A method for main-companion cooperative evasion control of a spacecraft under the escort of a companion star

Abstract

The present application relates to a kind of main satellite of star companion under the spacecraft main satellite cooperative evasion control method, it is applied to the non-cooperative target such as space debris, malfunction spacecraft when facing unknown intention approach, task spacecraft is cooperated with star companion in the vicinity of orbit and carries out evasion in one pursuit one escape one guard scene.First, the dynamic model of relative motion state including non-cooperative target, guard satellite and task spacecraft is established;Then, the cost function of both sides of differential game is constructed using the idea of differential game;After that, the Hamilton-Jacobi method is used to solve Riccati equation, and the full-state linear feedback control solution of task spacecraft and satellite is obtained.The present application can avoid non-cooperative target approaching important on-orbit task spacecraft as much as possible, and assist task spacecraft to evade the potential threat of direct collision from the target through the active shielding of satellite, which is consistent with the engineering practice.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of main and escorting satellite cooperative evasion control method under satellite escort, especially when there is a satellite for escort in the vicinity of mission spacecraft, face the unknown approach of non-cooperative target such as space debris, malfunction spacecraft, it is applied to the scene of pursuit and evasion game between mission spacecraft and non-cooperative target under the participation of escort satellite.The non-cooperative target approaches, design is blocked using escort satellite, position is in the midpoint or nearby of the line connecting mission spacecraft and non-cooperative target, avoid the orbit maneuver control method that non-cooperative target directly impacts mission spacecraft due to the non-timely evasion of mission spacecraft, belongs to the field of spacecraft orbit control. BACKGROUND

[0002] In the development process of space technology, the number of satellites in orbit increases with each passing day, at the same time, a large number of space debris, malfunction spacecraft also come one after another, and spacecraft for space on-orbit service will be threatened by multiple potential collisions, which may be the collision of space debris and mission spacecraft, the approach of some cooperative or non-cooperative spacecraft to mission spacecraft in active or out-of-control state, etc. To cope with such potential space threats, especially when the mission spacecraft has a satellite escort, the safety of the main mission spacecraft can be fully protected by the satellite. Both the mission spacecraft and the escort satellite need to adopt certain control strategies to reduce the collision threat of non-cooperative targets by actively adjusting the orbit of the two satellites to reduce the collision threat of non-cooperative targets, i.e. main and escorting satellite cooperative evasion control under satellite escort.

[0003] Research on spacecraft pursuit and evasion game mainly focuses on the development of autonomous approach technology for non-cooperative targets. The research ideas can be roughly divided into two methods: one is a unilateral optimal control method based on robust control theory, and the other is a bilateral optimal control method based on differential game theory.

[0004] The unilateral optimal control method based on robust control theory has certain applicability to the approach control problem of space debris and malfunction spacecraft. However, when establishing the control system, this method is difficult to accurately reflect the antagonism between non-cooperative targets and mission spacecraft, and only solves the approach control problem of non-cooperative targets to mission spacecraft.

[0005] In contrast, the bilateral optimal control method based on differential game theory can obtain the saddle point solution of non-cooperative targets and mission spacecraft under a certain specific countermeasure. The control strategy provided by this saddle point solution is more reasonable and feasible, and can be used as the control strategy for mission spacecraft safety evasion.

[0006] Differential game theory is a mathematical model and theoretical method for dynamic reality containing cooperative and antagonistic elements. It uses differential equations to describe the dynamic process of two or more parties in a game. In the plane, Anderson studied the pursuit-evasion problem of two spacecraft, which used maximum thrust. First, the standard solution was obtained by solving the two-point boundary value problem, and then the Riccati equation was integrated in reverse. By differentiating the current state from the ideal state, the updated value of the conjugate state was obtained. Liu Jianfeng et al. studied the anti-collision problem of formation satellites based on the boundary layer theory of qualitative differential game, and obtained the collision and non-collision areas of satellite formation. Zhang Qiuhua et al. also studied the pursuit-evasion problem of two spacecraft in the near-earth coplanar circular orbit based on the boundary layer theory of qualitative differential game. They studied the problem of constructing a nonlinear boundary layer and solving a linear boundary layer for two spacecraft in the pursuit-evasion problem in the coordinate system, and obtained the optimal control of two spacecraft in the boundary layer. In the literature, the fixed dwell period differential game problem in the pursuit-evasion of two spacecraft was studied. The method of combining genetic algorithm with multiple shooting method was used to obtain the numerical solution of open-loop optimal control.

