CN-117508645-B - Radial underactuated spacecraft chase game low-dimensional control method

CN117508645BCN 117508645 BCN117508645 BCN 117508645BCN-117508645-B

Abstract

The invention discloses a method for controlling a radial underactuated spacecraft chase game in low dimension, which comprises the following steps of S1, constructing a 24-dimension two-point boundary value problem and a high-dimension game optimal control strategy of a radial underactuated spacecraft optimal time game based on a differential countermeasure theory, S2, deducing a state condition of the problem of reducing the underactuated high-dimension two-point boundary value into a 12-dimension two-point boundary value, and designing the low-dimension game optimal control strategy. The method demonstrates the feasibility of underactuated chase-escaping game when the radial thrust is lost, deduces a low-dimensional optimal time game control strategy for realizing three-dimensional chase-escaping only through trace direction and normal thrust, expands theoretical analysis and engineering application of the underactuated spacecraft, and can be used for application of interception, on-orbit service, approaching of an out-of-control spacecraft and the like of the underactuated spacecraft.

Inventors

SHAO JIANG
ZHOU QINGRUI
YANG YING
SONG YINGYING
Diao Jingdong
WANG HUI
ZHENG WEI
SUN CHANGHAO

Assignees

中国空间技术研究院

Dates

Publication Date: 20260508
Application Date: 20231124

Claims (2)

1. The radial underactuated spacecraft chase game low-dimensional control method is characterized by comprising the following steps of: S1, constructing a 24-dimensional two-point boundary value problem and a high-dimensional game optimal control strategy of a radial underactuated spacecraft optimal time game based on a differential countermeasure theory; s2, deducing a state condition of the problem of reducing the underactuated high-dimensional two-point boundary value into a 12-dimensional two-point boundary value, and designing a low-dimensional game optimal control strategy; in the step S1, specifically, the method includes: step S11, giving a chase-fleing game scene, namely assuming that a virtual pilot spacecraft flies on a near-ground circular orbit, a radial underactuated tracker and a radial underactuated evasion device are arranged nearby, and constructing a local-vertical-local-horizontal coordinate system by taking the center of mass of the pilot as an origin, wherein a player Or (b) The relative distance and relative velocity to the pilot are expressed as And Wherein, subscript Or (b) Respectively representing a tracker and an escape; The underradial drive dynamics equation of the chase-and-evasion game is expressed as (1) Wherein, the Indicating the under-actuated control acceleration and having , And Respectively represent players Control acceleration in the track and normal directions Representing nonlinear relative orbital dynamics, specifically expressed as Wherein, the Is the dimension argument of the pilot, And The angular velocity and the angular acceleration are respectively, Representing the radius of the track of the pilot, Representing players Or (b) Is used for the track radius of the track, And has , And Respectively represent a navigator and a player Is used for the track angular velocity of the track, Is the gravitational constant of the earth; from linear system theory, it is known that the closed loop system is controllable in the case of underradial driving, and the above formula (1) is linearized (2) In the formula, Representing an initial state of the player, the initial state including a relative position and a relative speed, , In the form of a system matrix, , , Is a control matrix; step S12, based on differential countermeasure theory, the differential game of the radial underactuated tracker and the escape device is constructed as follows (3) Wherein, the The control acceleration of the player P is indicated, Indicating the control acceleration of player E, and having ; In an optimal time differential game, the tracker attempts to minimize the intercept time Capturing the escapement, while the escapement endeavours to extend the maximum interception time The secondary cost function of the underactuated chase-escaping game is constructed as (4) Wherein, the Performance indexes of the secondary differential game are represented; Step S13, solving saddle point strategy pairs, and introducing an underactuated Hamiltonian And under-actuated termination conditions Under-actuated Hamiltonian And under-actuated termination conditions Respectively denoted as (5) (6) Wherein, the Representing the lagrangian multiplier and, For the co-state variables of the tracker, ; As a cooperative variable of the escapement, ; And The position component and the velocity component of the tracker cooperative variable respectively, And The position component and the velocity component of the escape cooperative variable respectively, and satisfy the following relation: (7) saddle point strategy satisfies the accompanying equation And terminal boundary conditions , wherein, Or (b) Then accompanying equation And terminal boundary conditions Represented as (8) (9) According to cross-sectional conditions The following equation is obtained: (10) Wherein, the Indicating the relative speed of the tracker and pilot, Indicating the relative speed of the evacuator and the pilot; The optimal time game strategies for the underradial drive tracker and the escape device are respectively as follows: (11) (12) in the formula, And Representing the maximum acceleration of the tracker and the escapement respectively, Representing player P's high-dimensional optimal time gaming strategy, Representing player E high-dimensional optimal time gaming strategy; Equations (6) to (10) form the problem of 24-dimensional two-point boundary values of two players under the radial underactuated condition, and the underactuated saddle point strategy pairs in equations (11) and (12) are control laws of an underactuated game tracker and an escape device, so that the tracker and the escape device can complete three-dimensional chase-and-escape game under the action of the control laws.
2. The radial under-actuated spacecraft chase gaming low-dimensional control method according to claim 1, characterized in that in said step S2, it specifically comprises: step S21, definition In the event of an error condition, Is a new cooperative variable and And Respectively representing the position and the velocity components of the cooperative variables; Then the differential game model of formula (3) and the accompanying equation of formula (8) are simplified into (13) From the definition of the error state, the initial condition is known to be (14) While the location condition of interception is expressed as (15) Wherein, the Representing the relative distance of the tracker from the pilot, Representing the relative distance of the evacuator from the pilot; the new cooperative variable can be known to satisfy the following formula according to the cross-sectional condition of formula (9) (16) Step S22, according to equation (7), the cooperative variables of the tracker and the escapement in the differential game satisfy the following relation (17) The high-dimensional game strategy shown in equations (11) and (12) can be rewritten to the following low-dimensional form (18) (19) Wherein, the Representing a low-dimensional optimal time gaming strategy for player P, Representing a low-dimensional optimal time gaming strategy for player E; equations (13) to (19) are the problem of the boundary values of the two points of the low-dimensional structure of the chase game of the constructed radial underactuated spacecraft.

