshold is 10.

[0101] Step S45: Otherwise, enter the next pulse stage to calculate the updated optimal tracking strategy and optimal escape strategy until the tracker uses the optimal tracking strategy and the escaper uses the optimal escape strategy to play the pursuit and escape game and the preset game conditions are met, or the number of pulse stages experienced is greater than the preset game stage threshold, and the updated optimal tracking strategy and optimal escape strategy are used as the initial game strategy.

[0102] In some embodiments, the game condition is that the remaining interception time is less than the tracker's pulse interval or less than the evader's pulse interval, and the remaining interception time represents the time required for the tracker to intercept the evader.

[0103] In some embodiments, since the spacecraft is assumed to have equally spaced pulses and the waiting time is not considered, the number of remaining pulses depends entirely on the remaining interception time of the game and satisfies the following formula:

[0104]

[0105] Among them, N Est Indicates the number of remaining pulses, floor indicates the rounding down function, Indicates the estimated remaining intercept time.

[0106] In some embodiments, for the initial game strategy that has been obtained, the iterative process from the initial solution to the exact solution can be completed by shooting method, wherein the iterative design variables are constructed according to the pulse maneuver sequence of the tracker, the pulse maneuver sequence of the escaper and the game deadline in the initial game strategy. The pulse maneuver sequence of the tracker includes Δv P1 ,...,Δv PN , where Δv P1 ,...,Δv PN represent the speed of the pursuer under the action of the 1st... to the Nth pulse respectively. The pulse maneuver sequence of the escaper includes Δv E1 ,...,Δv EN , Δv E1 ,...,Δv EN They represent the speed of the escaper under the action of pulses 1... to N, P represents the pursuer, E represents the escaper, and N represents the number of pulses. Therefore, the iterative design variables include:

[0107] X=[Δv P1 ,...,Δv PN ,Δv E1 ,...,Δv EN ,κ P1 ,...,κ PN ,κ E1 ,...,κ EN ,λ Pr0 ,λ Er0 ,λ Pv0 ,t f ] T

[0108] Where X represents the iterative design variable, t f represents the game deadline in the initial game strategy, i.e., the interception moment, κ P1 ,...,κ PN Denotes the Lagrange multiplier corresponding to different trackers, κ E1 ,...,κ EN Denotes the Lagrange multiplier corresponding to different escapers, λPr0, λ Er0, λ Pv0, They represent the position co-state of the tracker at the initial moment, the position co-state of the escaper at the initial moment, and the velocity co-state of the tracker at the initial moment respectively.

[0109] Please refer to Figure 3 In some embodiments, step S4 iteratively solves the initial game strategy based on iterative design variables, multi-point boundary value configuration expressions, pulse intervals, pulse amplitudes, and situational awareness delays to obtain the optimal pulse maneuver strategy, including steps S47 to S49, which are described in detail below.

[0110] Step S47: Construct the trajectory of the tracker at different pulse phases and the trajectory of the escaper at different pulse phases.

[0111] In some embodiments, since the timing of the tracker pulse maneuver is not consistent with the timing of the escaper pulse maneuver, for the tracker, The first segment of the trajectory can be obtained by integrating the following formula:

[0112]

[0113] in, represents the position of the spacecraft in the first trajectory, represents the velocity of the spacecraft in the first trajectory, represents the position co-state of the spacecraft, represents the velocity co-state of the spacecraft, v i Indicates the speed of the tracker, g i represents the gravitational acceleration of the spacecraft, represents the position of the tracker immediately after the initial pulse. It represents the speed of the tracker immediately after the initial pulse. It represents the position co-state of the tracker immediately after the initial pulse. represents the velocity co-state of the tracker at the instant after the initial pulse, r P0 represents the position of the tracker at the initial moment, v P0 represents the speed of the tracker at the initial moment, λ Pr0 represents the position co-state of the tracker at the initial moment, λ Pv0 Represents the velocity covariance of the tracker at the initial moment.

[0114] In some embodiments, for the escaper, the first trajectory can be obtained by integrating the following formula:

[0115]

[0116] In some embodiments, if the number of pulses is greater than or equal to two, the k-th trajectory of the pursuer and escaper can be obtained by integrating the following equation:

[0117]

[0118] Step S48: Generate a trajectory end error expression based on the trajectory of the tracker at different pulse phases and the trajectory of the escaper at different pulse phases.

