Spacecraft cluster cooperative attitude control method in interference and fault mixed situation

Abstract

The present application relates to a kind of spacecraft cluster attitude cooperative control method under the interference fault mixed situation, for the problem that multiple-source interference and executor fault mixed make spacecraft cluster attitude cooperative control performance decline, first, for the rigid spacecraft cluster system containing leader and follower, establish leader attitude model, and establish the follower attitude model containing executor fault and multiple-source interference;Second, introduce hysteresis quantizer to the control input of follower is quantized, to reduce the communication burden of satellite;Third, design distributed observer, estimate the attitude of leader under dynamic communication topology;Finally, combined with distributed observer, design spacecraft attitude cooperative controller based on adaptive parameter identification, ensure that the attitude of follower can track the attitude of leader.The present application realizes spacecraft cluster attitude cooperative control without continuous communication under the interference and fault mixed situation, with higher robustness, lower energy consumption, easy to implement the characteristics of engineering.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of spacecraft control, and particularly relates to a spacecraft cluster attitude cooperative control method under interference fault mixed situation, mainly applied to distributed attitude cooperative control of spacecraft cluster containing actuator faults and multi-source interference, and communication time of each spacecraft is given based on a lag quantizer. BACKGROUND

[0002] Spacecraft cluster adopts a cooperative mode of multiple small spacecrafts, has advantages of short development cycle, low launch cost, flexible design, fast response, etc., and can meet the current growing and changing space mission requirements. In space tasks such as gravity field measurement and gravitational wave detection, the attitudes of each spacecraft in the spacecraft cluster need to be kept in a certain regular cooperative mode. During the space flight of the spacecraft cluster, it is inevitable to be affected by environmental disturbances such as solar radiation torque and gravity gradient torque, and these disturbances will cause the attitude of the spacecraft to deviate, so that the cooperative mode of the spacecraft cluster is destroyed. At the same time, after the spacecraft cluster system works for a certain time, the actuators, sensors and controllers of the spacecraft may have faults such as performance degradation, and these faults will also cause the attitude measurement and attitude pointing of the spacecraft to deviate. It is urgent to study the spacecraft cluster attitude cooperative control under the mixed situation of interference and fault.

[0003] In addition, in the existing spacecraft cluster attitude cooperative control scheme, continuous communication between the controller and the actuator is mostly required. However, in actual situations, the hardware capability of the on-board equipment is limited and cannot support continuous communication mode. Therefore, the attitude cooperative control scheme without continuous communication under the mixed situation of interference and fault also needs further research.

[0004] To meet the demand of complex spatial perception tasks and adapt to the game confrontation situation, the topology of cluster communication changes from static to dynamic. However, the current research on spacecraft cluster attitude cooperative control is mainly based on the fixed communication topology, and there is little research on attitude cooperative control technology under dynamic communication topology. The spacecraft anti-jamming attitude cooperative control method based on event-triggered communication is proposed in Chinese patent application CN202010174427.9, which considers the attitude cooperative control method of event-triggered communication between spacecrafts under external environmental disturbance, but only discusses the case under fixed communication topology, without considering the possibility of dynamic communication topology and actuator failure. Chinese patent application CN202211178812.6 proposes a spacecraft formation attitude cooperative control method based on event-triggering, which considers the influence of disturbance, but only considers external disturbance, without considering internal disturbance of spacecraft. Chinese patent application CN202110528568.0 proposes a flexible spacecraft finite-time attitude cooperative control method for actuator failure, which studies the case of actuator failure of flexible spacecraft, but ignores the constraints of on-board equipment capacity, and the failed actuator still needs to receive control signals and make signal conversion. The paper "Distributed fixed-time output feedback attitude cooperative tracking control of multi-spacecraft system" proposes a distributed fixed-time attitude cooperative controller based on integral sliding mode, which can realize the attitude cooperation of multiple spacecrafts under the condition of unmeasurable angular velocity. The paper "Multi-spacecraft attitude finite-time distributed cooperative control based on super-twisting algorithm" proposes a distributed attitude cooperative control method based on supper-twisting algorithm and integral sliding mode. The above two papers have achieved good control effect, but they are based on the design of attitude cooperative control scheme under fixed communication topology, without considering the communication topology changes caused by enemy communication attacks and other factors, which is difficult to apply directly in engineering.

