Track pursuit game processing method and device, terminal equipment and storage medium

Abstract

The invention discloses an orbit pursuit game processing method and device, terminal equipment and a storage medium, and relates to the field of aviation game computation.The method comprises the steps that a unilateral optimal interception problem is processed based on a pseudo-spectral method, a tracking unilateral initial co-state quantity is obtained, and the unilateral optimal interception problem is obtained based on a deconstruction bilateral pursuit game problem; and calculating the bilateral pursuit game problem through a preset optimization algorithm by taking the tracking unilateral initial co-state quantity as a guess value to obtain a pursuit bilateral optimal result. The method can guarantee the convergence of the algorithm while improving the calculation precision.

Description

Technical Field

[0001] The present application relates to the field of orbital game calculation, and in particular to an orbital pursuit and escape game processing method, device, terminal equipment and storage medium. Background Art

[0002] With the development and progress of aerospace technology, orbital motion control and strategic game of spacecraft have become an indispensable part of modern aerospace technology. Among them, the orbital pursuit and escape game (OPEG) problem is a complex and crucial issue, especially for the strategic confrontation between non-cooperative spacecraft. The core of this kind of problem lies in the dynamic strategy design between the pursuing spacecraft and the escaping spacecraft to achieve the optimal tracking or escape effect under the constraints of orbital dynamics and specific operational restrictions.

[0003] However, the currently used methods for solving the spacecraft orbit pursuit and escape game, such as the direct method and the indirect method, although they have certain advantages in simplifying calculations and model construction, these methods still have certain shortcomings in solution accuracy, initial value dependence and algorithm stability. In the process of solving the spacecraft orbit pursuit and escape game problem, it is impossible to simultaneously guarantee the accuracy and convergence of the algorithm. Summary of the invention

[0004] The main purpose of this application is to provide an orbital pursuit and escape game processing method, device, terminal equipment and storage medium, aiming to improve the calculation accuracy of the spacecraft orbital pursuit and escape game algorithm while ensuring the convergence of the algorithm.

[0005] To achieve the above objectives, the present application provides a track pursuit and escape game processing method, the method comprising:

[0006] Based on the pseudo-spectral method, the unilateral optimal interception problem is processed to obtain the tracking unilateral initial co-state quantity, and the unilateral optimal interception problem is obtained based on the deconstruction of the bilateral pursuit and escape game problem;

[0007] The tracking unilateral initial co-state quantity is used as a guess value, and the bilateral pursuit and escape game problem is calculated through a preset optimization algorithm to obtain the bilateral pursuit and escape optimal result.

[0008] In one embodiment, the step of processing the unilateral optimal interception problem based on the pseudo-spectral method to obtain the tracking unilateral initial co-state quantity includes:

[0009] The optimal interception time is obtained by using the pseudo-spectral method of collocation construction that complies with the co-state mapping theorem to solve the unilateral optimal interception problem.

[0010] Based on the optimal interception time, a co-state mapping equation is constructed through a Lagrange multiplier of nonlinear programming to obtain a tracking unilateral terminal co-state quantity;

[0011] The escaped unilateral terminal co-state quantity is obtained according to the tracked unilateral terminal co-state quantity, and the tracked unilateral initial co-state quantity is obtained based on the tracked unilateral terminal co-state quantity and the escaped unilateral terminal co-state quantity.

[0012] In one embodiment, the step of obtaining the escaped unilateral terminal co-state amount according to the tracked unilateral terminal co-state amount, and obtaining the tracked unilateral initial co-state amount based on the tracked unilateral terminal co-state amount and the escaped unilateral terminal co-state amount includes:

[0013] Based on the co-state boundary value of the bilateral pursuit-escape game problem and the tracking unilateral terminal co-state, the escaping unilateral terminal co-state is obtained;

[0014] According to the tracking unilateral terminal costate quantity and the escaping unilateral terminal costate quantity, the preset trajectory dynamics model and the preset costate equation are reversely integrated to obtain the tracking unilateral initial costate quantity and the escaping unilateral initial costate quantity.

[0015] In one embodiment, before the step of obtaining the escaping unilateral terminal co-state quantity based on the co-state quantity boundary value of the bilateral pursuit-escape game problem and the tracking unilateral terminal co-state quantity, the step further includes:

[0016] Based on the relative distance between the two terminals and the preset co-state equation, the boundary value of the co-state quantity of the bilateral pursuit and escape game problem is obtained.

[0017] In one embodiment, the step of using the tracking unilateral initial co-state quantity as a guess value and calculating the bilateral pursuit and escape game problem through a preset optimization algorithm to obtain the bilateral pursuit and escape optimal result includes:

[0018] Based on the bilateral pursuit-escape game problem and the preset constraints, a local optimization problem is constructed with the tracking unilateral initial co-state quantity and the escape unilateral initial co-state quantity as guess values;

[0019] The local optimization problem is calculated by a preset optimization algorithm to obtain a bilateral optimal result of pursuit and escape, and the bilateral optimal result of pursuit and escape includes a bilateral optimal control rate and an optimal trajectory of pursuit and escape.

[0020] In one embodiment, the step of calculating the local optimization problem by a preset optimization algorithm to obtain the bilateral optimal result of pursuit and escape includes:

[0021] Based on the trajectory dynamics model, the preset co-state equation and the guessed value, the local optimization problem is calculated by a preset sequential quadratic programming algorithm to obtain an optimal estimate;

[0022] According to the preset unilateral initial state quantity of tracking, the unilateral initial state quantity of escaping and the optimal estimated value, the trajectory dynamics model and the co-state equation are forward integrated to obtain the optimal result of the bilateral pursuit and escape.

[0023] In one embodiment, the step of calculating the local optimization problem based on the trajectory dynamics model, the preset co-state equation and the guessed value by using a preset sequential quadratic programming algorithm to obtain the optimal estimated value includes:

[0024] Based on the trajectory dynamics model, the preset co-state equation, the cost function and the guess value, the preset sequential quadratic programming algorithm is used to optimize the bilateral initial co-state quantity of the pursuit and escape game problem and the terminal game time to obtain the optimal estimate.

[0025] In addition, to achieve the above purpose, the present application also proposes a track pursuit and escape game processing device, the track pursuit and escape game processing device comprising:

[0026] A tracking unilateral initial co-state quantity calculation module is used to process the unilateral optimal interception problem based on the pseudo-spectral method to obtain the tracking unilateral initial co-state quantity. The unilateral optimal interception problem is obtained based on the deconstruction of the bilateral pursuit and escape game problem.

[0027] The bilateral pursuit and escape game problem calculation module is used to use the tracking unilateral initial co-state quantity as a guess value, calculate the bilateral pursuit and escape game problem through a preset optimization algorithm, and obtain the bilateral pursuit and escape optimal result.