[0007] However, the application of existing differential game theory in the field of aerospace is mostly used in the field of space rendezvous and docking to solve the problem of how to quickly approach the docking spacecraft. There are few studies on the control problem of spacecraft actively avoiding non-cooperative targets such as space debris based on differential game theory. This research field is aimed at on-orbit safety, and there are few published achievements at home and abroad, and it is relatively limited. In particular, the study of mission spacecraft and escort satellite cooperative avoidance control in the presence of escort satellite scenarios.

SUMMARY

[0008] The purpose of the present application is to solve the space application scenario of approaching task spacecraft to non-cooperative target (faulty spacecraft or space debris), the task spacecraft needs to be controlled, to avoid the potential threat of non-cooperative target approaching for unknown reasons, to avoid space collision and other safety accidents, at the same time, the task spacecraft relies on the escort advantage of the satellite, uses this game maneuver control method to make reasonable maneuver, avoids the possibility of non-cooperative target directly impacting the task spacecraft, as far as possible to improve the fuel consumption required by the non-cooperative target approaching the task spacecraft, increases the time cost of its approach, so as to avoid the threat of the task spacecraft from the non-cooperative target as far as possible, avoid collision accidents with non-cooperative target, and improve the safety factor of the task spacecraft. In such a scenario, the defense spacecraft cooperates with the escape action of the task spacecraft, and in this case, the game relationship between the three is essentially a new two-party confrontation spacecraft pursuit and escape differential game problem. This method proposes an evasive strategy for the task spacecraft under the escort of the satellite, in the process of the non-cooperative target approaching, the satellite keeps its relative position on the line connecting the task spacecraft and the non-cooperative target through orbit maneuver control, and transfers the collision and other safety threats from the non-cooperative target to the satellite, and through continuous maneuver, the task spacecraft and the satellite jointly avoid the approach of the non-cooperative target.

[0009] In view of the above problems, the technical scheme of the present application is as follows: first, only the relative orbit motion of the non-cooperative target, the escort satellite and the task spacecraft is considered, a dynamic model containing the relative motion state of the escort satellite, the non-cooperative target and the task spacecraft is established, that is, the C-W equation; then the idea of differential game is used to construct the cost function of the two parties of the game; finally, the Hamilton-Jacobi method is used to solve the Riccati equation, and the full-state linear feedback control solution of the task spacecraft is obtained.

[0010] Taking the scenario that a non-cooperative target approaches a task spacecraft while a protective satellite cooperates to protect the task spacecraft as an example, the specific operation steps are as follows:

[0011] Step 1: apply the present application based on the following assumptions

[0012] In order to obtain an accurate dynamic model under this scenario and solve the expression of the maneuver control law, the following assumptions 1-4 must be made:

[0013] Assumption 1: Since the time of non-cooperative target approaching and the maneuvering avoidance of the task spacecraft is very short compared with the orbit period, the influence of orbit perturbation force is ignored, and the orbit motion of the non-cooperative target, the protective satellite and the task spacecraft is simplified as a two-body problem;

[0014] Assumption 2: The reference orbits of the relative motion of the non-cooperative target, the escort satellite and the mission spacecraft are all circular orbits, and the second-order small quantity is ignored when the relative orbit motion equation, i.e., the C-W equation, is established;

[0015] Assumption 3: The radius of the reference orbit is much larger than the range of the orbit maneuver of the spacecraft;

