CN-120030793-B - Real-time solving method for spacecraft orbit chase escaping game

CN120030793BCN 120030793 BCN120030793 BCN 120030793BCN-120030793-B

Abstract

A real-time solving method for a spacecraft orbit chase-escaping game relates to the field of real-time solving of spacecraft orbit chase-escaping games. The problem that the saddle point solution based on the maximum principle of the existing spacecraft escape game needs to solve the boundary value problem, the demand of on-orbit application is difficult to meet by a heuristic method or a nonlinear programming method, and the problem of the biggest obstruction of the on-orbit application of the game theory is caused no matter the calculation time or the guarantee of convergence. The method comprises the steps of solving an equivalent unilateral minimum time optimal control equation by utilizing the separation property of a Hamiltonian and a linear common mode equation, fitting a polynomial to obtain a transformation matrix by adopting a least square method based on the unilateral minimum time optimal control equation, determining an analysis boundary by utilizing a dynamic ellipsoid, wherein the terminal time is the boundary of a reaching set, solving the zero point of f (t f ) to obtain the optimal game time and the optimal game strategy based on the terminal geometric condition, and realizing the online solving of the spacecraft chase game.

Inventors

YE DONG
JIA ZHEN
TANG XU
XIAO YAN
TANG SHENGYONG
ZHANG GANG
SUN ZHAOWEI

Assignees

哈尔滨工业大学

Dates

Publication Date: 20260508
Application Date: 20250224

Claims (6)

1. The real-time solving method for the spacecraft orbit chase escaping game is characterized by comprising the following steps of: Step 1, solving an equivalent unilateral minimum time optimal control equation by utilizing the separation property of a Hamiltonian and a linear common-mode equation; Step 2, fitting a polynomial to obtain a transformation matrix by using a least square method based on the unilateral minimum time optimal control equation in the step 1 Determining an analysis boundary by using a dynamic ellipsoid, wherein the terminal time is the boundary of a reaching set, and solving a judgment equation based on the terminal geometric condition Obtaining optimal game time and an optimal game strategy, namely realizing online solving of the spacecraft chase escaping game; The method for confirming the single-side minimum time in the step 1 comprises the following steps: wherein tf is the game end time, R is a positive real number set, rp and re are the tracking spacecraft position and the escape spacecraft position vector respectively; the unilateral minimum time optimal control equation in the step1 is as follows: Wherein, the H is a double-sided Hamiltonian, u p is tracking spacecraft optimal control, u e is escape spacecraft optimal control, In order to track the spacecraft velocity cooperative variables, In order to escape from the spacecraft velocity cooperative variables, Is a Lagrangian multiplier; The method for determining the analysis boundary by using the dynamic ellipsoids in the step2 comprises the following steps: the main axis of the dynamic ellipsoid is obtained by calculating the scaling factor, and the calculation method comprises the following steps: Wherein, the Is the order of the polynomial, Is a pending polynomial coefficient; in step 2, a polynomial is fitted by a least square method based on the unilateral minimum time optimal control equation in step 1 to obtain a transformation matrix The method of (1) is as follows: Wherein, the V is a feature vector corresponding to orthogonal decomposition; , wherein, rzir and rzsr are zero input position vector and zero state position vector respectively; Judgment equation The method comprises the following steps: 。
2. The method for solving the spacecraft orbit chase flight game in real time according to claim 1, wherein the step 2 further comprises the step of decomposing the terminal time into control input responses for reaching the boundary of the set.
3. The real-time solving method of the spacecraft orbit chase flight game according to claim 2, wherein the method for decomposing the boundary of the arrival set with the terminal time to obtain the control input response is as follows: Wherein, the 、 The CW equation state transition matrices, respectively.
4. A method of real-time solving for a spacecraft orbit chase flight game according to claim 3, wherein the zero state response Centrally symmetric about the origin, i.e. , Wherein the method comprises the steps of N is the track angular velocity.
5. An electronic device includes a memory, a processor, and a memory controller stored in the memory and executable on the processor A computer program running, characterized in that the processor implements the steps of the method according to any one of claims 1 to 4 when said computer program is executed.
6. A computer readable storage medium storing a computer program, characterized in that the computer program when executed by a processor implements the steps of the method according to any one of claims 1 to 4.

