A method and device for generating game strategies based on spacecraft

Abstract

A method and device for generating a game strategy based on a spacecraft, including obtaining the state quantity of the spacecraft in an imaging game scenario and the constraint upper bounds and constraint lower bounds corresponding to multiple imaging influencing factors, constructing a multi-factor imaging differential game model for the spacecraft, converting the multi-factor imaging differential game model into a two-point boundary value expression, and solving the strategy for the two-point boundary value expression based on the parameters corresponding to the state quantity, the parameters corresponding to the constraint upper bound, the parameters corresponding to the constraint lower bound, and a preset particle swarm optimization algorithm to obtain the optimal game control strategy. The method solves the technical problem that in the game task of spacecraft pursuit, the equilibrium strategy is often solved by a single-factor game model, and the optimal or balanced strategy of multiple parties cannot be obtained.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft control technology, and in particular to a method and device for generating a game strategy based on a spacecraft. Background Art

[0002] Differential games are mathematical modeling and solving tools with a solid theoretical foundation, based on the principles of optimal control and game theory, and take the game of general control systems as the research object. Differential game games model a game confrontation problem as a bilateral or multilateral optimal control problem. All participants jointly form a multi-player differential system. The system contains concepts such as constraints, objective functions, and equilibrium solutions, and ultimately aims to solve the optimal or balanced strategy outcomes of multiple parties. Differential games are widely used in political, economic, and military game scenarios. Typical application examples in engineering include robots, aircraft air combat, missile interception, and spacecraft pursuit. However, in the past differential game models, they were often single-factor game models, such as games for distance. In actual game tasks, games are often not only conducted for distance, but also for multiple factors such as fuel consumption, optical conditions, and relative speed. The traditional linear quadratic differential game model is only a weighted average of various factors, and it is impossible to specifically control whether each constraint meets the boundary constraints, which has major defects. Summary of the invention

[0003] The main technical problem solved by the present invention is that in the game task of spacecraft pursuit, the equilibrium strategy is often solved by a single-factor game model, and the optimal or balanced strategy for multiple parties cannot be obtained.

[0004] According to the first aspect, an embodiment provides a method for generating a game strategy based on a spacecraft, characterized in that it includes:

[0005] Obtaining the state quantity of the spacecraft in the imaging game scenario and the constraint upper bounds and constraint lower bounds corresponding to multiple imaging influencing factors; the state quantity includes line of sight distance, rate of change of line of sight distance, Euler angle and angular velocity; the imaging influencing factors include distance factor, angle factor, linear velocity factor and angular velocity factor, wherein the multiple imaging influencing factors affect the imaging condition of the spacecraft in the imaging game scenario;

[0006] Constructing a multi-factor imaging differential game model of the spacecraft, and converting the multi-factor imaging differential game model into a two-point boundary value expression; the multi-factor imaging differential game model includes a state equation constructed according to the state quantity and a payment function constructed according to the approximate switch functions corresponding to the multiple imaging influencing factors;

[0007] Based on the parameters corresponding to the state quantity, the parameters corresponding to the upper bound of the constraint, the parameters corresponding to the lower bound of the constraint and a preset particle swarm optimization algorithm, the two-point boundary value expression is strategically solved to obtain an optimal game control strategy.

[0008] In some embodiments, converting the multi-factor imaging differential game model into a two-point boundary value expression includes:

[0009] Constructing a Hamiltonian function according to the state equation and a preset co-state quantity, solving a co-state equation corresponding to the Hamiltonian function based on the approximate switching function and the state quantity, and constructing a canonical equation according to the co-state equation and the state equation;

[0010] Constructing a control quantity function corresponding to the Hamiltonian function, and solving the control quantity function to obtain the optimal thrust direction angle corresponding to the spacecraft; wherein the control quantity function includes the control quantity parameters in the Hamiltonian function, and the optimal thrust direction angle includes the optimal thrust direction angle within the orbital plane and the optimal thrust direction angle outside the orbital plane;

[0011] An optimal control equation is constructed according to the optimal thrust direction angle, and a two-point boundary value expression is constructed based on the regular equation, the optimal control equation and preset boundary conditions.

[0012] In some embodiments, the optimal control equation includes:

[0013] ,

[0014] in, represents the optimal control equation, represents the control amount of the pursuer or escaper in the spacecraft, represents the covariance quantity, represents the unit direction vector of the optimal thrust, represents the optimal thrust direction angle in the orbital plane, represents the optimal thrust direction angle outside the orbital plane, T Represents the transpose symbol.

[0015] In some embodiments, the two-point boundary value expression is as follows:

[0016] ,

[0017] in, represents the state equation in the two-point boundary value expression, represents the regular equation in the two-point boundary value expression, Represents the state quantity, represents the covariance quantity, represents the optimal control equation of the tracker in the spacecraft, represents the optimal control equation of the escape device in the spacecraft, represents the initial boundary conditions of the state quantity, represents the preset boundary conditions, Represents the boundary conditions of the covariate.

[0018] In some embodiments, the Hamiltonian function includes:

[0019] ,

[0020] in, represents the Hamiltonian function, and represents the term related to the Lagrangian index in the Hamiltonian function, represents the terms related to the dynamic model in the Hamiltonian function, represents the covariance quantity, T represents the transpose symbol, represents the target state equation corresponding to the state equation, represents the state quantity in the state equation, represents the control quantity of the tracker in the spacecraft, represents the control quantity of the escape vehicle in the spacecraft.