[0028] In addition, to achieve the above-mentioned purpose, the present application also proposes a track pursuit and escape game processing device, which includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, and the computer program is configured to implement the steps of the track pursuit and escape game processing method as described above.

[0029] In addition, to achieve the above-mentioned purpose, the present application also proposes a storage medium, which is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by the processor, the steps of the track pursuit and escape game processing method described above are implemented.

[0030] The orbital pursuit and escape game processing method, device, terminal device and storage medium proposed in the embodiments of the present application process the unilateral optimal interception problem through the pseudo-spectral method to obtain the unilateral initial costate quantity for tracking. The unilateral optimal interception problem is obtained based on the deconstruction of the bilateral pursuit and escape game problem; the unilateral initial costate quantity for tracking is used as the guess value, and the bilateral pursuit and escape game problem is calculated through a preset optimization algorithm to obtain the bilateral optimal result of pursuit and escape. The present application deconstructs the bilateral orbital pursuit and escape game problem and calculates the unilateral optimal interception problem deconstructed from the bilateral pursuit and escape game problem according to the pseudo-spectral method, so as to obtain the initial guess value for subsequent processing of the bilateral pursuit and escape game problem as an optimization algorithm, thereby avoiding the problem of guessing the initial value of the costate quantity involved in calculating the bilateral pursuit and escape game problem, thereby improving the robustness of the algorithm while ensuring the convergence of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0032] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0033] Figure 1 This is a flow chart of the first embodiment of the track pursuit and escape game processing method of the present application;

[0034] Figure 2 This is a flow chart of Embodiment 2 of the track pursuit and escape game processing method of this application;

[0035] Figure 3 This is a flow chart of Embodiment 3 of the track pursuit and escape game processing method of this application;

[0036] Figure 4 This is a flow chart of the fourth embodiment of the track pursuit and escape game processing method of the present application;

[0037] Figure 5 This is a flowchart of Embodiment 5 of the track pursuit and escape game processing method of this application;

[0038] Figure 6 This is a flow chart of Embodiment 6 of the track pursuit and escape game processing method of this application;

[0039] Figure 7 This is a flow chart of Embodiment 7 of the track pursuit and escape game processing method of this application;

[0040] Figure 8 This is a schematic diagram of the step-by-step solution framework of the track pursuit and escape game processing method of this application;

[0041] Fig. 9 This is a schematic diagram of the simulation verification trajectory of the track pursuit and escape game processing method of this application;

[0042] Fig.10 This is a schematic diagram of the module structure of the track pursuit and escape game processing device of the embodiment of the present application;

[0043] Fig.11 Schematic diagram of the device structure of the hardware operating environment involved in the track pursuit and escape game processing method in the embodiment of the present application.

[0044] The purpose, features and advantages of this application will be further described in conjunction with the embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0045] It should be understood that the specific embodiments described herein are only used to explain the technical solutions of the present application and are not used to limit the present application.

[0046] In order to better understand the technical solution of the present application, a detailed description will be given below in conjunction with the accompanying drawings and specific implementation methods.

[0047] The main solution of the present application is: to process the unilateral optimal interception problem based on the pseudo-spectral method to obtain the unilateral initial costate quantity for tracking, and the unilateral optimal interception problem is obtained based on the deconstruction of the bilateral pursuit game problem; using the unilateral initial costate quantity for tracking as the guess value, the bilateral pursuit game problem is calculated through a preset optimization algorithm to obtain the bilateral optimal result of pursuit. The present application deconstructs the bilateral orbital pursuit game problem and calculates the unilateral optimal interception problem deconstructed from the bilateral pursuit game problem according to the pseudo-spectral method, to obtain the initial guess value for subsequent processing of the bilateral pursuit game problem as an optimization algorithm, thereby avoiding the problem of guessing the initial value of the costate quantity involved in calculating the bilateral pursuit game problem, improving the robustness of the algorithm while also ensuring the convergence of the algorithm.

[0048] This embodiment takes into account that, with the development and progress of aerospace technology, orbital motion control and strategic games of spacecraft have become an indispensable part of modern aerospace technology, and among them, the orbital pursuit and escape game (OPEG) problem is a complex and crucial issue. However, the currently used methods for solving the spacecraft orbital pursuit and escape game, such as the direct method and the indirect method, although they have certain advantages in simplifying calculations and model construction, these methods still have certain shortcomings in solution accuracy, initial value dependence and algorithm stability. In the process of solving the spacecraft orbital pursuit and escape game problem, it is impossible to simultaneously guarantee the accuracy and convergence of the algorithm.

[0049] Based on this, an embodiment of the present application proposes a solution, by deconstructing the bilateral track pursuit game problem and calculating the unilateral optimal interception problem deconstructed from the bilateral pursuit game problem according to the pseudo-spectral method, the tracking unilateral initial costate quantity in the unilateral optimal interception problem is obtained, and then it is used as the guess value of the optimization algorithm to process the bilateral pursuit game problem, thereby avoiding the problem of guessing the initial value of the costate quantity involved in calculating the bilateral pursuit game problem, improving the robustness of the algorithm while also ensuring the convergence of the algorithm.

[0050] Based on this, this application proposes a first embodiment of the track pursuit and escape game processing method, please refer to Figure 1 The track pursuit and escape game processing method includes steps S10 to S20:

[0051] Step S10, processing the unilateral optimal interception problem based on the pseudo-spectral method to obtain the tracking unilateral initial co-state quantity, wherein the unilateral optimal interception problem is obtained based on deconstructing the bilateral pursuit and escape game problem;

[0052] When a spacecraft is moving in space, it will be affected by multiple forces and will no longer move according to the Kepler orbit. Usually, the biggest influence on low-Earth orbit spacecraft is the non-spherical gravitational perturbation J2 of the Earth. Most previous studies have used linear relative dynamics models to simplify calculations. It is advisable to use the CW model in the close-range orbital pursuit and escape game problem (LDOPEG). However, when the two spacecraft are far apart, a large linearization error will occur. Therefore, this application selects the spacecraft orbital dynamics model in the Cartesian coordinate system, and considers the gravity of the central celestial body point mass and the J2 perturbation term to calculate and solve the bilateral orbital pursuit and escape game problem. That is, for the spacecraft orbital pursuit and escape game problem considering the J2 perturbation (that is, the influence of the non-spherical shape of the Earth on the orbit), the Hamiltonian function of the problem can be constructed by applying the Pontryagin minimum principle, and then this optimal control problem is transformed into solving a two-point boundary value problem with 24 dimensions. The solution to the two-point boundary value problem represents the optimal strategy for the pursuit and escape behavior between spacecraft.

[0053] The bilateral pursuit and escape game problem refers to the pursuit and escape problem in which the tracking spacecraft and the escaping spacecraft use the thrust provided by their respective thrusters to pursue the relative distance between the two terminals (Equation 3) under the constraints of orbital dynamics (Equation 1) and space environment (Equation 2). The goal of the tracking spacecraft is to intercept the escaping spacecraft at the terminal game time and shorten the game time as much as possible, while the goal of the escaping spacecraft is to extend the game time as much as possible.