[0119]

[0120] Step S49: Using the shooting method as the iterative algorithm, the iterative design variable as the iterative correction value, the multi-point boundary value configuration expression as the constraint condition, the pulse interval, pulse amplitude, and situation awareness delay as input parameters, the initial game strategy is iteratively solved according to the trajectory end error expression to obtain the optimal pulse maneuvering strategy.

[0121] In some embodiments, the trajectory end error expression can be used as a constraint limit on the error of the end position in multiple trajectories of the pursuer and the escaper, and the shooting method is used as the iterative algorithm, the iterative design variables are used as the iterative correction values, the multi-point boundary value configuration expression is used as the constraint condition, and the pulse interval, pulse amplitude, and situation awareness delay are used as input parameters to iteratively solve the initial game strategy to obtain the optimal pulse maneuvering strategy.

[0122] Please refer to Figure 4a 、 Figure 4b 、 Figure 4c and Figure 4d It can be seen that in some embodiments, in the pursuit-escape pulse maneuver game scenario, the tracker's orbital position is [a P ,e P ,i P ,Ω P ,θ uP ]=[6778.137km,0,0°,0°,0°], the orbital position of the escape vehicle is [a E ,e E ,i E ,Ω E ,θ uE ]=[6878.137km,0,0°,0°,1.5°], where a P represents the semi-major axis of the tracker, e P represents the eccentricity of the tracker, i P represents the tracker's orbital inclination, Ω P represents the right ascension of the tracker's ascending node, θ up Indicates the latitude argument of the tracker. The pulse interval of the tracker is T P is 1000s, the pulse interval of the escaper is TE is 1000s, and the pulse amplitude of the tracker is ΔV P max =150m / s, the pulse amplitude of the escaper is ΔV E max =50m / s, tracker's situational awareness delay τ P is 0s, the situational awareness delay τ of the escape device E The tracker and the escaper differ in orbital altitude by 100 km and phase angle by 1.5°. Both parties perform pulse maneuvers sequentially, with the escaper taking the initiative and the tracker taking the initiative. Assuming that the tracker has no situational awareness delay, that is, the tracker can perform pulse maneuvers immediately after the escaper applies the pulse, then this game will be completed within one pulse cycle. The interception time corresponding to the Steinberg equilibrium solution where both parties adopt the optimal pulse maneuver strategy is 961 seconds. Figure 4a 、 Figure 4b 、 Figure 4c and Figure 4d As can be seen, the optimal pulse maneuver directions for both the pursuer and the evader are nearly identical. Temporally, the pulse moments of the pursuer and evader coincide, a situation very similar to a simultaneous decision game. However, in reality, the two are quite different. The fundamental difference lies in the fact that the pursuer possesses a broader set of situational information than the evader, as the pursuer observes the evader's most recent situation. From a solution perspective, this solution is not a Nash equilibrium either. This is because if the pursuer's strategy is fixed, the evader will not actively maintain an interception relationship with the pursuer when freely choosing pulse directions, so interception is not guaranteed.

[0123] Please refer to Figure 5a 、 Figure 5b 、 Figure 5c and Figure 5d It can be seen that in some embodiments, in the pursuit-escape pulse maneuver game scenario, the tracker's orbital position is [a P ,e P ,i P ,Ω P ,θ uP ]=[6778.137km,0,0°,0°,0°], the orbital position of the escape vehicle is [a E ,e E ,i E ,Ω E ,θ uE ]=[6878.137km,0,0°,0°,4°]. Tracker pulse interval T P is 1000s, the pulse interval of the escaper is T E is 1000s, and the pulse amplitude of the tracker is ΔV P max =150m / s, the pulse amplitude of the escaper is ΔV E max =50m / s, tracker's situational awareness delay τP is 100s, the situational awareness delay τ of the escape device E The phase angle between the pursuer and the evader is 4°, and considering the 100s situational awareness delay, the game cannot be completed within the 1000s interval between single pulses, and it will evolve into a multi-pulse interception game. Since the pursuer finally intercepted the evader in 1862.8s, the game is ultimately a two-pulse game. The absolute trajectory, relative trajectory, distance change, and pulse direction of the game are shown in Figure 2. Figure 5a 、 Figure 5b 、 Figure 5c and Figure 5d As shown in Figure 2, it can be found that the optimal pulse directions of the pursuer and the escaper are still approximately parallel, and the optimal pulse direction is not always along the tangent direction of the trajectory.

[0124] Please refer to Figure 6 In some embodiments, a device for generating an optimal strategy for a spacecraft pulse game includes a data preparation module 10 , a model construction module 20 , a multi-point edge value conversion module 30 and a game strategy generation module 40 .