[0016] Assumption 4: The non-cooperative target, the escort satellite and the mission spacecraft adopt finite continuous thrust for orbit maneuver control, and the influence of the orbit perturbation force can be ignored;

[0017] Step 2: A dynamic model containing the relative motion states of the non-cooperative target, the escort satellite and the mission spacecraft is established; specifically including the following steps:

[0018] Step 2.1: Define the coordinate system

[0019] The object of the present application is a spacecraft in the geocentric orbit coordinate system;

[0020] a. Geocentric equatorial inertial coordinate system f i (O i x i y i z i )

[0021] The origin of the geocentric equatorial inertial coordinate system is fixed at the center of the Earth O i , the O i x i axis is in the equatorial plane and points to the vernal equinox, the O i y i axis is in the equatorial plane and is perpendicular to the O i x i axis and points to the east, and the O i z i axis forms a right-handed orthogonal coordinate system with the O i x i and O i y i axes;

[0022] b. Reference spacecraft orbit coordinate system f o (O o x o y o z o )

[0023] The reference spacecraft O is defined as the position of the mass center of the mission spacecraft E at the initial time, and the origin of the reference spacecraft orbit coordinate system is fixed at the mass center O o of the spacecraft, the O o x o axis points to the mass center of the spacecraft O in the direction of the geocenter; and the O o y oThe axis is perpendicular to the velocity direction of the reference spacecraft in the orbital plane; O o x o The axis is perpendicular to the velocity direction of the reference spacecraft in the orbital plane; O o z o The axis is perpendicular to the velocity direction of the reference spacecraft in the orbital plane; O o x o , O o y o The axis is perpendicular to the velocity direction of the reference spacecraft in the orbital plane; O

[0024] Step 2.2: Establish a spacecraft game relative position relationship of one pursuit, one escape and one escort

[0025] For the mission spacecraft E, in addition to the expectation of maintaining the relative distance with the non-cooperative target spacecraft P in the game, the companion star D can also actively block the line of sight of the non-cooperative target spacecraft P using its own volume, that is, the companion star D can be on the straight line of PE during the approaching process.

[0026] The relative position relationship of the mission spacecraft E, the companion star D and the non-cooperative target P is as follows:

[0027] η(r D -r P )=(r E -r P ) (1)

[0028] Wherein, r E represents the position vector of the mission spacecraft E in the geocentric equatorial inertial coordinate system; r D represents the position vector of the companion star D in the geocentric equatorial inertial coordinate system; r P represents the position vector of the non-cooperative target P in the geocentric equatorial inertial coordinate system; η represents the coefficient for determining the relative distance between the mission spacecraft E, the companion star D and the non-cooperative target P.

[0029] Step 2.3: Establish a dynamic model containing the relative motion state of the non-cooperative target, the companion star and the mission spacecraft

[0030] Based on assumptions 1-4, the C-W equation of the mission spacecraft E, the companion star D and the non-cooperative target P is established:

[0031]

[0032]

[0033]

[0034] Wherein, n represents the orbital angular velocity of the circular orbit where the mission spacecraft, the companion star or the non-cooperative target is located; represents the velocity and acceleration of the mission spacecraft E; Velocity and acceleration of the chaser spacecraft C expressed in the chaser spacecraft C's reference frame; Velocity and acceleration of the non-cooperative target P expressed in the chaser spacecraft C's reference frame; E Velocity and acceleration of the non-cooperative target P expressed in the chaser spacecraft C's reference frame; D Velocity and acceleration of the non-cooperative target P expressed in the chaser spacecraft C's reference frame; P Orbital control quantities of the mission spacecraft E, the chaser spacecraft D and the non-cooperative target P expressed in the chaser spacecraft C's reference frame (if it is a space debris, there is no active orbital control quantity, and it is regarded as a zero vector).