[0021] In some embodiments, solving the co-state equation corresponding to the Hamiltonian function based on the approximate switching function and the state quantity includes:

[0022] Decomposing the Hamiltonian function into a Lagrangian index-related function and a dynamic model-related function;

[0023] Expanding the Lagrangian index related function into an expression corresponding to the approximate switching function, and expanding the dynamic model related function into an expression corresponding to the state quantity;

[0024] Derivation is performed based on the Hamiltonian function and the state quantity, and an expression corresponding to the approximate switching function and an expression corresponding to the approximate switching function are substituted into the derived function to obtain a co-state equation.

[0025] In some embodiments, the step of solving the control amount function to obtain the optimal thrust direction angle corresponding to the spacecraft includes:

[0026] Constructing a first expression based on the control quantity function, the in-plane direction angle corresponding to the tracker in the spacecraft, and the out-of-plane direction angle corresponding to the tracker in the spacecraft;

[0027] Constructing a second expression based on the control quantity function, the in-plane direction angle corresponding to the escaper in the spacecraft, and the out-of-plane direction angle corresponding to the escaper in the spacecraft;

[0028] Solving the first thrust direction angle expression and the second thrust direction angle expression of the first expression and the second expression respectively under the preset reference condition;

[0029] Based on a preset reference quadrant, an optimal thrust direction angle within a plane corresponding to the first thrust direction angle expression is determined, and an optimal thrust direction angle outside a plane corresponding to the second thrust direction angle expression is determined.

[0030] In some embodiments, the payment function includes:

[0031] ,

[0032] ,

[0033] ,

[0034] ,

[0035] ,

[0036] in, represents the payment function, Indicates the time when the game starts. Indicates the time when the game ends. represents the approximate switching function corresponding to the distance factor, represents the approximate switching function corresponding to the angle factor, represents the approximate switching function corresponding to the line speed factor, represents the approximate switching function corresponding to the angular velocity factor, represents an adjustable power base, represents the line-of-sight distance between the two spacecraft, represents the upper bound of the sight distance, represents the lower bound of the line of sight distance, represents the normalized line of sight distance, Indicates the angle, represents the upper bound of the angle constraint, represents the lower bound of the angle constraint, represents the normalized angle, Indicates the line speed, represents the upper bound of the linear velocity, represents the lower bound of the linear velocity, represents the normalized linear velocity, represents the angular velocity, represents the upper bound of the angular velocity, represents the lower bound of the angular velocity, represents the normalized angular velocity.

[0037] In some embodiments, the two-point boundary value expression is solved strategically based on the parameter corresponding to the state quantity, the parameter corresponding to the upper bound of the constraint, the parameter corresponding to the lower bound of the constraint, and a preset particle swarm optimization algorithm to obtain the optimal game control strategy, including:

[0038] Optimizing the boundary conditions of the costate quantity in the two-point boundary value expression according to the state quantity, the parameter corresponding to the upper bound of the constraint, the parameter corresponding to the lower bound of the constraint, and the initial value corresponding to the preset costate quantity to obtain an updated two-point boundary value expression;

[0039] The particle swarm optimization algorithm is used to solve the updated two-point boundary value expression to obtain the optimal game control strategy.

[0040] According to the second aspect, an embodiment provides a spacecraft-based game strategy generation device, including:

[0041] Memory, used to store programs;

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

[0043] According to the above-mentioned embodiment of the method and device for generating a game strategy based on a spacecraft, since a multi-factor imaging differential game model of a spacecraft is constructed, the model can be compatible with a single-factor game model and take into account the actual multi-factor influence. The multi-factor imaging differential game model is converted into a two-point boundary value expression, and the two-point boundary value expression is solved strategically based on the parameters corresponding to the state quantity, the parameters corresponding to the upper bound of the constraint, the parameters corresponding to the lower bound of the constraint, and the preset particle swarm optimization algorithm, so as to achieve the solution of the equilibrium strategy of the co-state optimization, and thus the obtained optimal game control strategy has better effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A flowchart of a method for generating a game strategy based on a spacecraft according to an embodiment of the present application;

[0045] Figure 2a is a function graph of a bidirectional switching function in one-dimensional space of an embodiment, Figure 2b A function graph of a two-dimensional bidirectional switch function in an embodiment;

[0046] Figure 3 A flowchart of converting a multi-factor imaging differential game model into a two-point boundary value expression according to an embodiment;

[0047] Figure 4 A flowchart of an embodiment of solving a co-state equation corresponding to a Hamiltonian function based on an approximate switching function and a state quantity;

[0048] Figure 5 A flowchart of an embodiment of solving the control quantity function to obtain the optimal thrust direction angle corresponding to the spacecraft;

[0049] Figure 6 A flowchart of an embodiment of the invention is to solve the two-point boundary value expression based on the parameters corresponding to the state quantity, the parameters corresponding to the upper bound of the constraint, the parameters corresponding to the lower bound of the constraint and the preset particle swarm optimization algorithm to obtain the optimal game control strategy;

[0050] Figure 7a , Figure 7b , Figure 7c and Figure 7d They are respectively the corresponding changes of the four different imaging influencing factors in the game process in Example 1;

[0051] Figure 8a , Figure 8b , Figure 8c and Figure 8d They are respectively the corresponding changes of the four different imaging influencing factors in the second embodiment during the game process;

[0052] Fig. 9 The comparison results of time consumption and accuracy between the methods in Example 1 and Example 2 and the existing method under the same computing conditions are shown. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below by specific embodiments in conjunction with the accompanying drawings. Wherein similar elements in different embodiments adopt associated similar element numbers. In the following embodiments, many detailed descriptions are for making the present application better understood. However, those skilled in the art can easily recognize that some features can be omitted in different situations, or can be replaced by other elements, materials, 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 part of the present application being overwhelmed by too much description, and for those skilled in the art, it is not necessary to describe these related operations in detail, and they can fully understand the related operations according to the description in the specification and the general technical knowledge in the art.