[0054] Among them, formula 1 represents the relationship between the spacecraft speed and position, formula 2 is used to calculate the process constraints, and formula 3 is used to calculate the terminal relative distance between the tracking spacecraft and the escaping spacecraft. Specifically, the formula is calculated as follows:

[0055]

[0056] Where r represents the position of the spacecraft in the Cartesian coordinate system, v represents the velocity of the spacecraft in the Cartesian coordinate system, represent the derivative of position and the derivative of velocity respectively, u represents the control of the spacecraft in the Cartesian coordinate system, μ=3.986×10 5 km 3 s -2 is the Earth’s gravitational constant, J2 = 1.0826 × 10 -3 is the J2 perturbation coefficient, R e =6378.165km is the average radius of the earth, x, y, z represent the x-axis, y-axis and z-axis of the Cartesian coordinate system respectively, j=P, E, P represents the pursuit spacecraft, and E represents the escape spacecraft.

[0057]

[0058] Among them, C is the process constraint, which is set to the minimum flight altitude of the spacecraft greater than 100km. The specific parameters have the same meaning as above. This formula reflects the influence of the dense atmospheric drag force at the ultra-low orbit altitude.

[0059]

[0060] Among them, t f represents the terminal game time, φ represents the terminal relative distance between the tracking spacecraft and the escaping spacecraft, and the other parameters have the same meanings as above.

[0061] Step S20, using the tracking unilateral initial co-state quantity as a guess value, calculating the bilateral pursuit and escape game problem through a preset optimization algorithm to obtain the bilateral pursuit and escape optimal result;

[0062] Specifically, since the escaping spacecraft has strong maneuverability, directly solving the bilateral pursuit and escape game problem is likely to not converge. Therefore, this application deconstructs the bilateral pursuit and escape game problem into a unilateral optimal interception problem, and then uses the Radau pseudo-spectral method to solve the unilateral optimal interception problem to obtain the initial guess value that is subsequently used as an optimization algorithm to process the bilateral pursuit and escape game problem.

[0063] As an implementation method, the bilateral pursuit and escape game problem is deconstructed into a unilateral optimal interception problem and a local optimization problem. The tracking unilateral initial costate obtained by solving the unilateral optimal interception problem using the Radau pseudospectral method can be used as the initial guess value of the local optimization problem. That is, the orbital pursuit and escape game problem can be deconstructed into two parts: "unilateral optimal interception problem" and "local optimization problem". First, the Radau pseudospectral method is used to solve the unilateral optimal interception problem (the first part) when the escaping spacecraft is not maneuvering, and the tracking unilateral initial costate is obtained. Then, the escaping spacecraft is added to the problem modeling. maneuverability, thereby constructing a local optimization problem (the second part) and taking the tracking unilateral initial costate as the initial guess value of the local optimization problem, and then solving the bilateral pursuit and escape game problem through the preset optimization algorithm to obtain the optimal control rate and the optimal flight trajectory. Among them, the preset optimization algorithm can be the sequential quadratic programming SQP algorithm. By using this method to calculate and solve the bilateral orbital pursuit and escape game problem, the problem of guessing the initial value of the costate in the traditional direct shooting method can be avoided. Among them, the tracking unilateral initial costate is the initial costate of the tracking spacecraft in the unilateral optimal interception problem.

[0064] The orbital pursuit and escape game processing method proposed in the embodiment of the present application processes the unilateral optimal interception problem through the pseudo-spectral method to obtain the unilateral initial costate quantity for tracking. The unilateral optimal interception problem is obtained based on the deconstruction of the bilateral pursuit and escape game problem; using the unilateral initial costate quantity for tracking as the guess value, the bilateral pursuit and escape game problem is calculated through a preset optimization algorithm to obtain the bilateral optimal result of pursuit and escape. The present application deconstructs the bilateral orbital pursuit and escape game problem and calculates the unilateral optimal interception problem deconstructed from the bilateral pursuit and escape game problem according to the pseudo-spectral method, to obtain the initial guess value for subsequent processing of the bilateral pursuit and escape game problem as an optimization algorithm, thereby avoiding the problem of guessing the initial value of the costate quantity involved in calculating the bilateral pursuit and escape game problem, thereby improving the robustness of the algorithm while also ensuring the convergence of the algorithm.

[0065] Based on the first embodiment of the present application, in the second embodiment of the present application, the same or similar contents as those in the above-mentioned embodiment 1 can be referred to the above introduction, and will not be repeated in the following. Figure 2 , for step S10 in the track pursuit and escape game processing method, the unilateral optimal interception problem is processed based on the pseudo-spectral method to obtain the tracking unilateral initial co-state quantity, and the unilateral optimal interception problem is refined based on the deconstruction of the bilateral pursuit and escape game problem, wherein the refined steps include S11 to S13:

[0066] Step S11, processing the unilateral optimal interception problem by using a pseudo-spectral method of point-matching construction that conforms to the co-state mapping theorem to obtain the optimal interception time;

[0067] Step S12, based on the optimal interception time, constructing a co-state mapping equation through a Lagrange multiplier of nonlinear programming to obtain a tracking unilateral terminal co-state quantity;

[0068] Step S13, obtaining the escaped unilateral terminal co-state quantity according to the tracked unilateral terminal co-state quantity, and obtaining the tracked unilateral initial co-state quantity based on the tracked unilateral terminal co-state quantity and the escaped unilateral terminal co-state quantity;

[0069] The orbital pursuit and escape game processing method proposed in this application is divided into two steps. The first step is to construct and solve the unilateral optimal interception problem. In this step, the Radau pseudo-spectral method is used to solve the unilateral optimal interception problem to obtain the tracking unilateral initial costate quantity, which is the initial guess value of the next step "local optimization problem".

[0070] Specifically, the Radau pseudospectral method based on the Legendre-Gauss-Radau collocation method that conforms to the co-state mapping theorem is used to solve the unilateral optimal interception problem to obtain the optimal interception time. In the solution process, the Lagrange multiplier (Karush-Kuhn-Tucker multiplier) of nonlinear programming is used to construct the co-state mapping equation to obtain the tracking unilateral terminal co-state quantity. (i.e., the terminal costate quantity of the tracking spacecraft in the unilateral optimal interception problem), this process is also called costate mapping.

[0071] Then, after obtaining the tracking unilateral terminal co-state quantity, the escape unilateral terminal co-state quantity is obtained according to the obtained tracking unilateral terminal co-state quantity. (i.e., the terminal co-state quantity of the escaping spacecraft in the unilateral optimal interception problem). Specifically, according to the co-state boundary value (Equation 4) of the bilateral orbital pursuit game problem (i.e., the spacecraft orbital pursuit game problem), the terminal co-state quantity of the escaping spacecraft is calculated. (Formula 5).