[0035] The state space variables of the chaser spacecraft C, the non-cooperative target P and the chaser spacecraft D relative to the reference satellite S in the reference satellite S's reference frame can be expressed as

[0036]

[0037]

[0038]

[0039] Wherein, the state space variables are expressed as

[0040]

[0041]

[0042]

[0043] The system matrix A and the control matrix B are as follows

[0044]

[0045]

[0046] Considering the relative motion position relationship constraints in the mission requirements, the state space vector of the control system is defined

[0047]

[0048] In combination with equations (5)-(13), the state space vector is defined as

[0049]

[0050] Let

[0051]

[0052]

[0053] Equation (13) can be simplified as

[0054]

[0055] Step 3: Control law design of the mission spacecraft and the chaser spacecraft

[0056] Step 3.1: Construct the system cost function for the mission spacecraft and its escort satellite.

[0057] Based on the control requirements of the non-cooperative objective P, the mission spacecraft E, and the escort spacecraft D, the cost function is constructed using the concept of differential games:

[0058]

[0059] Where t0 represents the initial moment when the mission spacecraft and its escort satellite begin their evasive maneuvers, t f This indicates the moment when the game-playing confrontation ends; the cost corresponding to the spacecraft's state at a certain moment is represented as... Q in the formula b R E R D R P For adjustable control parameters; for the mission spacecraft and its escort satellite system, the expected cost function J(x) is... b ,u E ,u D ,u P It reaches a local minimum value;

[0060] Step 3.2: Construct the Hamiltonian function

[0061] Constructing the Hamiltonian function for a linear control system:

[0062] H(t,x b ,u E ,u D ,u P ,λ)=h(x b ,u E ,u D ,u P )+λ T ·f(t,x b ,u E ,u D ,u P (19)

[0063] Wherein, the costate variable is represented by λ; the function f(t,x) b ,u E ,u D ,u P ) is represented as f(t,x) b ,u E ,u D ,u P )=Ax E2 +B E u E +Bu D +BP u P ;

[0064] According to the extreme condition of the system, the following can be obtained:

[0065]

[0066] The solution of the control system when taking extreme value can be obtained from formula (20):

[0067]

[0068] The cost function J can be finally formed into the form of a quadratic form about x b :

[0069]

[0070] Wherein, P(t) is constant in the countermeasure time, and the coordination state variable takes the value

[0071] Step 3.3: solving the evasion control law of the task spacecraft and the cooperative escort control law of the escort satellite

[0072] The solution of the final Hamilton-Jacobi equation can be converted into the solution of the Riccati differential equation in the following form:

[0073]

[0074] The solved P is substituted into λ, and finally, the linear full-state feedback evasion control solution of the task spacecraft E and the cooperative escort control law of the escort satellite D can be obtained:

[0075]

[0076]

[0077] The spacecraft main-satellite cooperative evasion control method under the escort of the satellite has the advantages and effects that:

[0078] 1) In the scene that the non-cooperative target such as space debris and faulty spacecraft approaches the task spacecraft, by giving the relative position relationship constraints of the non-cooperative target, the escort satellite and the task spacecraft, the dynamic equation described by the system state space is established, the cost function of the countermeasures parties is constructed by using the differential countermeasure game theory, the Riccati equation is solved by using the Hamilton-Jacobi method, the evasion control law of the task spacecraft and the cooperative escort control law of the satellite are obtained, and the shielding of the escort satellite is used to make the task spacecraft not have the possibility of collision with the non-cooperative target.

[0079] 2) The application can effectively deal with non-cooperative targets without the ability of maneuvering control, and the task spacecraft can also complete the threat avoidance when the control law of the non-cooperative target takes the initiative to approach, and the guard satellite will always keep its position in the middle of the task spacecraft and the non-cooperative target, thus preventing the non-cooperative target from colliding with the task spacecraft directly, so the application is more suitable for engineering practice.