[0005] In summary, the existing methods lack high-precision attitude cooperative control methods under dynamic communication topology in the presence of actuator failure, actuator vibration disturbance, external environmental disturbance and other multi-source disturbances. Therefore, it is urgent to study the spacecraft distributed attitude cooperative control method based on anti-jamming technology. SUMMARY

[0006] Aiming at the problem of spacecraft cluster attitude anti-interference cooperative tracking control under dynamic communication topology, the spacecraft cluster attitude cooperative control method under interference fault mixed situation is provided to overcome the shortcomings of the prior art, which is a spacecraft attitude cooperative tracking control method based on adaptive technology, which can accurately estimate the attitude and angular velocity of the leader spacecraft under dynamic topology, and also realizes the rapid estimation of actuator fault, interference and input quantization coefficient;The finite time sliding mode control method is adopted to enable the follower spacecraft to track the leader attitude signal, thereby improving the accuracy and anti-interference ability in the spacecraft cluster attitude cooperative control process under dynamic topology.

[0007] In order to achieve the above purpose, the technical scheme is adopted as follows:

[0008] A spacecraft cluster attitude cooperative control method under interference fault mixed situation, comprising the following steps:

[0009] Firstly, for the rigid spacecraft cluster system containing leaders and followers, based on the modified Rodrigues parameter, the attitude kinematics and dynamics of the leader with partial information unknown are modeled;Secondly, considering the mixed situation of actuator fault and multi-source interference of the follower, the attitude kinematics and dynamics model of the follower is established;Finally, the algebraic graph theory is used to describe the dynamic communication topology structure of the spacecraft cluster system;

[0010] Secondly, in view of the problem of large communication resource loss between the follower controller and the actuator, a lag quantizer is introduced to quantize the control input of the follower, so as to reduce the on-board communication burden;

[0011] Thirdly, for the leader attitude kinematics and dynamics model established in the first step, a distributed observer based on adaptive parameter identification is designed to estimate the attitude and angular velocity of the leader under dynamic topology;

[0012] Fourthly, based on the leader attitude and angular velocity estimation value obtained in the third step, a spacecraft anti-interference adaptive controller is designed by using the finite time sliding mode control method, so as to ensure that the follower can track the attitude and angular velocity of the leader, and complete the spacecraft cluster attitude cooperative control method under interference fault mixed situation.

[0013] Further, in the first step, 1 leader and n follower spacecrafts are considered, wherein 0# spacecraft represents the leader, and 1-n# spacecraft represents the follower;

[0014] Firstly, the following notations are defined: represents the set of r real vectors; represents the set of r x r real matrices;diag{·} represents a diagonal matrix;blockdiag{·} represents a block diagonal matrix; denotes the block matrix formed by multiplying each element of matrix A with matrix B; I e denotes the identity matrix of dimension e x e; m e M denotes that element m belongs to set M; denotes that all elements of set M are elements of set N; || · || denotes the Euclidean norm of a vector; | · | denotes the absolute value of a real number; A T denotes the transpose matrix of matrix or vector A; denotes the first order derivative of vector a with respect to time; denotes the second order derivative of vector a with respect to time; denotes the derivative of vector with respect to time; × denotes the following skew-symmetric matrix:

[0015]

[0016] The leader's attitude model is expressed in modified Rodrigues parameters as:

[0017]

[0018] ω0= C0v0,

[0019] wherein denotes the modified Rodrigues parameters of the leader, which are used to express the orientation of the leader body frame with respect to the inertial frame; denotes the derivative of σ0 with respect to time; denotes the angular velocity of the leader body frame with respect to the inertial frame; is a known constant matrix; is a matrix of which part of the information is unknown; denotes the derivative of v0 with respect to time;

[0020] It is assumed that the minimal polynomial of the leader system matrix S0 has no multiple roots and that the real part of all its eigenvalues is zero; it is assumed that there exists an integer satisfying and there exists a positive real number such that:

[0021]

[0022] wherein

[0023] The follower's attitude model is expressed in modified Rodrigues parameters as:

[0024]

[0025]

[0026] wherein denotes the modified Rodrigues parameters of the follower i; denotes the angular velocity of the body frame of the follower i with respect to the inertial frame; is the inertia matrix of the follower i; p i (t) is the failure coefficient of the actuator of the follower i, 0 < |p i (t)|≤1; denotes the control torque of the follower i, which is also the expected output value of the actuator of the follower i; denotes the drift fault signal of the actuator; denotes the vibration disturbance torque of the actuator of the follower i; denotes the external environment disturbance torque of the follower i; both the actuator drift fault and the disturbance are bounded values; G(σ i ) is defined as:

[0027]

[0028] Switching graph is adopted to describe the dynamic communication topology among the spacecrafts in the cluster, where h(t) denotes the switching signal of the communication topology, which takes values from the set denotes the node set composed of the spacecrafts; denotes the edge set formed by the communication relationship among the spacecrafts; h(t) is a right-continuous function, and for any t k-1 ≤t<t k , there exists such that h(t) = p, where t k -t k-1 ≥τ d , τ d > 0, k = 1, 2,...; the node 0 in the node set denotes the leader 0, and the node i denotes the follower i; the edge (j, i) belongs to the edge set ∑ h(t) , where i = 1,..., n, j = 0, 1,..., n, if and only if the follower i can obtain the information of the follower j at time t;

[0029] The neighbor set of the follower i is defined as where the neighbor set contains all the spacecrafts that can send information to the follower i at time t, which are also called the neighbor spacecrafts of the follower i; finally, the adjacency matrix of the switching graph is defined as where if (j, i) ∈∑ h(t) , then a ij (t) > 0, otherwise a ij (t) = 0; considering that the spacecraft does not send information to itself in practical applications, aii (t) = 0.

[0030] Further, the second step, the hysteresis quantizer is described as:

[0031]

[0032] where τ i represents the i-th control torque; Q i represents the latest value of Q i at time t, and i δ i and p i,j are intermediate variables, whose specific forms are i represents the latest value of Q i,1 at time t, and is always equal to 0. When 0 ≤ t ≤ T i,h , T i represents the time when Q i (τ i,1 ) changes, h = 1, 2, 3,..., 0 ≤ T i,2 ≤ T i,3 ≤... ≤ +∞; when T i,h < t ≤ T i,h+1 , where Q i (τ i (T i,h )) represents the quantized value of control torque τ i at time T i,h .

[0033] Define variables:

[0034]

[0035]

[0036] Then Q i (τ i ) is rewritten as follows:

[0037] Q i (τ i ) = q i,1 (t)τ i + q i,2 (t).

[0038] Since therefore:

[0039] ​

[0040] where, ε i > 0 represents the minimum value of ε i , represents the maximum value of a i (t), and the symbol represents the universal quantifier "any"; thus, the pose model of the follower i introduced by the lag quantizer is represented as:

[0041]

[0042]

[0043] where, represents the kth diagonal element of Q i,1 (t) ; represents the kth diagonal element of Q i,2 (t) ; the lumped disturbance d i (t) = d i1 (t) + d i2 (t) ; p i (t) is the failure fault coefficient of the follower i's actuator, 0 < | p i (t) | < 1.

[0044] Further, in the third step, the pose error of the follower i and the follower j is defined as:

[0045]

[0046] The distributed observer is designed as:

[0047]

[0048]

[0049]

[0050] where, represents the estimated value of the follower i to the leader angular velocity frequency ; represents the estimated value of the follower j to the leader angular velocity frequency ; represents the estimated value of the follower i to the leader system matrix S0; represents the estimated value of the follower i to v0, represents the to-be-designed parameter; is an intermediate variable, and the specific form is denotes the follower i pose estimate denotes the follower j pose estimate error of denotes the follower i pose estimate error of ij (t) is the adjacency matrix of the communication topology graph at time t is the element of if follower i can obtain the leader's information, then i0 (t) > 0, otherwise i0 (t) = 0.