[0072]

[0073] Among them, λ j1 (t f ),λ j2 (t f ),λ j3 (t f ),λ j4 (t f ),λ j5 (t f ),λ j6 (t f ) represents the terminal co-state of the two spacecraft in the pursuit-escape game problem.

[0074]

[0075] Subsequently, based on the tracking unilateral terminal costate quantity and the escape unilateral terminal costate quantity, the above-mentioned orbital dynamics formula (Formula 1) and the preset costate equation (Formula 6) are reversely integrated to obtain the tracking unilateral initial costate quantity.

[0076]

[0077] Among them, λ· i1 ,λ· i2 ,λ· i3 ,λ· i4 ,λ· i5 ,λ· i6 They represent the co-states λ of the two spacecraft in the bilateral orbital pursuit game problem. i1 ,λ i2 ,λ i3 ,λ i4 ,λ i5 ,λ i6 The derivative of .

[0078] As an implementation method, considering the spacecraft orbit pursuit game problem with J2 perturbation (i.e., the impact of the non-spherical shape of the earth on the orbit), the Hamiltonian function of the problem can be constructed by applying the Pontryagin minimum principle, and then the optimal control problem is transformed into solving a two-point boundary value problem with 24 dimensions. The solution to the two-point boundary value problem represents the optimal strategy for the pursuit behavior between spacecraft. Therefore, the above costate equation (Equation 6) can be obtained according to the Hamiltonian function (Equation 7) and the orbital dynamics formula (Equation 1).

[0079]

[0080] Where fj is the right side of the orbital dynamics formula (Equation 1), is the co-state quantity.

[0081] Substituting the Hamiltonian function (Equation 7) into the orbital dynamics formula (Equation 1) yields Equation 8:

[0082]

[0083] Among them, the boundary value of the Hamiltonian equation of the terminal time free differential game is shown in Equation 9:

[0084] H(t f )=-1 (9)

[0085] Among them, t f It is the terminal game time.

[0086] Then, the co-state equation that the co-state quantity of the saddle point solution needs to satisfy can be obtained through the expression of the Hamiltonian function, that is, the above-mentioned co-state equation (Formula 6) is obtained.

[0087] The track pursuit and escape game processing method proposed in the embodiment of the present application processes the unilateral optimal interception problem through the pseudo-spectral method of point configuration that conforms to the comorphic mapping theorem to obtain the optimal interception time; based on the optimal interception time, the comorphic mapping equation is constructed through the Lagrange multiplier of nonlinear programming to obtain the tracking unilateral terminal comorphic quantity; according to the tracking unilateral terminal comorphic quantity, the escaping unilateral terminal comorphic quantity is obtained, and based on the tracking unilateral terminal comorphic quantity and the escaping unilateral terminal comorphic quantity, the tracking unilateral initial comorphic quantity is obtained, which can improve the convergence of the algorithm.

[0088] Based on the second embodiment of the present application, in the third embodiment of the present application, the same or similar contents as those in the above-mentioned second embodiment can refer to the above introduction, and will not be repeated in the following. Figure 3 , for step S13 in the track pursuit and escape game processing method, the escape unilateral terminal co-state quantity is obtained according to the tracking unilateral terminal co-state quantity, and the tracking unilateral initial co-state quantity is obtained based on the tracking unilateral terminal co-state quantity and the escape unilateral terminal co-state quantity, and the refinement is performed, wherein the refinement steps include S131-S132:

[0089] Step S131, obtaining the escaping unilateral terminal co-state quantity based on the co-state quantity boundary value of the bilateral pursuit-escape game problem and the tracking unilateral terminal co-state quantity;

[0090] Step S132, according to the tracking unilateral terminal co-state quantity and the escaping unilateral terminal co-state quantity, reversely integrate the preset trajectory dynamics model and the preset co-state equation to obtain the tracking unilateral initial co-state quantity and the escaping unilateral initial co-state quantity;

[0091] Specifically, after obtaining the tracking unilateral terminal co-state quantity, the terminal co-state quantity of the escaping spacecraft can be calculated through the co-state quantity boundary value (Formula 4) of the bilateral pursuit and escape game problem, wherein the co-state quantity boundary value of the bilateral pursuit and escape game problem can be obtained according to the preset co-state quantity boundary value calculation formula (Formula 10), the relative distance between the two terminals (Formula 3) and the co-state equation (Formula 6), as follows:

[0092]

[0093] Where ψ = t f +υ T φ, υ=[υ1υ2υ3] is the terminal Lagrange multiplier. Substituting the relative distance between the two terminals (Equation 3) into the co-state equation (Equation 6), the co-state boundary value (Equation 4) of the bilateral orbital pursuit game problem (i.e., the spacecraft orbital pursuit game problem) can be obtained. Then, according to the co-state boundary value (Equation 4) and the tracking unilateral terminal co-state, the terminal co-state of the escaping spacecraft can be obtained. The escaped unilateral terminal co-state quantity is calculated After that, the above orbital dynamics formula (Formula 1) and the preset co-state equation (Formula 6) are reversely integrated to finally obtain the tracking unilateral initial co-state quantity and the escape unilateral initial co-state quantity.

[0094] The orbital pursuit and escape game processing method proposed in the embodiment of the present application obtains the escaping unilateral terminal costate quantity based on the costate quantity boundary value of the bilateral pursuit and escape game problem and the tracking unilateral terminal costate quantity; according to the tracking unilateral terminal costate quantity and the escaping unilateral terminal costate quantity, the preset trajectory dynamics model and the preset costate equation are reversely integrated to obtain the tracking unilateral initial costate quantity and the escaping unilateral initial costate quantity, which provides a data basis for the subsequent calculation of the bilateral orbital pursuit and escape game problem using a sequential quadratic programming algorithm.

[0095] Based on the third embodiment of the present application, in the fourth embodiment of the present application, the same or similar contents as those in the third embodiment can be referred to the above introduction, and will not be described in detail later. Figure 4 In step S131 of the track pursuit and escape game processing method, before obtaining the escape unilateral terminal co-state quantity based on the co-state quantity boundary value of the bilateral pursuit and escape game problem and the tracking unilateral terminal co-state quantity, the method further includes step S1301:

[0096] Step S1301, based on the relative distance between the two terminals and the preset co-state equation, obtain the co-state boundary value of the bilateral pursuit game problem;

[0097] Substituting the relative distance between the two terminals (Formula 3) into the co-state equation (Formula 6), we can obtain the co-state boundary value of the orbital pursuit game problem (i.e., the spacecraft orbital pursuit game problem) (Formula 4). Therefore, after obtaining the co-state quantity of the tracking unilateral terminal, we can obtain the co-state quantity of the escaping unilateral terminal based on the co-state boundary value of the bilateral pursuit game problem and the co-state quantity of the tracking unilateral terminal.