[0054] In addition, the features, operations or characteristics described in the specification can be combined in any appropriate manner to form various implementations. At the same time, the steps or actions in the method description can also be interchanged or adjusted in a manner that is obvious to those skilled in the art. Therefore, the various sequences in the specification and the drawings are only for the purpose of clearly describing a certain embodiment and are not meant to be a required sequence, unless otherwise specified that a certain sequence must be followed.

[0055] The serial numbers assigned to the components herein, such as "first", "second", etc., are only used to distinguish the objects described and do not have any order or technical meaning. The "connection" and "coupling" mentioned in this application, unless otherwise specified, include direct and indirect connections (couplings).

[0056] Please refer to Figure 1 In an embodiment of the present invention, a method for generating a game strategy based on a spacecraft is proposed, including steps S10 to S30, which are described in detail below.

[0057] Step S10: Obtain the state quantity of the spacecraft in the imaging game scenario and the constraint upper bounds and constraint lower bounds corresponding to multiple imaging influencing factors.

[0058] In some embodiments, the imaging game scenario refers to a scenario in which a pursuer and an escaper in a spacecraft compete with each other during pursuit and escape. The state quantity of the spacecraft in the imaging game scenario is ,in, is the line-of-sight distance between the pursuer and the escaper in the spacecraft, and It represents the two Euler angles from the inertial system to the line of sight system in the order of '3-2'. Indicates the rate of change of sight distance, and represents the angular velocity corresponding to the two Euler angles, T Represents the transpose symbol.

[0059] In some embodiments, multiple imaging influencing factors of a spacecraft in an imaging game scenario include distance factors, angle factors, linear velocity factors, and angular velocity factors, wherein the multiple imaging influencing factors affect the situation in which the pursuer and the escaper in the spacecraft compete with each other and shoot each other and form images during the pursuit and escape process. The upper and lower bounds of the constraints corresponding to the multiple imaging influencing factors refer to the ranges in which the parameters corresponding to the imaging influencing factors are constrained.

[0060] Step S20: construct a multi-factor imaging differential game model of the spacecraft, and convert the multi-factor imaging differential game model into a two-point boundary value expression.

[0061] In some embodiments, the multi-factor imaging differential game model includes a state equation constructed based on state quantities and a payment function constructed based on approximate switching functions corresponding to a plurality of imaging influencing factors.

[0062] In some embodiments, the state equation constructed based on the state quantity is as follows:

[0063] ,

[0064] in, Indicates the state change of the line of sight distance in the state equation, Indicates the rate of change of sight distance, and It represents the state change of the two Euler angles in the state equation from the inertial system to the line of sight system in the '3-2' sequence. and represents the angular velocity corresponding to the two Euler angles, represents the rate of change of the line of sight distance in the state equation, and Represents the state change of the Euler angle in the state equation, is the line-of-sight distance between the pursuer and the escaper in the spacecraft, and It represents the two Euler angles from the inertial system to the line of sight system in the order of '3-2'. , and Represents the gravitational acceleration difference between the tracker and the escaper in the spacecraft on the three coordinate axes in the line of sight coordinate system The weight on , and They represent the three components of the control quantity of the tracker, , and They represent the three components of the control quantity of the escape device respectively.

[0065] In some embodiments, ,in, Indicates the control amount of the pursuer or escaper, Indicates a tracker or escapee. They represent the components of the pursuer or escaper under different control quantities, represents the in-plane direction angle of the control quantity in three-dimensional space, represents the out-of-plane direction angle of the control volume in three-dimensional space, T Indicates the transposed sign. It is assumed that the magnitude of the control quantity is constant and the direction is free.

[0066] In some embodiments, for a spacecraft, the game objective of the tracker is to maximize the effective imaging time, while the goal of the escaper is to minimize the effective imaging time. Therefore, the payoff function of the game between the tracker and the escaper is the accumulated effective imaging time, which can be calculated by the following integral formula:

[0067] ,

[0068] ,

[0069] in, is the payment function, Represents different imaging influencing factors, represents the upper bound of the imaging influencing factors, represents the lower bound of the imaging influencing factors, The switching function representing different imaging influencing factors, Indicates the time when the game starts. Indicates the time when the game ends. Indicates the number of different imaging influencing factors.

[0070] In some embodiments, the switch functions of different imaging influencing factors represent whether the corresponding constraints are satisfied.

[0071] In some embodiments, since the above payment function can strictly calculate the effective imaging time according to the boundary constraints, but the switch payment function is not differentiable at the critical point of the boundary constraints, this will make the game become a non-differentiable game, resulting in the inability to strictly use the traditional differential game theory. In order to solve this problem, a similar Sigmoid Function constructor to represent the approximate switching function. Sigmoid Function , as the base of the power function increases, the function graph is closer to the 0-1 switch. Sigmoid The multiplication of functions can realize a two-way switch, corresponding to the upper and lower bounds of the constraints. The function graph can be referred to Figure 2a As shown, high-dimensional images that consider multiple constraint boundaries can refer to Figure 2b shown.

[0072] In some embodiments, the constructed approximate switching function is in the form of:

[0073] ,

[0074] ,

[0075] ,

[0076] ,

[0077] In some embodiments, represents the approximate switching function corresponding to the distance factor, represents the approximate switching function corresponding to the angle factor, represents the approximate switching function corresponding to the line speed factor, represents the approximate switching function corresponding to the angular velocity factor, represents an adjustable power base, represents the line-of-sight distance between the two spacecraft, represents the upper bound of the sight distance, represents the lower bound of the line of sight distance, represents the normalized line of sight distance, Indicates the angle, represents the upper bound of the angle constraint, represents the lower bound of the angle constraint, represents the normalized angle, Indicates the line speed, represents the upper bound of the linear velocity, represents the lower bound of the linear velocity, represents the normalized linear velocity, represents the angular velocity, represents the upper bound of the angular velocity, represents the lower bound of the angular velocity, represents the normalized angular velocity.