[0125] The data preparation module 10 is used to obtain the pulse interval, pulse amplitude and situational awareness delay of the pursuer in the pursuit-escape pulse maneuver game scenario, as well as the pulse interval, pulse amplitude and situational awareness delay of the evader; wherein the pulse interval refers to the time interval between two adjacent pulses.

[0126] The model construction module 20 is used to construct a sequential pulse differential countermeasure model, and to construct the Hamiltonian function and interior point function sequence of the tracker and the Hamiltonian function and interior point function sequence of the escaper; wherein the sequential pulse differential countermeasure model includes constraint equations constructed according to the pulse interval and pulse amplitude.

[0127] The multi-point boundary value conversion module 30 is used to construct a multi-point boundary value configuration expression based on the boundary conditions of the Hamiltonian function of the tracker, the boundary conditions of the Hamiltonian function of the escaper, the boundary conditions of the co-state variables in the Hamiltonian function, the sequential pulse differential game model, the Hamiltonian function and interior point function sequence of the tracker, and the Hamiltonian function and interior point function sequence of the escaper.

[0128] The game strategy generation module 40 is used to solve the initial game strategies corresponding to the tracker and the evader, and construct the corresponding iterative design variables based on the initial game strategies. The initial game strategies are iteratively solved based on the iterative design variables, multi-point boundary value configuration expressions, pulse intervals, pulse amplitudes and situational awareness delays to obtain the optimal pulse maneuver strategy.

[0129] In some embodiments, a device for generating an optimal strategy for a spacecraft pulse game is characterized by comprising: a memory for storing a program; and a processor for implementing a game strategy generation method by executing the program stored in the memory.

[0130] Those skilled in the art will appreciate that all or part of the functions of the various methods in the above embodiments can be implemented by hardware or by computer program. When all or part of the functions in the above embodiments are implemented by computer program, the program can be stored in a computer-readable storage medium, and the storage medium can include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to implement the above functions. For example, the program is stored in the memory of the device, and when the program in the memory is executed by the processor, all or part of the above functions can be implemented. In addition, when all or part of the functions in the above embodiments are implemented by computer program, the program can also be stored in a storage medium such as a server, another computer, disk, optical disk, flash disk or mobile hard disk, and saved in the memory of the local device by downloading or copying, or the system of the local device is updated. When the program in the memory is executed by the processor, all or part of the functions in the above embodiments can be implemented.

[0131] The above examples are used to illustrate the present invention, which are only used to help understand the present invention and are not intended to limit the present invention. Those skilled in the art can make several simple deductions, modifications or substitutions based on the concept of the present invention.

Claims

1. A method for generating an optimal strategy for a spacecraft impulse game, characterized in that: include: Obtain the pulse interval, pulse amplitude, and situational awareness delay of the pursuer, as well as the pulse interval, pulse amplitude, and situational awareness delay of the evader, in a pursuit-escape pulse maneuver game scenario; wherein the pulse interval refers to the time interval between two adjacent pulses; Constructing a sequence pulse differential game model, and constructing the Hamiltonian function and interior point function sequence of the tracker and the Hamiltonian function and interior point function sequence of the escaper; wherein the sequence pulse differential game model includes constraint equations constructed according to the pulse interval and the pulse amplitude; Constructing a multi-point boundary value configuration expression based on the boundary conditions of the Hamiltonian function of the tracker, the boundary conditions of the Hamiltonian function of the escaper, the boundary conditions of the co-state variables in the Hamiltonian function, the sequential pulse differential game model, the Hamiltonian function and interior point function sequence of the tracker, and the Hamiltonian function and interior point function sequence of the escaper; Starting from the first pulse phase of a preset multiple pulse phases: Acquire the initial orbital positions of the tracker and the escaper in the current pulse phase, wherein the initial orbital position of the tracker and the initial orbital position of the escaper are preset for each pulse phase; When there is a pulse thrust on the pursuer and the escaper, solving the pursuer's pulse maneuver strategy and the escaper's pulse maneuver strategy based on the pursuer's initial orbital position and the escaper's initial orbital position, wherein the pursuer's pulse maneuver strategy includes a plurality of pursuit strategies and the escaper's pulse maneuver strategy includes a plurality of escape strategies; Selecting the optimal tracking strategy among the pulse maneuver strategies of the pursuer, and selecting the optimal escape strategy among the pulse maneuver strategies of the escaper; If the tracker satisfies the preset game conditions when using the optimal tracking strategy and the escaper satisfies the optimal escaping strategy in the pursuit-escape game, or the number of pulse phases experienced is greater than a preset pulse phase threshold, the optimal tracking strategy and the optimal escaping strategy are used as the initial game strategies; Otherwise, the system enters the next pulse phase to calculate the updated optimal tracking strategy and optimal escaping strategy until the preset game conditions are met when the tracker uses the optimal tracking strategy and the escaping device uses the optimal escaping strategy to play the pursuit-escape game, or the number of pulse phases experienced is greater than the preset game phase threshold. The updated optimal tracking strategy and optimal escaping strategy are used as the initial game strategies. The game conditions are that the remaining interception time is less than the tracker's pulse interval or less than the escaping device's pulse interval. The remaining interception time represents the time required for the tracker to intercept the escaping device. The corresponding iterative design variables are constructed according to the initial game strategy. The initial game strategy is iteratively solved based on the iterative design variables, the multi-point boundary value configuration expression, the pulse interval, the pulse amplitude, and the situational awareness delay to obtain the optimal pulse maneuver strategy.