[0098] The orbital pursuit and escape game processing method proposed in the embodiment of the present application obtains the boundary value of the costate quantity of the bilateral pursuit and escape game problem through the relative distance of the bilateral terminals and the preset costate equation; based on the costate quantity boundary value of the bilateral pursuit and escape game problem and the tracking unilateral terminal costate quantity, the escaping unilateral terminal costate quantity is obtained; according to the tracking unilateral terminal costate quantity and the escaping unilateral terminal costate quantity, the preset trajectory dynamics model and the preset costate equation are reversely integrated to obtain the tracking unilateral initial costate quantity and the escaping unilateral initial costate quantity, which provides a data basis for the subsequent calculation of the bilateral orbital pursuit and escape game problem using the sequential quadratic programming algorithm.

[0099] Based on the fourth embodiment of the present application, in the fifth embodiment of the present application, the same or similar contents as those in the fourth embodiment can be referred to the above introduction, and will not be repeated in the following. Figure 5 , for step S20 in the track pursuit and escape game processing method, the tracking unilateral initial co-state quantity is used as a guess value, and the bilateral pursuit and escape game problem is calculated by a preset optimization algorithm to obtain the bilateral optimal result of pursuit and escape, and the refinement steps include S21 to S22:

[0100] Step S21, based on the bilateral pursuit-escape game problem and preset constraints, using the tracking unilateral initial co-state quantity and the escaping unilateral initial co-state quantity as guess values, constructing a local optimization problem;

[0101] Step S22, calculating the local optimization problem by a preset optimization algorithm to obtain a bilateral optimal result of pursuit and escape, wherein the bilateral optimal result of pursuit and escape includes a bilateral optimal control rate and an optimal trajectory;

[0102] The local optimization problem (i.e., the second part) obtained by deconstructing the bilateral orbital pursuit and escape game problem uses the result of the unilateral optimal interception problem (i.e., the first part). That is, it can be understood that the local optimization problem uses the tracking unilateral initial costate quantity and the escape unilateral initial costate quantity (i.e., the initial moment costate quantity of the tracking spacecraft and the escape spacecraft) as guessed values, and is constructed by fully considering all constraints (including the maneuverability of the escape spacecraft).

[0103] Subsequently, the local optimization problem is processed by the sequential quadratic programming algorithm, and the solution (including the bilateral optimal control rate and the optimal flight trajectory) of the original spacecraft orbit pursuit game problem (i.e., the bilateral orbit pursuit game problem) can be obtained.

[0104] The track pursuit and escape game processing method proposed in the embodiment of the present application is based on the bilateral pursuit and escape game problem and the preset constraints, and uses the tracking unilateral initial costate quantity and the escape unilateral initial costate quantity as guess values ​​to construct a local optimization problem; the local optimization problem is calculated by a preset optimization algorithm to obtain the bilateral pursuit and escape optimal result, and the bilateral pursuit and escape optimal result includes the bilateral pursuit and escape optimal control rate and the optimal trajectory. The present application improves the overall calculation efficiency by using the sequential quadratic programming (SQP) algorithm used in the local optimization problem to calculate the bilateral pursuit and escape optimal control rate and the optimal trajectory.

[0105] Based on the fifth embodiment of the present application, in the sixth embodiment of the present application, the same or similar contents as those in the fifth embodiment can be referred to the above description, and will not be described in detail later. Figure 6, for step S22 in the track pursuit and escape game processing method, the local optimization problem is calculated by a preset optimization algorithm to obtain the bilateral optimal result of pursuit and escape, and the refinement steps include S221 to S222:

[0106] Step S221, based on the trajectory dynamics model, the preset co-state equation and the guessed value, the local optimization problem is calculated by a preset sequential quadratic programming algorithm to obtain an optimal estimate;

[0107] Step S222, according to the preset tracking unilateral initial state quantity, the escape unilateral initial state quantity and the optimal estimated value, the trajectory dynamics model and the co-state equation are forward integrated to obtain the pursuit and escape bilateral optimal result;

[0108] Specifically, the optimization variables of the local optimization problem are constructed, where the optimization variables can include the initial co-state quantity of the tracking spacecraft, the initial co-state quantity of the escaping spacecraft, and the terminal game time in the bilateral orbital pursuit and escape game problem, with a total of 13 dimensions. Among them, the optimal control rate can be written as an explicit expression of the co-state quantity of the two spacecraft (Equation 11).

[0109]

[0110] Specifically, Equation 8 can be substituted into the Pontryagin minimum principle (Equation 12) to obtain an explicit expression of the co-state quantities of the two spacecraft (Equation 11), where the parameters have the same meanings as above.

[0111]

[0112] Furthermore, the sequential quadratic programming algorithm is used to iteratively find the optimal value of the optimization variable. The orbital dynamics (Equation 1) and the co-state equation (Equation 6) are used in the optimization, and the cost function is the terminal game time t f , using the 13-dimensional equality constraint ceq (Equation 13), the final converged solution is the optimal estimate of the optimization variable.

[0113]

[0114] Among them, B λ is the terminal co-state constraint (Eq. 14), H(t f ) is the terminal Hamiltonian (Equation 15).

[0115]

[0116]

[0117] Furthermore, using the optimized [λ P (t0)λ E (t0)tf ] and the tracking spacecraft and the escape spacecraft’s initial state vectors, forward-integrate the orbital dynamics (Equation 1) and the co-state equation (Equation 6), and obtain the bilateral optimal control rate and the optimal trajectory (i.e., the optimal control rate and the optimal flight trajectory of the tracking spacecraft and the escape spacecraft).

[0118] The orbital pursuit and escape game processing method proposed in the embodiment of the present application is based on the trajectory dynamics model, the preset costate equation and the guessed value, and the local optimization problem is calculated by a preset sequential quadratic programming algorithm to obtain the optimal estimate value; according to the preset tracking unilateral initial state quantity, the escape unilateral initial state quantity and the optimal estimate value, the trajectory dynamics model and the costate equation are forward integrated to obtain the bilateral optimal result of pursuit and escape, and a two-step solution framework is constructed to solve the bilateral orbital pursuit and escape game problem step by step, avoiding the problem of initial value guessing of costate quantity in the traditional direct shooting method and improving the robustness of the algorithm.

[0119] Based on the sixth embodiment of the present application, in the seventh embodiment of the present application, the same or similar contents as those in the sixth embodiment can be referred to the above introduction, and will not be described in detail later. Figure 7 , for step S21 in the track pursuit and escape game processing method, based on the trajectory dynamics model, the preset co-state equation and the guess value, the local optimization problem is calculated by a preset sequential quadratic programming algorithm to obtain the optimal estimate value for refinement, wherein the refinement step includes S2211:

[0120] Step S2211, based on the trajectory dynamics model, the preset co-state equation, the cost function and the guess value, the preset sequential quadratic programming algorithm is used to optimize the bilateral initial co-state quantity of the pursuit and escape game problem and the terminal game time to obtain the optimal estimated value;

[0121] Based on orbital dynamics (Equation 1) and the costate equation (Equation 6), the cost function (Equation 16) is used to optimize the optimization variables of the local optimization problem through sequential quadratic programming. The optimization variables to be optimized include the initial costate quantity of the bilateral pursuit and escape game problem and the terminal game time (i.e., the initial costate quantity of the tracking spacecraft in the escape game problem and the initial costate quantity of the escaping spacecraft in the pursuit and escape game problem), and the optimal estimate is obtained.