Description

Radial underactuated spacecraft chase game low-dimensional control method Technical Field The invention relates to the field of spacecraft chase escaping game, in particular to a radial underactuated spacecraft chase escaping game low-dimensional control method. Background Since the 60 s of the 20 th century, the number of spacecraft and space debris in space has also been increasing rapidly and continuously as space missiles have increased more and more frequently. The spacecraft chase-escaping game receives more and more attention in recent years due to the application prospect of the spacecraft chase-escaping game in the aspects of removing space debris and avoiding or approaching an uncontrolled spacecraft. Different from the unilateral optimization problem of classical non-motorized target spacecraft interception or intersection butt joint, the two sides have benefit conflicts in the escape game problem, namely, the tracking spacecraft try to approach the escape spacecraft and the escape spacecraft try to get rid of the tracking spacecraft. Therefore, this problem is generally regarded as a bilateral optimization problem and studied using differential countermeasure theory. The differential countermeasure theory proposed by Isaacs is a branch of game theory and can be used for analyzing various dynamic game problems such as missile interception, airplane fight, unmanned aerial vehicle cluster flight and the like. Notably, almost all current gaming strategies are designed based on fully driven relative orbital dynamics. In the local-vertical-local-horizontal coordinate system frame, the degree of freedom of the control input is smaller than that of the system controlled variable for under-actuated situations where radial or track thrust is lost. Thus, the fully-driven gaming strategy is not suitable for under-driven situations. According to the linear system theory, the system is controllable when the radial thrust is lost, so that the problem that the under-actuated spacecraft chase-escaping game is needed to be solved still exists is that firstly, a unilateral optimal feedback strategy of the intersection or formation flying behavior of the under-actuated spacecraft is solved through an optimal control method, and the under-actuated chase-escaping game belongs to the problem of bilateral optimization. Second, unlike full-drive chase-and-flee games, the lack of radial thrust may impose kinetic limitations on the player's flight trajectory. Then, how to construct the high-dimensional two-point boundary value problem by the differential countermeasure theory and give a high-dimensional under-actuated saddle point strategy is also a research key point. Finally, deriving the state of reducing the high-dimensional game problem into a low-dimensional problem and giving a low-dimensional game strategy to drive the tracker and the evade device to realize the three-dimensional chase game is also a great difficulty. Disclosure of Invention In order to solve the technical problems in the prior art, the invention aims to provide a radial underactuated spacecraft chase game low-dimensional control method, which is used for deducing an underactuated game strategy under optimal time through a differential countermeasure theory to construct a 24-dimensional two-point boundary value problem, deducing a 12-dimensional low-dimensional two-point boundary value problem by reducing the dimension of a high-dimensional two-point boundary value problem and obtaining a low-dimensional game strategy, so that a tracker and an evacuator complete three-dimensional zero-chase game under the action of trace direction and normal thrust. In order to achieve the aim of the invention, the invention provides a radial underactuated spacecraft chase game low-dimensional control method, which comprises the following steps: S1, constructing a 24-dimensional two-point boundary value problem and a high-dimensional game optimal control strategy of a radial underactuated spacecraft optimal time game based on a differential countermeasure theory; and S2, deducing a state condition of the problem of reducing the underactuated high-dimensional two-point boundary value into a 12-dimensional two-point boundary value, and designing a low-dimensional game optimal control strategy. According to one aspect of the present invention, in the step S1, the method specifically includes: Step S11, giving a chase-flee game scene, wherein a virtual pilot spacecraft flies on a near-ground circular orbit, a radial underactuated tracker and a radial underactuated evasion device are arranged nearby, and a local-vertical-local-horizontal coordinate system is constructed by taking the center of mass of the pilot as an origin, so that a player Or (b)The relative distance and relative velocity to the pilot are expressed asAndWherein, subscriptOr (b)Respectively representing a tracker and an escape; The underradial drive dynamics equation of the chase-and-evasion game is e