[0080] 3) The application is suitable for the space application scenario of the non-cooperative target approaching the task spacecraft, and the application requires the task spacecraft to be equipped with a guard satellite near the orbit, which has a wide application prospect in space safety application, can avoid potential threats such as direct collision of the task spacecraft with the space debris in orbit, active approach of the non-cooperative spacecraft, and impact of the faulty spacecraft, and can sacrifice the guard satellite to protect the safety of the important in-orbit task spacecraft, thus meeting the requirements of engineering practice and being suitable for engineering application. BRIEF DESCRIPTION OF DRAWINGS

[0081] Fig. 1 Schematic diagram for the non-cooperative target approaching the task spacecraft.

[0082] Fig. 2 Schematic diagram of the relative positions of the task spacecraft, the guard satellite, and the non-cooperative target. DETAILED DESCRIPTION

[0083] The following will be described in conjunction with the accompanying drawings Figs. 1-2 The following will be described in conjunction with the accompanying drawings

[0084] First, the initial conditions and related simulation parameters of the non-cooperative target, the guard satellite, and the task spacecraft are as follows:

[0085]

[0086] The following will be described in conjunction with the accompanying drawings

[0087] 1. The application is based on the following assumptions.

[0088] The assumptions are made according to step 1.

[0089] 2. A dynamic model including the relative motion states of the non-cooperative target, the guard satellite, and the task spacecraft is established.

[0090] 2.1 Define the coordinate system: define the related coordinate system according to step 2.1.

[0091] 2.2 Establishing the relative position relationship of the pursuer- evader- guardian spacecraft game

[0092] According to the aforementioned step 2.2, the relative position relationship of the non-cooperative target, the guardian satellite and the mission spacecraft is established, and the coefficient η = 1.2 is set.

[0093] 2.3 Establishing a dynamic model containing the relative motion state of the non-cooperative target, the satellite and the mission spacecraft

[0094] According to the aforementioned step 2.3, the dynamic model containing the relative motion state of the non-cooperative target, the satellite and the mission spacecraft is established.

[0095] 3. Control law design of the mission spacecraft and the guardian satellite

[0096] 3.1 Constructing the system cost function of the mission spacecraft and the guardian satellite

[0097] According to the aforementioned step 3.1, the cost function of the mission spacecraft and the guardian satellite is constructed:

[0098]

[0099] Where t0 represents the initial time when the mission spacecraft and the guardian satellite start to avoid the maneuver, and t f represents the time when the game confrontation ends; the cost corresponding to the state of the spacecraft at a certain time is represented as

[0100] In order to ensure the existence of the solution of the Riccati equation, the construction method of the weight coefficient matrix is as follows: Q b is a 6x6 diagonal matrix, and the first three parameters on the diagonal line represent the weight of the position of the spacecraft in the cost function b The weight in the cost function J, the last three parameters on the diagonal line represent the weight of the velocity of the spacecraft in the cost function The weight in the cost function, so we can set Where I3 is a 3x3 unit matrix; R E , R D , R P are 3x3 diagonal matrices, respectively representing the weight of the acceleration of the spacecraft corresponding to the subscript in the cost function, so we set R E = q e ·I3, R D = q d ·I3, R P = q p ·I3.

[0101] The case values are:

[0102]

[0103] 3.2 Constructing the Hamiltonian function

[0104] Construct the Hamiltonian function according to the aforementioned step 3.2.

[0105] 3.3 Evasive control law of the mission spacecraft and cooperative escort control law of the escort satellite

[0106] Calculate the evasive control law of the mission spacecraft and the cooperative escort control law of the escort satellite according to the aforementioned step 3.3.

[0107] In summary, the present application adopts the orbit maneuver control scheme based on differential game, in which the non-cooperative target adopts the control law corresponding to the saddle point solution in the same scene, the mission spacecraft adopts the evasive control law formula (24) in an analytical form, and the satellite adopts the cooperative escort control law formula (25) in an analytical form, which can assist the mission spacecraft to evade the direct collision with the non-cooperative target.