[0122]

[0123] The specific meanings of the parameters are the same as above.

[0124] The orbital pursuit and escape game processing method proposed in the embodiment of the present application is based on the trajectory dynamics model, the preset costate equation, the cost function and the guess value, and optimizes the bilateral initial costate quantity and terminal game time of the bilateral pursuit and escape game problem through a preset sequential quadratic programming algorithm to obtain the optimal estimate, thereby improving the calculation efficiency.

[0125] Reference Figure 8 , Figure 8 This is a schematic diagram of the step-by-step solution framework for the track pursuit and escape game processing method of this application.

[0126] like Figure 8 As shown in the figure, represents the state vectors of the two spacecraft, represents the control vectors of the two spacecraft, ε represents the maximum allowable error of the Radau pseudospectral method, represents the optimal interception time, represents the terminal co-state of the tracking spacecraft in the unilateral optimal interception problem, represents the initial co-state of the tracking spacecraft in the unilateral optimal interception problem, represents the initial co-state of the escaping spacecraft in the unilateral optimal interception problem, represents the estimated value of the initial co-state of the tracking spacecraft in the pursuit-escape game problem, represents the estimated value of the initial co-state of the escaping spacecraft in the pursuit-escape game problem, t0 represents the initial time of the game, Represents the estimated value of the terminal game time.

[0127] Specifically, Figure 8 As shown, the calculation process of the bilateral track pursuit and escape game problem is divided into two processes; the first process is the processing of the unilateral optimal interception problem;

[0128] The first step is to use the Radau pseudo-spectral method constructed by Legendre-Gauss-Radau collocation that conforms to the co-state mapping theorem to solve the unilateral optimal interception problem to obtain the optimal interception time. In the solution process, the Lagrange multiplier (Karush-Kuhn-Tucker multiplier) of nonlinear programming is used to construct the co-state mapping equation to obtain the terminal co-state quantity of the tracking spacecraft in the unilateral optimal interception problem. This process is also called co-state mapping. The second step is to calculate the terminal co-state quantity of the escaping spacecraft through the co-state quantity boundary value (Equation 4) of the spacecraft orbit pursuit and escape game problem. (Equation 5), the third step is to use the terminal co-state quantity of the tracking spacecraft in the unilateral optimal interception problem and the terminal co-state of the escaping spacecraft The initial co-state quantity of the tracking spacecraft in the unilateral optimal interception problem can be obtained by inversely integrating the spacecraft orbital dynamics (Eq. 1) and the co-state equation (Eq. 4): and the initial co-state of the escaping spacecraft

[0129] The second process is to deal with the local optimization problem;

[0130] Among them, the first step is to construct the optimization variables of the local optimization problem. Specifically, the optimization variables include the initial costate quantity of the tracking spacecraft, the initial costate quantity of the escaping spacecraft and the terminal game time in the bilateral orbital pursuit and escape game problem, a total of 13 dimensions.

[0131] In the second step, the sequential quadratic programming algorithm is used to iteratively find the optimal value of the optimization variable. The spacecraft orbital dynamics (Equation 1) and the co-state equation (Equation 4) are used in the optimization. The cost function is the terminal game time t f , using the 13-dimensional equality constraint ceq (Equation 13), the final converged solution is the optimal estimate of the optimization variable.

[0132] The third step is to use the optimized [λ P (t0)λ E (t0)t f ] and the tracking spacecraft and the escaping spacecraft's initial state vectors, and forward integrate the spacecraft orbital dynamics and co-state equations to obtain the optimal control rate and optimal flight trajectory of the tracking spacecraft and the escaping spacecraft.

[0133] In addition, in order to verify the calculation accuracy and efficiency of the bilateral track pursuit game problem, this application simulates the obtained numerical results, as follows:

[0134] The tracking spacecraft and the escaping spacecraft with different orbital altitudes, different orbital inclinations, and different initial relative distances are selected as examples for analysis. The specific values ​​are shown in Table 1. The Radau pseudospectral method is set to 15 subintervals, each interval uses a 6th-order collocation point, and the maximum allowable error is set to ε = 10 -8 The upper limit of the number of iterations of the sequential quadratic programming algorithm is set to 102, and the constraint tolerance is set to 10-6. The simulation computer platform uses a single machine with the hardware configuration of AMD Ryzen5-5600HCPU@3.3GHz and 16GB RAM, and the simulation platform is MATLAB.

[0135] Among them, 6 examples are selected to verify the proposed step-by-step hybrid optimization algorithm. The specific values ​​of the examples and the thrust configuration of the pursuit spacecraft are given in Table 1, where g = 9.798 m·s -2 It can be seen from Table 1 that the thrust of the pursuit spacecraft is greater than that of the escape spacecraft, which is a necessary condition for successful interception. Note that this application converts the spherical coordinates into classical orbital elements, and then converts the orbital elements into Cartesian coordinates in the inertial system.

[0136]

[0137] The algorithm solution results are shown in Table 2 below, where t cpu represents the running time of the algorithm, including Radau pseudospectral method and sequential quadratic programming. f )+1 reflects the degree of constraint satisfaction, R miss represents the terminal relative distance of the pursuing spacecraft, t OSIP represents the time (in minutes) required for the tracking spacecraft to intercept in the unilateral optimal interception problem, t f represents the duration of the game of chasing and escaping spacecraft (in minutes), is the terminal gaming time, Fig. 9 The 3D trajectory diagrams of the six examples are clearly shown, where the solid lines represent the optimal trajectories in the pursuit-escape game problem and the dotted lines represent the flight trajectories in the unilateral optimal interception problem.

[0138] From the results in Table 2, it can be seen that all examples can obtain converged solutions within 10 seconds, and the calculation error of the terminal game time does not exceed 0.44%, which shows that the co-state quantity of the unilateral optimal interception problem is a good initial value guess of the co-state quantity of the bilateral orbital pursuit game problem, reflecting the effectiveness of the step-by-step solution framework proposed in this application. In terms of constraint satisfaction, the value of case 2 in the prior art is -1.5e-5, and the value of case 4 is -2e-5, while the values ​​calculated by this application are 4e-11 and 1.2e-9 respectively, which better meet the constraints, indicating that the results calculated by the method of this application are closer to the optimal saddle point solution. In the terminal game results, the terminal relative distances of the 6 examples are all at the level of one hundredth of a millimeter, which reflects the high precision of the step-by-step hybrid calculation method of this application.