[0051] Further, the fourth step, in combination with the distributed observer in the third step, designs a spacecraft anti-interference adaptive controller as follows:

[0052] Let denote the maximum value of the diagonal elements of Q i,1 (t) at time t, introduce the parameter:

[0053]

[0054]

[0055] where inf denotes the lower bound function, sup denotes the upper bound function, Define the tracking error of the pose of follower i and its angular velocity relative to the observer estimate as where denotes the rotation matrix of the inertial coordinate system to the body coordinate system of follower i; introduce the variable:

[0056]

[0057]

[0058] where G -1 (σ i,e ) denotes the inverse matrix of matrix G(σ i,e ), sgn(·) denotes the standard sign function, The stabilizing function is designed as:

[0059]

[0060] where c i > 0 is a parameter to be designed, is the estimate of θ i ; the adaptive law is designed as:

[0061]

[0062]

[0063] in, It is η i The estimated value, and These are the parameters to be designed. Based on these parameters, the controller is designed as follows:

[0064]

[0065] in, These are the parameters to be designed.

[0066] Based on the above design, the distributed observer can accurately estimate the leader's attitude and angular velocity, while the adaptive anti-interference controller can control the follower to track the observer's state estimate of the leader, thus indirectly realizing the follower's attitude tracking of the leader.

[0067] The advantages of this invention compared to the prior art are as follows:

[0068] This invention relates to a spacecraft swarm attitude cooperative control method under mixed interference and fault conditions. Addressing the shortcomings of existing methods in lacking high-precision attitude cooperative control capabilities under dynamic communication topologies when actuator failures and multi-source interference occur, this invention designs an adaptive law to estimate actuator failures and multi-source interference, enabling follower spacecraft to still track the leader's attitude even under mixed actuator failures and multi-source interference conditions, thus achieving strong robustness of the spacecraft cooperative controller. Furthermore, existing spacecraft swarm attitude cooperative control schemes require the spacecraft controller to continuously send control signals to the actuators. This invention introduces a hysteresis quantizer to determine the communication timing, significantly reducing the communication burden while ensuring tracking performance. Attached Figure Description

[0069] Figure 1 This is a system block diagram of a spacecraft cluster attitude cooperative control method under mixed interference and fault conditions according to the present invention.

[0070] Figure 2 This invention relates to the communication topology of a spacecraft cluster in a method for coordinated attitude control of a spacecraft cluster under mixed interference and fault conditions. Detailed Implementation

[0071] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0072] like Figure 1 As shown, the spacecraft cluster attitude cooperative control method under mixed interference and fault conditions of the present invention includes the following steps:

[0073] Firstly, the leader's attitude kinematics and dynamics model is established for the leader-follower rigid spacecraft formation system with unknown attitude angular velocity frequency. Then, the attitude kinematics and dynamics model of the follower is described by the modified Rodrigues parameters considering the actuator failure and multi-source disturbance. Finally, the dynamic communication topology of the spacecraft formation system is described by the algebraic graph theory.

[0074] Secondly, the quantizer is introduced to describe the discontinuous change of the spacecraft control input.

[0075] Thirdly, the nonlinear distributed observer based on adaptive parameter identification is designed to estimate the leader's attitude and attitude angular velocity according to the leader's attitude kinematics and dynamics model established in the first step.

[0076] Finally, the spacecraft anti-disturbance adaptive controller is designed based on the finite time sliding mode control method to complete the spacecraft formation attitude anti-disturbance cooperative control method under dynamic topology using the leader's attitude and attitude angular velocity estimated in the third step.

[0077] The specific implementation steps are as follows:

[0078] Firstly, consider a leader and n followers spacecrafts, where 0# spacecraft represents the leader and 1~n# spacecraft represents the follower. First, define the following notations: denotes the set of r real vectors; denotes the set of r x r real matrices; diag{·} denotes the diagonal matrix; blockdiag{·} denotes the block diagonal matrix; denotes the block matrix formed by multiplying each element of matrix A with matrix B; I e is the e x e identity matrix; m ∈ M means that element m belongs to set M; denotes that all elements of set M are elements of set N; ||·|| denotes the Euclidean norm of a vector; |·| denotes the absolute value of a real number; the symbol denotes the universal quantifier "for all"; denotes the first-order derivative of vector a with respect to time; denotes the second-order derivative of vector a with respect to time; for vector x × denotes the following skew-symmetric matrix:

[0079]

[0080] The leader's attitude model is represented by the modified Rodrigues parameters as follows:

[0081]

[0082] ω0= C0v0,

[0083] wherein, σ0denotes the leader's modified Rodrigues parameters, which are used to represent the orientation of the leader's body-fixed coordinate frame relative to the inertial coordinate frame, and the initial pose is set as σ0= [0, 0, 0] T ; ω0denotes the angular velocity of the leader's body-fixed coordinate frame relative to the inertial coordinate frame, and the initial value can be taken as v0= [0.005, -0.005, -0.01, -0.005] T ; is a known constant matrix, which can be taken as is a matrix of which part of information is unknown;

[0084] It is assumed that the minimal polynomial of the leader system matrix S0has no repeated roots and the real part of all eigenvalues of the minimal polynomial is 0. Without loss of generality, it is assumed that there exists an integer satisfying and there exists a positive real number such that:

[0085]

[0086] wherein, S0can be taken as

[0087] The pose model of the follower i is represented by modified Rodrigues parameters as:

[0088]

[0089]

[0090] wherein, σ1denotes the modified Rodrigues parameters of the follower i, and the initial pose is set as σ1= [0.3, 0.1, 0] T , σ2= [0.2, 0, 0.1] T , σ3= [0.1, 0, 0.2] T , σ4= [0, 0.1, 0.1] T ; ω1denotes the angular velocity of the follower i's body-fixed coordinate frame relative to the inertial coordinate frame, and the initial angular velocity is all set as [0, 0, 0] T ; is the rotational inertia matrix of the follower i, which can be taken as diag{5.5, 6.14, 2.18} kg·m 2 ; p i(t) is the failure coefficient of the actuator of the follower i, 0 < |p i (t) | < 1, preferably 0.5; represents the control torque of the follower i, which is also the expected output value of its actuator; represents the drift fault signal of the actuator, preferably 0.0075 * [sin(6t), sin(6t), sin(6t)]; T N x m; represents the actuator vibration interference torque suffered by the follower i, preferably represents the external environmental interference torque suffered by the follower i, preferably where n0 represents the orbital angular velocity of the spacecraft, preferably n0 = 0.0011 rad / s; the actuator drift fault and the interference are both bounded values. G(σ i ) is defined as:

[0091]

[0092] Switching graph is adopted to describe the dynamic communication topology between spacecrafts in the cluster, where h(t) represents the switching signal of the communication topology, which takes the value set represents the node set composed of spacecrafts; represents the edge set formed by the communication relationship of spacecrafts. Specifically, h(t) is a right-continuous function, and for any t k-1 ≤ t < t k (where t k - t k-1 ≥ τ d , τ d > 0, k = 1, 2,...). There exists such that h(t) = p; the node 0 in the node set represents the leader 0, and the node i represents the follower i; at time t, the edge (j, i) (where i = 1,..., n, j = 0, 1,..., n.) belongs to the edge set Σ h(t) if and only if the follower i can obtain the information of the follower j. In addition, the neighbor set of the follower i can be defined as where the neighbor set contains all spacecrafts that can send information to the follower i at time t, which are also called neighbor spacecrafts of the follower i. Finally, the adjacency matrix of the switching graph is defined as where if (j, i) ∈ Σ h(t) , then a ij (t) > 0, otherwise a ij(t) = 0; considering that in practical application spacecraft does not send information to itself, a ii (t) = 0. The spacecraft cluster communication topology can be selected as shown in the communication topology graph Figure 2 The switching signal can be set as:

[0093]

[0094] k = 0, 1, 2..., T = 4s.

[0095] Secondly, the hysteresis quantizer is introduced to quantize the control torque of the follower dynamics, and the discontinuous change of the spacecraft control input is described. The specific form of the hysteresis quantizer is:

[0096]

[0097] Where, τ i represents the i-th control torque; Q i (τ i ) represents the quantized value corresponding to the control torque τ i ; δ i and p i,j are intermediate variables, and the specific forms are respectively a i can be taken as 0.1, and ε i can be taken as 0.87. represents the latest value of Q i before t time, and is always equal to 0. When 0≤t≤T i,1 , T i,h represents the time when Q i (τ i ) changes, h = 1, 2, 3,..., 0≤T i,1 ≤T i,2 ≤T i,3 ≤...≤+∞; when T i,h <t≤T i,h+1 , Where Q i (τ i (T i,h )) represents the quantized value corresponding to the control torque τ i at T i,h time.