2. The optimal strategy generation method according to claim 1, characterized in that: The initial game strategy includes the pulse maneuver sequence of the pursuer, the pulse maneuver sequence of the escaper and the game deadline. The pulse maneuver sequence of the pursuer includes Δv P1 ,...,Δv PN , where Δv P1 ,...,Δv PN represent the speed of the pursuer under the action of the 1st... to the Nth pulse respectively. The pulse maneuver sequence of the escaper includes Δv E1 ,...,Δv EN , Δv E1 ,...,Δv EN represent the speed of the escaper under the action of the 1st... to Nth pulses respectively, P represents the pursuer, E represents the escaper, and N represents the number of pulses; The iterative design variables include: X=[Δv P1 ,...,D vPN ,Δv E1 ,...,Δv EN ,k P1 ,...,k PN ,k E1 ,...,k EN ,l Pr0 ,l Er0 ,l Pv0 ,t f ] T Wherein, X represents the iterative design variable, t f represents the game deadline in the initial game strategy, i.e., the interception time, κ P1 ,...,κ PN Denotes the Lagrange multiplier corresponding to different trackers, κ E1 ,...,κ EN Denotes the Lagrange multiplier corresponding to the different escapers, λ Pr0 ,λ Er0 ,λ Pv0 They represent the position co-state of the tracker at the initial moment, the position co-state of the escaper at the initial moment, and the velocity co-state of the tracker at the initial moment respectively.

3. The optimal strategy generation method according to claim 1, characterized in that: The interior point function sequence of the tracker and the interior point function sequence of the escaper include: F ik =c ik x ik +k ik s ik ,i=P,E Among them, Φ ik represents the interior point function sequence of the spacecraft, γ ik and κ ik represents the Lagrange multiplier of the spacecraft, χ ik represents the position difference of the spacecraft, σ ik represents the velocity impulse inequality of the spacecraft, P represents the tracker, E represents the escaper, k represents the time node, k=1,2,...,N, N represents the number of pulses, wherein when i=P, the spacecraft refers to the tracker, and when i=E, the spacecraft refers to the escaper.

4. The optimal strategy generation method according to claim 1, wherein: The Hamiltonian function of the tracker and the Hamiltonian function of the escaper include: Among them, H i represents the Hamiltonian function of the spacecraft, P represents the pursuer, E represents the escaper, T represents the transposed symbol, represents the position co-state of the spacecraft, v i represents the speed of the spacecraft, represents the velocity co-state of the spacecraft, g i represents the gravitational acceleration of the spacecraft, wherein when i=P, the spacecraft is the pursuer, and when i=E, the spacecraft is the escaper.

5. The optimal strategy generation method according to claim 1, wherein: The constraint equations include: N f :=r P (t f )-r E (t f )=0 Wherein, P represents the tracker, E represents the escaper, represents the instant after the pulse acts on the spacecraft, represents the instant before the pulse acts on the spacecraft, χ ik represents the position difference of the spacecraft, represents the position of the spacecraft immediately after the pulse, represents the position of the spacecraft immediately before the pulse, σ ik The velocity impulse inequality for the spacecraft, Δv ik represents the velocity difference of the spacecraft, represents the velocity of the spacecraft immediately after the pulse, The velocity of the spacecraft immediately before the pulse, ΔV i max represents the maximum pulse amplitude of the spacecraft, k represents the time node, N i represents the number of pulses of the spacecraft, N f represents the intercept constraint at the terminal position, t f represents the interception time, r P (t f ) represents the position of the tracker at the moment of interception, r E (t f ) represents the position of the escape vehicle at the moment of interception, wherein when i=P, the spacecraft refers to the pursuer, and when i=E, the spacecraft refers to the escape vehicle.