[0139]

[0140] This application also provides a track pursuit and escape game processing device, please refer to Fig.10 , the track pursuit and escape game processing device includes:

[0141] A tracking unilateral initial co-state quantity calculation module 10 is used to process the unilateral optimal interception problem based on the pseudo-spectral method to obtain the tracking unilateral initial co-state quantity, wherein the unilateral optimal interception problem is obtained based on deconstructing the bilateral pursuit and escape game problem;

[0142] The bilateral pursuit and escape game problem calculation module 20 is used to use the tracking unilateral initial co-state quantity as a guess value, calculate the bilateral pursuit and escape game problem through a preset optimization algorithm, and obtain the bilateral pursuit and escape optimal result;

[0143] Optionally, the tracking unilateral initial co-state quantity calculation module 10 is further used for:

[0144] The optimal interception time is obtained by using the pseudo-spectral method of collocation construction that complies with the co-state mapping theorem to solve the unilateral optimal interception problem.

[0145] Based on the optimal interception time, a co-state mapping equation is constructed through a Lagrange multiplier of nonlinear programming to obtain a tracking unilateral terminal co-state quantity;

[0146] The escaped unilateral terminal co-state quantity is obtained according to the tracked unilateral terminal co-state quantity, and the tracked unilateral initial co-state quantity is obtained based on the tracked unilateral terminal co-state quantity and the escaped unilateral terminal co-state quantity.

[0147] Optionally, the tracking unilateral initial co-state quantity calculation module 10 is further used for:

[0148] Based on the co-state boundary value of the bilateral pursuit-escape game problem and the tracking unilateral terminal co-state, the escaping unilateral terminal co-state is obtained;

[0149] According to the tracking unilateral terminal co-state quantity and the escaping unilateral terminal co-state quantity, the preset trajectory dynamics model and the preset co-state equation are reversely integrated to obtain the tracking unilateral initial co-state quantity and the escaping unilateral initial co-state quantity.

[0150] Optionally, the tracking unilateral initial co-state quantity calculation module 10 is further used for:

[0151] Based on the relative distance between the two terminals and the preset co-state equation, the boundary value of the co-state quantity of the bilateral pursuit and escape game problem is obtained.

[0152] Optionally, the bilateral pursuit-escape game problem calculation module 20 is further used to:

[0153] Based on the bilateral pursuit-escape game problem and the preset constraints, a local optimization problem is constructed with the tracking unilateral initial co-state quantity and the escape unilateral initial co-state quantity as guess values;

[0154] The local optimization problem is calculated by a preset optimization algorithm to obtain a bilateral optimal result of pursuit and escape, and the bilateral optimal result of pursuit and escape includes a bilateral optimal control rate and an optimal trajectory of pursuit and escape.

[0155] Optionally, the bilateral pursuit-escape game problem calculation module 20 is further used to:

[0156] Based on the trajectory dynamics model, the preset co-state equation and the guessed value, the local optimization problem is calculated by a preset sequential quadratic programming algorithm to obtain an optimal estimate;

[0157] According to the preset unilateral initial state quantity of tracking, the unilateral initial state quantity of escaping and the optimal estimated value, the trajectory dynamics model and the co-state equation are forward integrated to obtain the optimal result of the bilateral pursuit and escape.

[0158] Optionally, the bilateral pursuit-escape game problem calculation module 20 is further used to:

[0159] Based on the trajectory dynamics model, the preset co-state equation, the cost function and the guess value, the preset sequential quadratic programming algorithm is used to optimize the bilateral initial co-state quantity of the pursuit and escape game problem and the terminal game time to obtain the optimal estimate.

[0160] The orbital pursuit and escape game processing device provided in the present application adopts the orbital pursuit and escape game processing method in the above-mentioned embodiment, which can improve the calculation accuracy while ensuring the convergence of the algorithm. Compared with the prior art, the beneficial effects of the orbital pursuit and escape game processing device provided by the present application are the same as the beneficial effects of the orbital pursuit and escape game processing method provided in the above-mentioned embodiment, and other technical features in the orbital pursuit and escape game processing device are the same as the features disclosed in the above-mentioned embodiment method, which will not be repeated here.

[0161] The present application provides a track pursuit and escape game processing device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the track pursuit and escape game processing method in the above-mentioned embodiment one.

[0162] Reference below Fig.11 , which shows a schematic diagram of the structure of a track pursuit and escape game processing device suitable for implementing the embodiment of the present application. The track pursuit and escape game processing device in the embodiment of the present application may include but is not limited to mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Descriptions), PMPs (Portable Media Players), vehicle-mounted terminals (such as vehicle-mounted navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. Fig.11 The track pursuit and escape game processing device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present application.

[0163] like Fig.11As shown, the track pursuit game processing device may include a processing device 1001 (such as a central processing unit, a graphics processor, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM: Read Only Memory) 1002 or a program loaded from a storage device 1003 to a random access memory (RAM: Random Access Memory) 1004. In RAM1004, various programs and data required for the operation of the track pursuit game processing device are also stored. The processing device 1001, ROM1002 and RAM1004 are connected to each other via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to the I / O interface 1006: input devices 1007 including, for example, a touch screen, a touchpad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; output devices 1008 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; storage devices 1003 including, for example, a magnetic tape, a hard disk, etc.; and communication devices 1009. The communication device 1009 can allow the track pursuit and escape game processing device to communicate wirelessly or wired with other devices to exchange data. Although the track pursuit and escape game processing device with various systems is shown in the figure, it should be understood that it is not required to implement or have all the systems shown. More or fewer systems may be implemented or have alternatively.

[0164] The track pursuit and escape game processing device provided by the present application adopts the track pursuit and escape game processing method of the above embodiment, which improves the calculation accuracy while ensuring the convergence of the algorithm. Compared with the prior art, the beneficial effects of the track pursuit and escape game processing device provided by the present application are the same as the beneficial effects of the track pursuit and escape game processing method provided by the above embodiment, and the other technical features in the track pursuit and escape game processing device are the same as the features disclosed in the method of the previous embodiment, which will not be repeated here.

[0165] It should be understood that the various parts disclosed in this application can be implemented by hardware, software, firmware or a combination thereof. In the description of the above embodiments, specific features, structures, materials or characteristics can be combined in any one or more embodiments or examples in a suitable manner.

[0166] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0167] The present application provides a computer-readable storage medium having computer-readable program instructions (i.e., computer programs) stored thereon, and the computer-readable program instructions are used to execute the track pursuit and escape game processing method in the above-mentioned embodiment.