[0098] Define the variable:

[0099]

[0100]

[0101] Then Qi (τ i ) can be rewritten as follows:

[0102] Q i (τ i ) = q i,1 (t)τ i + q i,2 (t).

[0103] Since therefore:

[0104]

[0105] where, ε i > 0 represents the minimum value of ε i , and represents the maximum value of a i (t) symbol represents the universal quantifier "any". Therefore, the pose model of the follower i introducing the hysteresis quantizer can be expressed as:

[0106]

[0107]

[0108] where, represents the kth diagonal element of Q i,1 (t); represents the kth diagonal element of Q i,2 (t), the lumped disturbance d i (t) = d i1 (t) + d i2 (t); p i (t) is the failure fault coefficient of the follower i's actuator, 0 < | p i (t) | < 1.

[0109] Thirdly, for the leader spacecraft model established in the first step, the attitude error between the follower i and the follower j is defined as:

[0110]

[0111] Based on the adaptive parameter identification, a distributed observer is designed:

[0112]

[0113]

[0114]

[0115] where, denotes the estimated value of the leader angular velocity frequency by the follower i; denotes the estimated value of the leader angular velocity frequency by the follower j; denotes the estimated value of the leader system matrix S0by the follower i; denotes the estimated value of v0by the follower i, denotes the to-be-designed parameter; is an intermediate variable, and the specific form is denotes the error between the attitude estimation value of the follower i and the attitude estimation value of the follower j; denotes the error between the attitude estimation value of the follower i and the leader attitude σ0;a ij (t) is the adjacency matrix of the communication topology graph at time t , if the follower i can obtain the information of the leader, then a i0 (t) > 0, otherwise a i0 (t) = 0; the adjacency matrix element can be set as a 10 = 500, a 12 = 1, a 14 = 500, a 23 = 150, a 21 = 150, a 30 = 150, a 32 = 20, a 34 = 20, a 41 = 150, a 43 = 800.

[0116] Fourthly, based on the leader attitude and attitude angular velocity estimation values in the third step, a spacecraft anti-interference adaptive controller is designed based on a finite time sliding mode control method. Let denote the maximum value of the diagonal elements of Q i,1 (t) at time t, and introduce a parameter:

[0117]

[0118]

[0119] where, inf denotes a lower bound function, sup denotes an upper bound function, the tracking errors of the attitude and angular velocity of the follower i relative to the observer estimation values are defined as where denotes the rotation matrix from the inertial coordinate frame to the follower i body coordinate frame. Introduce the variable:

[0120]

[0121]

[0122] where G -1 (σ i,e ) denotes the inverse matrix of G(σ i,e ), sgn(·) denotes the standard sign function, The stabilizing function is designed as:

[0123]

[0124] where c i > 0 is the parameter to be designed, is the estimated value of θ i , and the initial value can be taken as The adaptive law is designed as:

[0125]

[0126]

[0127] where is the estimated value of η i , and the initial value can be taken as and are the parameters to be designed, which can be taken as 0.2 respectively. On this basis, the controller is designed as:

[0128]

[0129] where is the parameter to be designed, which can be taken as 0.01. The design parameters can be selected as [c1, c2, c3, c4] = [4, 4, 4, 4], [m 1,1 , m 2,1 , m 3,1 , m 4,1 ] = [0.02, 0.02, 0.02, 0.02], [m 1,2 , m 2,2 , m 3,2 , m 4,2 ] = [0.02, 0.02, 0.02, 0.02].

[0130] The spacecraft cluster attitude cooperative control method can guarantee that the follower spacecraft can track the attitude of the leader well under a dynamic communication topology even if affected by multi-source interference or actuator failure, attitude errors of the two can converge to a predetermined threshold, and the control signal is bounded. Meanwhile, compared with the controller without interference and fault estimation, the control effect can reach smaller attitude errors with lower energy consumption, meeting the requirements of high precision and low energy consumption.