[0078] In some embodiments, in the constructed approximate switching function, , , , The effect is equivalent to normalizing four physical quantities of different sizes, and then a unified b The value reflects the steepness of the function graph near the boundary. It is differentiable on the constraint boundary, so the theory of differential games can still be used.

[0079] In some embodiments, the payment function constructed according to the approximate switch functions corresponding to the multiple imaging influencing factors is as follows:

[0080] ,

[0081] in, represents the payment function, Indicates the time when the game starts. Indicates the time when the game ends. represents the approximate switching function corresponding to the distance factor, represents the approximate switching function corresponding to the angle factor, represents the approximate switching function corresponding to the line speed factor, Represents the approximate switching function corresponding to the angular velocity factor.

[0082] In some embodiments, the Nash equilibrium solution is the maximum and minimum solution of the payoff function , this solution represents a pair of optimal open-loop control strategies, corresponding to two open-loop optimal maneuvering imaging trajectories, satisfying the inequality properties of Nash equilibrium: .

[0083] In some embodiments, for the multi-factor imaging differential game model, the physical meaning of the Nash equilibrium solution is "guaranteed cumulative effective imaging time", which is the shortest guaranteed effective imaging time for the tracker and the longest guaranteed effective imaging time for the escaper. Assume that the completion of a reconnaissance mission of the tracker is defined as the completion of at least the cumulative If the tracker can change the initial conditions of the game, or improve its own mobility, so that the Nash equilibrium solution of the game , then the Nash equilibrium strategy is a winning strategy for the tracker, regardless of whether the opponent will maneuver or what kind of maneuver it will adopt.

[0084] Please refer to Figure 3 In some embodiments, step S20 converts the multi-factor imaging differential game model into a two-point boundary value expression, including steps S21 to S23, which are described in detail below.

[0085] Step S21: construct a Hamiltonian function according to the state equation and the preset co-state quantity, solve the co-state equation corresponding to the Hamiltonian function based on the approximate switching function and the state quantity, and construct a canonical equation according to the co-state equation and the state equation.

[0086] In some embodiments, constructing a Hamiltonian function according to the state equation and a preset co-state quantity includes:

[0087] The state equation is converted into the target state equation according to the preset reference form, and the Hamiltonian function is constructed according to the target state equation and the preset co-state quantity.

[0088] In some embodiments, the target state equation includes:

[0089] ,

[0090] in, represents the target state equation, represents the state quantity in the state equation, represents the control quantity of the tracker in the spacecraft, Represents the control quantity of the escape vehicle in the spacecraft.

[0091] In some embodiments, the Hamiltonian function includes:

[0092] ,

[0093] in, represents the Hamiltonian function, and represents the term related to the Lagrangian index in the Hamiltonian function, represents the terms related to the dynamic model in the Hamiltonian function, represents the covariance quantity, T represents the transpose symbol, represents the target state equation corresponding to the state equation, represents the state quantity in the state equation, represents the control quantity of the tracker in the spacecraft, Represents the control quantity of the escape vehicle in the spacecraft.

[0094] In some embodiments, the covariance , where the covariance Corresponding to six different state components , T Represents the transpose symbol.

[0095] Please refer to Figure 4 In some embodiments, step S21 solves the co-state equation corresponding to the Hamiltonian function based on the approximate switching function and the state quantity, including steps S211 to S213, which are described in detail below.

[0096] Step S211: decomposing the Hamiltonian function into a Lagrangian index related function and a dynamic model related function.

[0097] In some embodiments, represents the Hamiltonian function, represents the term related to the Lagrangian index in the Hamiltonian function, represents the term related to the dynamic model in the Hamiltonian function, so The corresponding functional expression is expressed as the Lagrange index related function, The corresponding functional expression is expressed as the dynamic model related function.

[0098] Step S212: Expand the Lagrangian index related function into an expression corresponding to the approximate switching function, and expand the dynamic model related function into an expression corresponding to the state quantity.

[0099] In some embodiments, due to The corresponding functional expression is expressed as the Lagrange index related function, The corresponding functional expression is expressed as the dynamic model related function, so the Lagrangian index related function and the dynamic model related function can be expanded as follows by combining the approximate switching function and the state quantity:

[0100] ,

[0101]

[0102]

[0103]

[0104] ,

[0105] in, represents the Lagrangian index correlation function, Expressed as a kinetic model related function, represents the approximate switching function corresponding to the distance factor, represents the approximate switching function corresponding to the angle factor, represents the approximate switching function corresponding to the line speed factor, represents the approximate switching function corresponding to the angular velocity factor, is the line-of-sight distance between the pursuer and the escaper in the spacecraft, and It represents the two Euler angles from the inertial system to the line of sight system in the order of '3-2'. Indicates the rate of change of sight distance, and represents the angular velocity corresponding to the two Euler angles, Represents the covariance Corresponding to six different state components, Represents the three components of the in-plane direction angle of the escaper's control quantity in three-dimensional space, Represents the three components of the in-plane direction angle of the tracker's control volume in three-dimensional space, n is expressed as the instantaneous orbital angular velocity of the escaper, They represent the parts of the gravitational acceleration difference between the pursuer and the escaper in the three-axis components of the line-of-sight coordinate system that are only related to the rotation Euler angle.

[0106] Step S213: Derivation is performed based on the Hamiltonian function and the state quantity, and the expression corresponding to the approximate switching function and the expression corresponding to the approximate switching function are substituted into the derived function to obtain the co-state equation.