[0108] The spacecraft main-satellite cooperative evasion control method under satellite escort introduced in the present application is characterized in that: in the space application scenario in which a non-cooperative target approaches a mission spacecraft, the mission spacecraft needs to evade under the cooperative escort of a satellite, and reasonable maneuver is performed by using the control method to as far as possible increase the fuel consumption of the non-cooperative target impacting the mission spacecraft, increase the pursuit time, and block the line of sight of the non-cooperative target by using the escort satellite. The method proposes a cooperative evasion strategy of the mission spacecraft and the escort satellite, so that the non-cooperative target, the escort satellite and the mission spacecraft are as far as possible kept on a straight line during the pursuit, so that the escort satellite can block the non-cooperative target from approaching by sacrificing itself to protect the important mission spacecraft. Taking a scenario in which a non-cooperative target approaches a mission spacecraft and a satellite provides escort as an example, first, a dynamic model of the relative motion state of one pursuit, one evasion and one escort is established; then, the idea of differential game is used to construct the cost function of the mission spacecraft and the satellite; thereafter, the Hamilton-Jacobi method is adopted to solve the Riccati equation to obtain the full-state linear feedback control solution of the mission spacecraft and the satellite. The method has not been researched in the field of spacecraft pursuit-evasion game, and has high practicability in real space missions, can as far as possible avoid other non-cooperative targets from approaching the on-orbit mission spacecraft, and evade the potential threat of impacting the mission spacecraft by cooperative protection of the satellite, thereby providing strong protection for the safety of important spacecraft.

Claims

1. A method for main satellite and companion satellite cooperative evasion control under the escort of a companion star, characterized in that, Comprising the following steps: Step 1: Set the following conditions: Condition 1: Simplify the orbital motion of the non-cooperative target, the escort satellite and the mission spacecraft into a two-body problem; Condition 2: The reference orbits of the relative motion of the non-cooperative target, the escort satellite and the mission spacecraft are all circular orbits, and when establishing the relative orbital motion equation, i.e. the C-W equation, the second-order small quantity is ignored; Condition 3: The radius of the reference orbit is much larger than the range of the spacecraft orbital maneuver; Condition 4: The non-cooperative target, the escort satellite and the mission spacecraft use finite continuous thrust for orbital maneuver control, and the influence of the perturbation force is ignored; Step 2: Establish a dynamic model containing the relative motion state of the non-cooperative target, the escort satellite and the mission spacecraft, specifically including: coordinate system definition; Establish the relative position relationship of the spacecraft game of one pursuit, one escape and one escort; Establish a dynamic model containing the relative motion state of the non-cooperative target, the satellite and the mission spacecraft; Step 3: Control law design of the mission spacecraft and the escort satellite, specifically including: constructing the system cost function of the mission spacecraft and the escort satellite; Construct the Hamilton function; Solve the avoidance control law of the mission spacecraft and the cooperative escort control law of the escort satellite.

2. The method of claim 1, wherein the method further comprises: In step 2, the coordinate system is defined for the spacecraft in the geocentric orbital coordinate system; a. Geocentric equatorial inertial coordinate system f i (O i x i y i z i ) The origin of the geocentric equatorial inertial coordinate system is fixed at the center of the Earth O i The x-axis is in the equatorial plane and points to the vernal equinox O i The y-axis is in the equatorial plane and points to the summer solstice O i The z-axis is perpendicular to the equatorial plane and points to the north O i The x-axis is in the equatorial plane and points to the vernal equinox O i The y-axis is in the equatorial plane and points to the summer solstice O i The x-axis is in the equatorial plane and points to the vernal equinox O i The y-axis is in the equatorial plane and points to the summer solstice O i The x-axis is in the equatorial plane and points to the vernal equinox O i The y-axis is in the equatorial plane and points to the summer solstice O i The x-axis is in the equatorial plane and points to the vernal equinox O i The y-axis is in the equatorial plane and points to the summer solstice O i The x-axis is in the equatorial plane and points to the vernal equinox O i The y-axis is in the equatorial plane and points b.Reference to a spacecraft orbital coordinate system f o (O o x o y o z o ) The reference spacecraft O is defined such that its mass center coincides with the mass center of the mission spacecraft E at the initial time, and the origin of the reference spacecraft orbital coordinate system is fixed to the mass center of the spacecraft O o O o x o axis points in the direction of the mass center of the spacecraft O; O o y o axis is in the orbital plane and is perpendicular to the x o x o axis points in the direction of the velocity of the reference spacecraft; O o z o axis is perpendicular to the x o x o , O o y o axes form a right-handed orthogonal coordinate system.