6. The optimal strategy generation method according to claim 1, wherein: The sequential pulse differential game model also includes a state equation and a payoff function, wherein the state equation is constructed according to the orbital positions and velocities of the pursuer and the escaper.

7. The optimal strategy generation method according to claim 1, wherein: The iteratively solving the initial game strategy based on the iterative design variables, the multi-point boundary value configuration expression, the pulse interval, the pulse amplitude, and the situation awareness delay to obtain an optimal pulse maneuver strategy includes: Constructing the trajectory of the tracker at different pulse phases and the trajectory of the escaper at different pulse phases; Generate a trajectory end error expression according to the trajectory of the tracker at different pulse phases and the trajectory of the escaper at different pulse phases; The target shooting method is used as the iterative algorithm, the iterative design variable is used as the iterative correction value, the multi-point boundary value configuration expression is used as the constraint condition, the pulse interval, the pulse amplitude, and the situation awareness delay are used as input parameters, and the initial game strategy is iteratively solved according to the trajectory end error expression to obtain the optimal pulse maneuvering strategy.

8. An optimal strategy generation device for spacecraft impulse game, characterized in that: include: A data preparation module is used to obtain the pulse interval, pulse amplitude, and situational awareness delay of the pursuer in a pursuit-and-escape pulse maneuver game scenario, as well as the pulse interval, pulse amplitude, and situational awareness delay of the escaper; wherein the pulse interval refers to the time interval between two adjacent pulses; a model construction module for constructing a sequence pulse differential game model, and constructing a Hamiltonian function and an interior point function sequence of the tracker and a Hamiltonian function and an interior point function sequence of the escaper; wherein the sequence pulse differential game model includes a constraint equation constructed according to the pulse interval and the pulse amplitude; a multi-point boundary value conversion module, configured to construct a multi-point boundary value configuration expression based on the boundary conditions of the Hamiltonian function of the tracker, the boundary conditions of the Hamiltonian function of the escaper, the boundary conditions of the co-state variables in the Hamiltonian function, the sequential pulse differential game model, the Hamiltonian function and interior point function sequence of the tracker, and the Hamiltonian function and interior point function sequence of the escaper; A game strategy generation module is used to start from the first pulse phase of a preset plurality of pulse phases: Acquire the initial orbital positions of the tracker and the escaper in the current pulse phase, wherein the initial orbital position of the tracker and the initial orbital position of the escaper are preset for each pulse phase; When there is a pulse thrust on the pursuer and the escaper, solving the pursuer's pulse maneuver strategy and the escaper's pulse maneuver strategy based on the pursuer's initial orbital position and the escaper's initial orbital position, wherein the pursuer's pulse maneuver strategy includes a plurality of pursuit strategies and the escaper's pulse maneuver strategy includes a plurality of escape strategies; Selecting the optimal tracking strategy among the pulse maneuver strategies of the pursuer, and selecting the optimal escape strategy among the pulse maneuver strategies of the escaper; If the tracker satisfies the preset game conditions when using the optimal tracking strategy and the escaper satisfies the optimal escaping strategy in the pursuit-escape game, or the number of pulse phases experienced is greater than a preset pulse phase threshold, the optimal tracking strategy and the optimal escaping strategy are used as the initial game strategies; Otherwise, the system enters the next pulse phase to calculate the updated optimal tracking strategy and optimal escaping strategy until the preset game conditions are met when the tracker uses the optimal tracking strategy and the escaping device uses the optimal escaping strategy to play the pursuit-escape game, or the number of pulse phases experienced is greater than the preset game phase threshold. The updated optimal tracking strategy and optimal escaping strategy are used as the initial game strategies. The game conditions are that the remaining interception time is less than the tracker's pulse interval or less than the escaping device's pulse interval. The remaining interception time represents the time required for the tracker to intercept the escaping device. The corresponding iterative design variables are constructed according to the initial game strategy. The initial game strategy is iteratively solved based on the iterative design variables, the multi-point boundary value configuration expression, the pulse interval, the pulse amplitude, and the situational awareness delay to obtain the optimal pulse maneuver strategy.

9. An optimal strategy generation device for spacecraft impulse game, characterized in that: include: Memory, used to store programs; A processor, configured to implement the optimal strategy generation method according to any one of claims 1 to 7 by executing the program stored in the memory.

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