[0107] In some embodiments, since the Hamiltonian function can be regarded as two parts, namely, a Lagrangian index-related function and a dynamic model-related function, the co-state equation can also be decomposed into two parts as shown below:

[0108] ,

[0109] ,

[0110] ,

[0111] in, represents the Hamiltonian function, represents the Lagrangian index correlation function, Expressed as a kinetic model related function, Represents the state quantity, represents the co-state equation, represents the part of the co-state equation related to the Lagrangian index function, represents the part of the co-state equation related to the kinetic model related functions, Represents multiple components corresponding to the part of the co-state equation related to the dynamic model related functions, Represents multiple components corresponding to the part of the co-state equation related to the Lagrangian index function, T Represents the transpose symbol.

[0112] In some embodiments, further solving the above equations shows that the co-state equation for the Lagrangian index related function is:

[0113] ,

[0114] ,

[0115] ,

[0116] ,

[0117] ,

[0118] ,

[0119] in, Represents multiple components corresponding to the part of the co-state equation related to the Lagrangian index function, represents the Lagrangian index correlation function, represents the approximate switching function corresponding to the distance factor, represents the approximate switching function corresponding to the angle factor, represents the approximate switching function corresponding to the line speed factor, represents the approximate switching function corresponding to the angular velocity factor, is the line-of-sight distance between the pursuer and the escaper in the spacecraft, and It represents the two Euler angles from the inertial system to the line of sight system in the order of '3-2'. Indicates the rate of change of sight distance, and represents the angular velocity corresponding to the two Euler angles, Represents angular velocity.

[0120] In some embodiments, it is assumed that the component of the sunlight vector in the geocentric inertial system is , then, we have the following formula:

[0121] ,

[0122] ,

[0123] ,

[0124] ,

[0125] ,

[0126] ,

[0127] ,

[0128] ,

[0129] ,

[0130] In some embodiments, , and represents the component of the sunlight vector in the geocentric inertial system, represents the approximate switching function corresponding to the distance factor, represents the approximate switching function corresponding to the angle factor, represents the approximate switching function corresponding to the line speed factor, represents the approximate switching function corresponding to the angular velocity factor, is the line-of-sight distance between the pursuer and the escaper in the spacecraft, and It represents the two Euler angles from the inertial system to the line of sight system in the order of '3-2'. Indicates the rate of change of sight distance, and represents the angular velocity corresponding to the two Euler angles, represents an adjustable power base, represents the upper bound of the sight distance, represents the lower bound of the line of sight distance, represents the normalized line of sight distance, represents the upper bound of the angle constraint, represents the lower bound of the angle constraint, represents the normalized angle, represents the upper bound of the linear velocity, represents the lower bound of the linear velocity, represents the normalized linear velocity, represents the upper bound of the angular velocity, represents the lower bound of the angular velocity, represents the normalized angular velocity.

[0131] In some embodiments, further solving the above equations shows that the co-state equations for the related functions of the kinetic model are:

[0132] ,

[0133] ,

[0134] ,

[0135] ,

[0136] ,

[0137] in, Represents multiple components corresponding to the part of the co-state equation related to the dynamic model related functions, Expressed as a kinetic model related function, is the line-of-sight distance between the pursuer and the escaper in the spacecraft, and It represents the two Euler angles from the inertial system to the line of sight system in the order of '3-2'. Indicates the rate of change of sight distance, and represents the angular velocity corresponding to the two Euler angles, Represents the covariance Corresponding to six different state components, Represents the three components of the in-plane direction angle of the escaper's control quantity in three-dimensional space, Represents the three components of the in-plane direction angle of the tracker's control volume in three-dimensional space, n is expressed as the instantaneous orbital angular velocity of the escaper, They represent the parts of the gravitational acceleration difference between the pursuer and the escaper in the three-axis components of the line-of-sight coordinate system that are only related to the rotation Euler angle.

[0138] Step S22: construct a control quantity function corresponding to the Hamiltonian function, and obtain the optimal thrust direction angle corresponding to the spacecraft based on the control quantity function.

[0139] In some embodiments, the control quantity parameters related to the tracker and escaper in the spacecraft are extracted from the Hamiltonian function to construct a control quantity function corresponding to the Hamiltonian function. , the specific formula is as follows:

[0140] ,

[0141] in, is the control quantity function, , and They represent the three components of the control quantity of the tracker, , and They represent the three components of the control quantity of the escaper, Represents the in-plane direction angle of the tracker's control volume in three-dimensional space, represents the in-plane direction angle of the escaper’s control quantity in three-dimensional space, represents the out-of-plane direction angle of the tracker’s control volume in three-dimensional space, represents the out-of-plane direction angle of the escaper’s control quantity in three-dimensional space, is the line-of-sight distance between the pursuer and the escaper in the spacecraft, Represents the covariance Corresponding to six different state components, It represents the Euler angles from the inertial frame to the line of sight frame in the '3-2' sequence.

[0142] Please refer to Figure 5 In some embodiments, step S22 obtains the optimal thrust direction angle corresponding to the spacecraft based on the control quantity function, including steps S221 to S224, which are described in detail below.

[0143] Step S221: construct a first expression based on the control quantity function, the in-plane direction angle corresponding to the tracker in the spacecraft, and the out-of-plane direction angle corresponding to the tracker in the spacecraft.

[0144] In some embodiments, the first expression may refer to the following formula:

[0145] ,

[0146] ,

[0147] in, is the control quantity function, Represents the in-plane direction angle of the tracker's control volume in three-dimensional space, represents the out-of-plane direction angle of the tracker’s control volume in three-dimensional space, Represents the covariance Corresponding to six different state components, It represents the Euler angle from the inertial system to the line of sight system in the order of '3-2'. Indicates the control amount of the tracker.