[0131] The contents not described in detail in the specification of the present application belong to the prior art known to those skilled in the art.

Claims

1. A method for coordinated attitude control of a spacecraft cluster under mixed interference and fault conditions, characterized in that, Includes the following steps: The first step, for a rigid spacecraft swarm system containing a leader and followers, is to first model the attitude kinematics and dynamics of the leader, whose information is partially unknown, based on modified Rodrigues parameters. The second step is to establish the attitude kinematics and dynamics model of the followers, considering the situation of actuator failure and multi-source interference. Finally, algebraic graph theory is used to describe the dynamic communication topology of the spacecraft swarm system. The second step is to address the issue of high communication resource consumption between the follower controller and the actuator by introducing a hysteresis quantizer to quantize the control input of the follower, thereby reducing the burden on onboard communication. The third step involves designing a distributed observer based on adaptive parameter identification for the leader posture kinematics and dynamics model established in the first step, in order to estimate the leader posture and its angular velocity under dynamic topology. The fourth step involves designing an anti-interference adaptive controller for the spacecraft based on the estimated attitude and angular velocity of the leader obtained in the third step. This controller utilizes the finite-time sliding mode control method to ensure that the followers can track the attitude and angular velocity of the leader, thus completing the collaborative attitude control method for the spacecraft cluster under mixed interference and fault conditions.

2. The method for coordinated attitude control of a spacecraft cluster under mixed interference and fault conditions as described in claim 1, characterized in that: In the first step, consider 1 leader spacecraft and n follower spacecraft, where spacecraft #0 represents the leader and spacecraft #1 to #n represent the followers; First, define the following notation: The set of r real vectors; Let represent the set of r×r real matrices; diag{·} represents a diagonal matrix; blockdiag{·} represents a block diagonal matrix; This represents a block matrix formed by multiplying each element of matrix A with matrix B; I e It is an e×e-dimensional identity matrix; m∈M means that element m belongs to set M; The expression represents that all elements of set M are elements of set N; ||·|| represents the Euclidean norm of a vector; |·| represents the absolute value of a real number; A T Represents the transpose of matrix A or vector A; This represents the first derivative of vector a with respect to time. The second derivative of vector a with respect to time; the second derivative of vector a with respect to time. In terms of x × Represent the following skew-symmetric matrix: The leader's posture model, expressed using modified Rodrigue parameters, is as follows: ω0=C0v0, in, The modified Rodrigues parameter represents the leader's body coordinate system and is used to indicate the orientation of the leader's body coordinate system relative to the inertial coordinate system. Let σ0 be the derivative of σ0 with respect to time. This represents the angular velocity of the leader's body coordinate system relative to the inertial coordinate system; A known constant matrix; A matrix for which some information is unknown; This represents the derivative of v0 with respect to time. Assume that the minimal polynomial of the leader system matrix S0 has no repeated roots and that the real parts of all its eigenvalues ​​are 0; assume that there exist integers satisfy And there exist positive real numbers. Make: in, The pose model of follower i, expressed using modified Rodrigue parameters, is as follows: in, This represents the modified Rodrigues parameter of follower i; This represents the angular velocity of the follower i's body coordinate system relative to the inertial coordinate system; Let ρ be the rotational inertia matrix of follower i; i (t) is the failure coefficient of the follower i actuator, 0 < |ρ i (t)|≤1; This represents the control torque of follower i, which is also the expected output value of its actuator; This indicates a drift fault signal in the actuator; This represents the actuator vibration disturbance torque experienced by follower i; This represents the external environmental disturbance torque experienced by follower i; actuator drift faults and disturbances are both bounded values; G(σ) i ) is defined as: Using switching diagrams Describe the dynamic communication topology between spacecraft within the cluster, where h(t) represents the communication topology switching signal, and its value set is... This represents a set of nodes that make up a spacecraft. Let h(t) represent the edge set formed by spacecraft communication relationships; h(t) is a right-continuous function, and for any t k-1 ≤t<t k ,exist Make h(t) = p, where t k -t k-1 ≥τ d , τ d >0, k=1,2,...; Node set In the edge set ∑, node 0 represents the leader 0, and node i represents the follower i; at time t, edge (j,i) belongs to edge set ∑ if and only if follower i can obtain information about follower j. h(t) Where i = 1, ..., n, j = 0, 1, ..., n; The neighbor set of follower i is defined as Neighbor set This includes all spacecraft capable of sending information to follower i at time t; these spacecraft are also called follower i's neighbor spacecraft. Finally, the switching graph is defined. adjacency matrix Where (j,i)∈∑ h(t) Then a ij (t)>0, otherwise a ij (t) = 0; considering that in practical applications, spacecraft do not send information to themselves, a ii (t) = 0.