[0168] The computer-readable storage medium provided in the present application may be, for example, a USB flash drive, but is not limited to electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, systems or devices, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM: Random Access Memory), a read-only memory (ROM: Read Only Memory), an erasable programmable read-only memory (EPROM: Erasable Programmable Read Only Memory or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM: CD-ReadOnlyMemory), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, system or device. The program code contained on the computer-readable storage medium may be transmitted using any appropriate medium, including but not limited to: wires, optical cables, RF (Radio Frequency: Radio Frequency), etc., or any suitable combination of the above.

[0169] The above-mentioned computer-readable storage medium may be included in the track pursuit and escape game processing device; or it may exist independently without being assembled into the track pursuit and escape game processing device.

[0170] The above-mentioned computer-readable storage medium carries one or more programs. When the above-mentioned one or more programs are executed by the orbital pursuit and escape game processing device, the orbital pursuit and escape game processing device: processes the unilateral optimal interception problem based on the pseudo-spectral method to obtain the tracking unilateral initial costate quantity, and the unilateral optimal interception problem is obtained based on the deconstruction of the bilateral pursuit and escape game problem; uses the tracking unilateral initial costate quantity as a guess value, calculates the bilateral pursuit and escape game problem through a preset optimization algorithm, and obtains the bilateral pursuit and escape optimal result.

[0171] Computer program code for performing the operations of the present application may be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0172] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present application. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0173] The modules involved in the embodiments described in this application may be implemented by software or hardware, wherein the name of the module does not constitute a limitation on the unit itself in some cases.

[0174] The readable storage medium provided in this application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., computer programs) for executing the above-mentioned track pursuit and escape game processing method, and can improve the calculation accuracy while ensuring the convergence of the algorithm when calculating the bilateral track pursuit and escape game problem. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as the beneficial effects of the track pursuit and escape game processing method provided in the above-mentioned embodiment, and will not be repeated here.

[0175] The above descriptions are only some embodiments of the present application, and are not intended to limit the patent scope of the present application. All equivalent structural changes made using the contents of the present application specification and drawings under the technical concept of the present application, or direct / indirect applications in other related technical fields are included in the patent protection scope of the present application.

Claims

1. A method for processing a track pursuit game, characterized in that: The track pursuit and escape game processing method includes: Based on the pseudo-spectral method, the unilateral optimal interception problem is processed to obtain the tracking unilateral initial co-state quantity, and the unilateral optimal interception problem is obtained based on the deconstruction of the bilateral pursuit and escape game problem; The tracking unilateral initial co-state quantity is used as a guess value, and the bilateral pursuit and escape game problem is calculated through a preset optimization algorithm to obtain the bilateral pursuit and escape optimal result.

2. The method according to claim 1, characterized in that The step of processing the unilateral optimal interception problem based on the pseudo-spectral method to obtain the tracking unilateral initial co-state quantity includes: The optimal interception time is obtained by using the pseudo-spectral method of collocation construction that complies with the co-state mapping theorem to solve the unilateral optimal interception problem. Based on the optimal interception time, a co-state mapping equation is constructed through a Lagrange multiplier of nonlinear programming to obtain a tracking unilateral terminal co-state quantity; The escaped unilateral terminal co-state quantity is obtained according to the tracked unilateral terminal co-state quantity, and the tracked unilateral initial co-state quantity is obtained based on the tracked unilateral terminal co-state quantity and the escaped unilateral terminal co-state quantity.

3. The method according to claim 2, characterized in that The step of obtaining the escaped unilateral terminal co-state quantity according to the tracked unilateral terminal co-state quantity, and obtaining the tracked unilateral initial co-state quantity based on the tracked unilateral terminal co-state quantity and the escaped unilateral terminal co-state quantity comprises: Based on the co-state boundary value of the bilateral pursuit-escape game problem and the tracking unilateral terminal co-state, the escaping unilateral terminal co-state is obtained; According to the tracking unilateral terminal costate quantity and the escaping unilateral terminal costate quantity, the preset trajectory dynamics model and the preset costate equation are reversely integrated to obtain the tracking unilateral initial costate quantity and the escaping unilateral initial costate quantity.

4. The method according to claim 3, characterized in that Before the step of obtaining the escaping unilateral terminal co-state quantity based on the co-state quantity boundary value of the bilateral pursuit-escape game problem and the tracking unilateral terminal co-state quantity, the step further includes: Based on the relative distance between the two terminals and the preset co-state equation, the boundary value of the co-state quantity of the bilateral pursuit and escape game problem is obtained.

5. The method according to claim 4, characterized in that The step of using the tracking unilateral initial co-state quantity as a guess value and calculating the bilateral pursuit and escape game problem through a preset optimization algorithm to obtain the bilateral pursuit and escape optimal result includes: Based on the bilateral pursuit-escape game problem and the preset constraints, a local optimization problem is constructed with the tracking unilateral initial co-state quantity and the escape unilateral initial co-state quantity as guess values; The local optimization problem is calculated by a preset optimization algorithm to obtain a bilateral optimal result of pursuit and escape, and the bilateral optimal result of pursuit and escape includes a bilateral optimal control rate and an optimal trajectory of pursuit and escape.

6. The method according to claim 5, characterized in that The step of calculating the local optimization problem by using a preset optimization algorithm to obtain the optimal result of the pursuit and escape bilateral relationship includes: Based on the trajectory dynamics model, the preset co-state equation and the guessed value, the local optimization problem is calculated by a preset sequential quadratic programming algorithm to obtain an optimal estimate; According to the preset unilateral initial state quantity of tracking, the unilateral initial state quantity of escaping and the optimal estimated value, the trajectory dynamics model and the co-state equation are forward integrated to obtain the optimal result of bilateral pursuit and escape.

7. The method according to claim 6, characterized in that The step of calculating the local optimization problem based on the trajectory dynamics model, the preset co-state equation and the guessed value by using a preset sequential quadratic programming algorithm to obtain the optimal estimated value includes: Based on the trajectory dynamics model, the preset co-state equation, the cost function and the guessed value, the preset sequential quadratic programming algorithm is used to optimize the bilateral initial co-state quantity of the pursuit and escape game problem and the terminal game time to obtain the optimal estimated value.

8. A track pursuit and escape game processing device, characterized in that: The track pursuit and escape game processing device comprises: A tracking unilateral initial co-state quantity calculation module is used to process the unilateral optimal interception problem based on the pseudo-spectral method to obtain the tracking unilateral initial co-state quantity. The unilateral optimal interception problem is obtained based on the deconstruction of the bilateral pursuit and escape game problem. The bilateral pursuit and escape game problem calculation module is used to use the tracking unilateral initial co-state quantity as a guess value, calculate the bilateral pursuit and escape game problem through a preset optimization algorithm, and obtain the bilateral pursuit and escape optimal result.

9. A track pursuit and escape game processing device, characterized in that: The device comprises: a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the computer program is configured to implement the steps of the track pursuit and escape game processing method as claimed in any one of claims 1 to 7.

10. A storage medium, characterized in that: The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, the steps of the track pursuit and escape game processing method as described in any one of claims 1 to 7 are implemented.

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