[0148] In some embodiments, according to the calculus of variations or the maximum principle, the optimal thrust vector of the tracker should make the Hamiltonian function take a maximum value, and the optimal thrust vector of the escaper should make the Hamiltonian function take a minimum value, so the first expression and the second expression are solved.

[0149] Step S222: construct a second expression based on the control quantity function, the in-plane direction angle corresponding to the escape device in the spacecraft, and the out-of-plane direction angle corresponding to the escape device in the spacecraft.

[0150] In some embodiments, the second expression may refer to the following formula:

[0151] ,

[0152] ,

[0153] in, is the control quantity function, represents the in-plane direction angle of the escaper’s control quantity in three-dimensional space, represents the out-of-plane direction angle of the escaper’s control quantity in three-dimensional space, Represents the covariance Corresponding to six different state components, It represents the Euler angle from the inertial system to the line of sight system in the order of '3-2'. Indicates the control amount of the escaper.

[0154] Step S223: respectively solving the first thrust direction angle expression and the second thrust direction angle expression of the first expression and the second expression under the preset reference condition.

[0155] In some embodiments, the first thrust direction angle expression obtained by solving is:

[0156] ,

[0157] in, The first thrust direction angle expression of the tracker is: The expression of the first thrust direction angle of the escape vehicle is: and Represents the covariance The corresponding different state components are: Represents the line-of-sight distance between the pursuer and the escaper in the spacecraft.

[0158] In some embodiments, the expression of the second thrust direction angle obtained by solving is:

[0159] ,

[0160] in, The expression of the second thrust direction angle of the tracker is: The expression of the second thrust direction angle of the escape vehicle is: Represents the covariance The corresponding different state components are: It represents the Euler angle from the inertial system to the line of sight system in the order of '3-2'. represents the in-plane direction angle of the escaper’s control quantity in three-dimensional space, Represents the line-of-sight distance between the pursuer and the escaper in the spacecraft.

[0161] Step S224: Based on the preset reference quadrant, respectively determine the optimal thrust direction angle within the plane corresponding to the first thrust direction angle expression, and determine the optimal thrust direction angle outside the plane corresponding to the second thrust direction angle expression.

[0162] In some embodiments, the optimal thrust direction angle in the orbital plane is The quadrant can be uniquely determined based on the sign of the costate quantity:

[0163] ,

[0164] ,

[0165] ,

[0166] ,

[0167] In some embodiments, represents the optimal thrust direction angle of the pursuer or escaper in the orbital plane, and Represents the covariance The corresponding different state components are: Represents the line-of-sight distance between the pursuer and the escaper in the spacecraft.

[0168] In some embodiments, the optimal thrust direction angle outside the orbital plane is It can be determined as:

[0169] ,

[0170] In some embodiments, represents the optimal thrust direction angle of the pursuer or escaper in the orbital plane, Represents the covariance The corresponding different state components are: It represents the Euler angle from the inertial system to the line of sight system in the order of '3-2'. represents the in-plane direction angle of the escaper’s control quantity in three-dimensional space, Represents the line-of-sight distance between the pursuer and the escaper in the spacecraft.

[0171] In some embodiments, the optimal thrust direction angles of the pursuer and the escaper are the same.

[0172] Step S23: construct an optimal control equation according to the optimal thrust direction angle, and construct a two-point boundary value expression based on the regular equation, the optimal control equation and the preset boundary conditions.

[0173] In some embodiments, the optimal control equation includes:

[0174] ,

[0175] in, represents the optimal control equation, represents the control amount of the pursuer or escaper in the spacecraft, represents the covariance quantity, represents the unit direction vector of the optimal thrust, represents the optimal thrust direction angle in the orbital plane, represents the optimal thrust direction angle outside the orbital plane, T Represents the transpose symbol.

[0176] In some embodiments, a two-point boundary value expression is constructed based on the regular equation, the optimal control equation and the preset boundary conditions. The two-point boundary value expression is as follows:

[0177] ,

[0178] in, represents the state equation in the two-point boundary value expression, represents the regular equation in the two-point boundary value expression, Represents the state quantity, represents the covariance quantity, represents the optimal control equation of the tracker in the spacecraft, represents the optimal control equation of the escape device in the spacecraft, represents the initial boundary conditions of the state quantity, represents the preset boundary conditions, Represents the boundary conditions of the covariate.

[0179] In some embodiments, the boundary conditions of the co-state quantity can be determined by the transversal conditions. Since the initial value state is fixed, the terminal state is free, and the payment function does not contain a terminal value function related to the terminal state, the terminal of each co-state quantity is 0.

[0180] Step S30: Based on the parameters corresponding to the state quantity, the parameters corresponding to the upper bound of the constraint, the parameters corresponding to the lower bound of the constraint and the preset particle swarm optimization algorithm, the two-point boundary value expression is solved strategically to obtain the optimal game control strategy.

[0181] Please refer to Figure 6 In some embodiments, step S30 performs a strategy solution on the two-point boundary value expression based on the parameters corresponding to the state quantity, the parameters corresponding to the upper bound of the constraint, the parameters corresponding to the lower bound of the constraint, and a preset particle swarm optimization algorithm to obtain the optimal game control strategy, including steps S31 to S32, which are described in detail below.

[0182] Step S31: Optimize the boundary conditions of the costate quantity in the two-point boundary value expression according to the state quantity, the parameter corresponding to the upper bound of the constraint, the parameter corresponding to the lower bound of the constraint and the initial value corresponding to the costate quantity to obtain an updated two-point boundary value expression.

[0183] In some embodiments, the initial value corresponding to the co-state quantity is found:

[0184] ,

[0185] in, represents the initial value corresponding to the costate quantity, They correspond to the six different state components under the initial values ​​of the co-state quantity. T Represents the transpose symbol.