Description

Real-time solving method for spacecraft orbit chase escaping game Technical Field The invention relates to the technical field of real-time solving of spacecraft orbit chase escaping games, in particular to a real-time solving method of spacecraft orbit chase escaping games. Background Current space development and use is leading to increased congestion, track fragmentation, and risk of collisions and misinterpretations, and more space activities make "grey zones" appear. In this changing orbit environment, it is necessary to re-evaluate the viability and coping level of the spacecraft. Equilibrium solution computation is the core problem of game problems, which involves decisions in the policy space of both game parties. Nash equilibrium is the fundamental theory of game problems, and it studies how to calculate the optimal strategies for both parties in a multi-player dynamic game, i.e., the optimal benefits and optimal action strategies for both parties. In general, if an equilibrium solution to a gaming problem is available, this means that the gaming problem is solved, i.e. we know all knowledge about the gaming problem. The nature of the equalization solution ensures that the equalization strategy is the optimal strategy for the player in the face of the most clever and most rational opponents. However, from the standpoint of computational complexity, the game problem is an NP-hard problem, i.e., it cannot be solved in polynomial time. Thus, there is currently no general method to fully address the equalization solution computation. The calculation and searching of the equilibrium solution are the core and key of game problem research and are the basis of all strategy analysis. The spacecraft chase game is usually modeled as two-person zero-sum game of terminal free time, but the saddle point solution based on the maximum principle needs to solve the edge problem, and the current heuristic method or nonlinear programming method is difficult to meet the requirement of on-orbit application, and becomes the biggest obstacle for on-orbit application of the game theory no matter the calculation time or the convergence is ensured. Disclosure of Invention The method aims to solve the problem that in the prior art, saddle point solution of a spacecraft chase-and-escape game based on a maximum principle is required to solve the edge value, the current heuristic method or nonlinear programming method is difficult to meet the requirement of on-orbit application, and the problem of the biggest obstruction of on-orbit application of the game theory is caused no matter calculation time or convergence guarantee. The invention is realized by the following technical scheme for solving the technical problems: The invention provides a real-time solving method of a spacecraft orbit chase escaping game, which comprises the following steps: Step 1, solving an equivalent unilateral minimum time optimal control equation by utilizing the separation property of a Hamiltonian and a linear common-mode equation; Step 2, fitting a polynomial to obtain a transformation matrix by using a least square method based on the unilateral minimum time optimal control equation in the step 1 And determining an analysis boundary by using the dynamic ellipsoids, wherein the terminal time is the boundary of the arrival set, and solving the zero point of f (t f) based on the terminal geometric condition to obtain the optimal game time and the optimal game strategy, namely realizing the online solving of the spacecraft chase-and-flee game. Further, a preferred embodiment is provided, wherein the method for determining the single-side minimum time in step 1 is as follows: Wherein t f is game end time, R is positive real number set, and R p,re is tracking spacecraft position and escape spacecraft position vector respectively. Further, a preferred embodiment is provided, wherein the one-sided minimum time optimal control equation in step 1 is: Wherein, the H is a bilateral hamilton function, U p is a tracking spacecraft optimal control, U p is a tracking spacecraft feasible control set ,ue is an escape spacecraft optimal control, U e is an escape spacecraft feasible control set, lambda p,v is a tracking spacecraft speed cooperative variable, and lambda e,v is an escape spacecraft speed cooperative variable. Further, a preferred embodiment is provided, and step 2 further includes a step of decomposing the terminal time to reach the boundary of the set to obtain a control input response. Further, a preferred embodiment is provided, wherein the method for decomposing the terminal time into the boundary of the arrival set to obtain the control input response is as follows: r(t,τ)=rzir(t)+rzsr(t,τ) Wherein Φ 1、Φ2 is the state transition matrix of the CW equation, τ is the Lagrangian multiplier corresponding to the terminal constraint, and r zir、rzsr is the zero input position vector and the zero state position vector, respectively. Further, a preferred e