3. The method for coordinated attitude control of a spacecraft cluster under mixed interference and fault conditions as described in claim 2, characterized in that: In the second step, the hysteresis quantizer is described as follows: Where, τ i Q represents the i-th control torque; i (τ i ) represents the control torque τ i The corresponding quantization value; δ i and p i,j All are intermediate variables, and their specific forms are as follows: 0 < ε i <1, a i >0, j=1,2,3,...; Q i -(t) represents Q i The latest value before time t, and It is always equal to 0; when 0 ≤ t ≤ T i,1 , T i,h Q represents i (τ i The time at which the change occurs, h = 1, 2, 3, ..., 0 ≤ T i,1 ≤T i,2 ≤T i,3 ≤...≤+∞; when T i,h <t≤T i,h+1 , Q i (τ i (T i,h )) represents the control torque τ i In T i,h The quantized value corresponding to the time; Define variables: So Q i (τ i Rewrite it as follows: Q i (τ i )=q i,1 (t)τ i +q i,2 (t). because Therefore: q i,1 (t)≥λ i , in, ε i >0 indicates ε i The minimum value, Indicates a i The maximum value of (t), sign The universal quantifier "arbitrary" is used; therefore, the pose model of follower i with a hysteresis quantizer is represented as: in, Q represents i,1 The k-th diagonal element of (t); Q represents i,2 The k-th diagonal element of (t); lumped interference d i (t)=d i1 (t)+d i2 (t); ρ i (t) is the failure coefficient of the follower i actuator, 0 < |ρ i (t)|≤1.

4. The method for coordinated attitude control of a spacecraft cluster under mixed interference and fault conditions as described in claim 3, characterized in that: In the third step, the posture error between follower i and follower j is defined as: The distributed observer is designed as follows: in, Indicates the frequency of the angular velocity of follower i relative to the leader. The estimated value; This represents the frequency of the angular velocity of follower j relative to the leader. The estimated value; This represents the estimate of the leader system matrix S0 by follower i; This represents the follower i's estimate of v0. Indicates the parameters to be designed; As an intermediate variable, specifically in the form of This represents the pose estimate of follower i. With follower j pose estimate The error; This represents the pose estimate of follower i. Error with respect to leader's posture σ0; a ij (t) is the communication topology diagram at time t. adjacency matrix If a follower i can obtain information about the leader, then a i0 (t)>0, otherwise a i0 (t) = 0.

5. The method for coordinated attitude control of a spacecraft cluster under mixed interference and fault conditions according to claim 4, characterized in that: In the fourth step, combining the distributed observer from the third step, the spacecraft anti-interference adaptive controller is designed as follows: make Q represents time t i,1 (t) Maximum value of diagonal elements, introducing a parameter: Where inf represents the infimum function and supremum function represents the supremum function. Define the tracking errors of follower i's attitude and angular velocity relative to the observer's estimates as follows: in Represents the rotation matrix from the inertial coordinate system to the body coordinate system of follower i; introduce variables: Among them, G -1 (σ i,e ) represents matrix G(σ i,e The inverse matrix of ), where sgn(·) denotes the standard sign function. The stabilization function is designed as follows: Among them, c i >0 represents the parameter to be designed. It is θ i The estimated value; the adaptive law is designed as follows: in, It is η i The estimated value, and These are the parameters to be designed; Based on this, the controller is designed as follows: in, These are the parameters to be designed.

Images