[0186] In some embodiments, the parameter constraint range can be constructed based on the parameters corresponding to the upper constraint limit and the parameters corresponding to the lower constraint limit. ,when When , the payoff function of the game is maximized, When , the payoff function of the game is minimized, and the boundary conditions of the co-state quantity in the two-point boundary value expression are optimized to obtain the updated two-point boundary value expression as follows:

[0187] ,

[0188] In some embodiments, represents the state equation in the updated two-point boundary value expression, Indicates the parameter constraint range, Represents the state quantity, represents the covariance quantity, represents the unit direction vector of the optimal thrust, Represents the initial boundary conditions of the state quantity.

[0189] Step S32: using a preset particle swarm optimization algorithm to solve the updated two-point boundary value expression to obtain the optimal game control strategy.

[0190] In some embodiments, a preset particle swarm optimization algorithm is used to solve the optimization problem of the updated two-point boundary value expression, wherein the basic configuration for optimization using the preset particle swarm optimization algorithm is as follows: the population number is 4, the optimization generation is 50, and the value range of the initial value of the co-state can be determined according to the dimension difference of the state quantity as follows: .

[0191] Please refer to Figure 7a , Figure 7b , Figure 7c and Figure 7d In Example 1, at the initial moment, the escaper is in a geostationary orbit at an altitude of 35786 km from the ground, and the tracker is in the vicinity of the escaper's orbit. In the example, the initial orbital elements of the escaper are The initial trajectory of the tracker is expressed by the relative state quantity in the line of sight coordinate system , the parameter constraints in the spacecraft's payoff function are , , , , , . Throughout the process, the four factors that affect the tracker and the escaper are the sunlight angle, line of sight distance, sunlight angle change rate, and line of sight distance change rate. The main role of the game maneuver is to change the line of sight distance and the distance change rate. Compared with the free motion trajectory, the orbital maneuver does not change the sunlight angle and sunlight angle rate significantly, and the focus of the game is different. This is mainly because when the distance between the two parties is large, the line of sight is not easy to turn, and the acceleration required to turn the line of sight is also greater, so changing the distance is the most efficient escape method. Distance is the dominant factor in this game. If the tracker only plays a single-factor game based on distance, the actual effective imaging time is 326 s, but the effective imaging time under the multi-factor model is about 333 s, so the multi-factor strategy is more effective.

[0192] Please refer to Figure 8a , Figure 8b , Figure 8c and Figure 8dIn Example 2, at the initial moment, the escaper is in a geostationary orbit at an altitude of 35786 km above the ground, and the tracker is in the vicinity of the escaper's orbit. The number of initial orbital elements of the escaper is The initial trajectory of the tracker is expressed by the relative state quantity in the line of sight coordinate system , the parameter constraints in the spacecraft's payoff function are , , , , , . In the game process of this embodiment, the four imaging influencing factors are sunlight angle, line of sight, sunlight angle rate and line of sight distance rate. The above four imaging influencing factors will all play a role in the game, and multiple imaging influencing factors have crossed the boundary of a limited range. In this embodiment, the maneuverability of the escape vehicle is stronger. Therefore, the change of state quantity caused by the escape maneuver plays a dominant role in the equilibrium solution. At the initial moment, the four imaging influencing factors are all within the effective range, but the escape vehicle breaks the sunlight angle rate constraint, sunlight angle constraint, speed constraint and distance constraint respectively through maneuvers at 245 s, 326 s, 2008 s and 2070 s. Please refer to Figure 8c , the angular velocity of sunlight changes suddenly and exceeds the constraint range first, which is the most intense game factor in the early stage. Figure 7a The sunlight angle in Increase to It did not continue to rise afterwards, but instead decreased, indicating that this factor was coordinating the adjustment of other factors at this time, because the high and low values ​​of this factor outside the effective range are equivalent to the payment function. The sun angle rate exceeded the effective range temporarily, but then the sun angle and the other two factors were out of constraint for a long time, so that the tracker only completed about 245 seconds of imaging. However, if it is the uncontrolled free motion trajectory in Figure 8, the effective time of the tracker will exceed 1000 seconds. The escaper significantly widened the distance between the two parties.

[0193] Please refer to Fig. 9 The methods in Example 1 and Example 2 are performed under the same computing conditions as the existing method. Multiple operations are performed on each example and the average results are taken, showing a comparison in time consumption and accuracy.

[0194] Those skilled in the art will appreciate that all or part of the functions of the various methods in the above-mentioned embodiments can be implemented by hardware or by computer programs. When all or part of the functions in the above-mentioned embodiments are implemented by computer programs, 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-mentioned 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-mentioned functions can be implemented. In addition, when all or part of the functions in the above-mentioned embodiments are implemented by computer programs, 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 can be downloaded or copied and saved in the memory of the local device, or the system of the local device is updated, and when the program in the memory is executed by the processor, all or part of the functions in the above-mentioned embodiments can be implemented.

[0195] The above specific examples are used to illustrate the present invention, which is only used to help understand the present invention and is not intended to limit the present invention. For those skilled in the art, according to the concept of the present invention, some simple deductions, modifications or substitutions can be made.