3. The main-chaser cooperative avoidance control method of a spacecraft under the escort of a chaser according to claim 1 or 2, characterized in that: The relative position relationship of the mission spacecraft E, the satellite D and the non-cooperative target P is: η(r D -r P ) = (r E -r P ) (1) wherein r E represents the position vector of the mission spacecraft E in the geocentric equatorial inertial coordinate system; r D represents the position vector of the companion D in the geocentric equatorial inertial coordinate system; r P represents the position vector of the non-cooperative target P in the geocentric equatorial inertial coordinate system; η represents a coefficient for determining the relative distance between the mission spacecraft E, the companion D and the non-cooperative target P.

4. The method of claim 3, wherein the method further comprises: Based on conditions 1-4, the C-W equation of the mission spacecraft E, the satellite D and the non-cooperative target P is established: wherein n represents the orbital angular rate of the circular orbit in which the mission spacecraft, the companion, or the non-cooperative target is located; denotes the velocity, acceleration of the mission spacecraft E; denotes the velocity, acceleration of the companion D; denotes the velocity, acceleration of the non-cooperative target P; E denotes the velocity, acceleration of the mission spacecraft E; D denotes the velocity, acceleration of the companion D; P denotes the orbital control quantity of the mission spacecraft E, the companion D, and the non-cooperative target P.

5. The method of claim 4, wherein the method further comprises: The state space variable of the spacecraft relative to the reference satellite coordinate system is represented as: Wherein, the state space variable is represented as: The system matrix A and the control matrix B are in the following form:

6. The method of claim 5, wherein the method further comprises: Considering the relative motion position relationship constraints in the task requirements, the state space vector of the control system is defined as: Combining equations (5)-(13), let the state space vector be: Let, Then equation (13) is simplified as:

7. The main-chaser cooperative avoidance control method of a spacecraft under the escort of a chaser according to claim 1 or 4, characterized in that: In step 3, according to the control requirements of the non-cooperative target P, the mission spacecraft E and the escort spacecraft D, the cost function is constructed by using the idea of differential game: where t0 represents the initial time of the task spacecraft and the escort satellite starting to avoid the maneuver, t f represents the time when the game confrontation ends; the cost corresponding to the state of the spacecraft at a certain time is represented as Q b , R E , R D , R P are adjustable control parameters; for the task spacecraft and the escort satellite system, the expected cost function J(x b , u E , u D , u P ) is to be minimized.

8. The method of claim 7, wherein the method further comprises: The Hamilton function of the linear control system is constructed as: H(t,x b ,u E ,u D ,u P ,λ)=h(x b ,u E ,u D ,u P )+λ T ·f(t,x b ,u E ,u D ,u P ) (19) where the copula is denoted as λ; the function f(t, x b ,u E ,u D ,u P ) is denoted as f(t,x b ,u E ,u D ,u P ) = Ax E2 +B E u E +Bu D +B P u P ; According to the extreme value condition of the system, the solution of the control system when taking the extreme value is obtained as: The solution of the Hamilton-Jacobi equation is converted to the solution of the Riccati differential equation in the following form:

9. The method of claim 8, wherein the method further comprises: The cost function J ends up in the form of a quadratic form in x b J = xTQx where P(t) is constant during the game time, and the coordination variable takes values 10. The method of claim 9, wherein: Substitute P into λ, and finally the linear full-state feedback avoidance control solution of the mission spacecraft E and the cooperative escort control law of the escort satellite D are obtained: ​

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