Claims

1. A method for generating a game strategy based on a spacecraft, characterized in that: include: Obtaining the state quantity of the spacecraft in the imaging game scenario and the constraint upper bounds and constraint lower bounds corresponding to multiple imaging influencing factors; the state quantity includes line of sight distance, rate of change of line of sight distance, Euler angle and angular velocity; the imaging influencing factors include distance factor, angle factor, linear velocity factor and angular velocity factor, wherein the multiple imaging influencing factors affect the imaging condition of the spacecraft in the imaging game scenario; Constructing a multi-factor imaging differential game model of the spacecraft, wherein the multi-factor imaging differential game model includes a state equation constructed according to the state quantity and a payment function constructed according to the approximate switching functions corresponding to the multiple imaging influencing factors; constructing a Hamiltonian function according to the state equation and a preset co-state quantity, solving the co-state equation corresponding to the Hamiltonian function based on the approximate switching function and the state quantity, and constructing a canonical equation according to the co-state equation and the state equation; Constructing a control quantity function corresponding to the Hamiltonian function, and solving the control quantity function to obtain the optimal thrust direction angle corresponding to the spacecraft; wherein the control quantity function includes the control quantity parameters in the Hamiltonian function, and the optimal thrust direction angle includes the optimal thrust direction angle within the orbital plane and the optimal thrust direction angle outside the orbital plane; An optimal control equation is constructed according to the optimal thrust direction angle, and a two-point boundary value expression is constructed based on the regular equation, the optimal control equation and preset boundary conditions; wherein the payment function includes: ， ， ， ， ， in, represents the payment function, Indicates the time when the game starts. Indicates the time when the game ends. represents the approximate switching function corresponding to the distance factor, represents the approximate switching function corresponding to the angle factor, represents the approximate switching function corresponding to the line speed factor, represents the approximate switching function corresponding to the angular velocity factor, represents the approximate switching function corresponding to the distance factor, represents the approximate switching function corresponding to the angle factor, represents the approximate switching function corresponding to the line speed factor, represents the approximate switching function corresponding to the angular velocity factor, represents an adjustable power base, represents the line-of-sight distance between the two spacecraft, represents the upper bound of the sight distance, represents the lower bound of the line of sight distance, represents the normalized line of sight distance, Indicates the angle, represents the upper bound of the angle constraint, represents the lower bound of the angle constraint, represents the normalized angle, Indicates the line speed, represents the upper bound of the linear velocity, represents the lower bound of the linear velocity, represents the normalized linear velocity, represents the angular velocity, represents the upper bound of the angular velocity, represents the lower bound of the angular velocity, represents the normalized angular velocity; Based on the parameters corresponding to the state quantity, the parameters corresponding to the upper bound of the constraint, the parameters corresponding to the lower bound of the constraint and a preset particle swarm optimization algorithm, the two-point boundary value expression is strategically solved to obtain an optimal game control strategy.

2. The game strategy generation method according to claim 1, characterized in that: The optimal control equation includes: ， in, represents the optimal control equation, represents the control amount of the pursuer or escaper in the spacecraft, represents the covariance quantity, represents the unit direction vector of the optimal thrust, represents the optimal thrust direction angle in the orbital plane, represents the optimal thrust direction angle outside the orbital plane, T Represents the transpose symbol.

3. The game strategy generation method according to claim 2, characterized in that: The two-point boundary value expression is as follows: ， in, represents the state equation in the two-point boundary value expression, represents the regular equation in the two-point boundary value expression, Represents the state quantity, represents the covariance quantity, represents the optimal control equation of the tracker in the spacecraft, represents the optimal control equation of the escape device in the spacecraft, represents the initial boundary conditions of the state quantity, represents the preset boundary conditions, Represents the boundary conditions of the covariate.

4. The game strategy generation method according to claim 2, characterized in that: The Hamiltonian function includes: ， in, represents the Hamiltonian function, and represents the term related to the Lagrangian index in the Hamiltonian function, represents the terms related to the dynamic model in the Hamiltonian function, represents the co-state quantity, T represents the transposition symbol, represents the target state equation corresponding to the state equation, represents the state quantity in the state equation, represents the control quantity of the tracker in the spacecraft, represents the control quantity of the escape vehicle in the spacecraft.

5. The game strategy generation method according to claim 1, characterized in that: The step of solving the co-state equation corresponding to the Hamiltonian function based on the approximate switching function and the state quantity includes: Decomposing the Hamiltonian function into a Lagrangian index-related function and a dynamic model-related function; Expanding the Lagrangian index related function into an expression corresponding to the approximate switching function, and expanding the dynamic model related function into an expression corresponding to the state quantity; Derivation is performed based on the Hamiltonian function and the state quantity, and an expression corresponding to the approximate switching function and an expression corresponding to the approximate switching function are substituted into the derived function to obtain a co-state equation.

6. The method for generating a gaming strategy according to claim 1, wherein: The step of solving the control amount function to obtain the optimal thrust direction angle corresponding to the spacecraft includes: Constructing a first expression based on the control quantity function, the in-plane direction angle corresponding to the tracker in the spacecraft, and the out-of-plane direction angle corresponding to the tracker in the spacecraft; Constructing a second expression based on the control quantity function, the in-plane direction angle corresponding to the escaper in the spacecraft, and the out-of-plane direction angle corresponding to the escaper in the spacecraft; Solving the first thrust direction angle expression and the second thrust direction angle expression of the first expression and the second expression respectively under the preset reference condition; Based on a preset reference quadrant, an optimal thrust direction angle within a plane corresponding to the first thrust direction angle expression is determined, and an optimal thrust direction angle outside a plane corresponding to the second thrust direction angle expression is determined.

7. The game strategy generation method according to claim 1, characterized in that: The method of performing a strategy solution on the two-point boundary value expression based on the parameter corresponding to the state quantity, the parameter corresponding to the upper bound of the constraint, the parameter corresponding to the lower bound of the constraint and a preset particle swarm optimization algorithm to obtain an optimal game control strategy includes: Optimizing the boundary conditions of the costate quantity in the two-point boundary value expression according to the state quantity, the parameter corresponding to the upper bound of the constraint, the parameter corresponding to the lower bound of the constraint, and the initial value corresponding to the preset costate quantity to obtain an updated two-point boundary value expression; The particle swarm optimization algorithm is used to solve the updated two-point boundary value expression to obtain the optimal game control strategy.

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

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