Multi-rigid-body satellite cooperative control method under common attitude constraint

Abstract

The invention discloses a multi-rigid-body satellite cooperative control method under a common attitude constraint, and the method comprises the steps: building the attitude kinematics and dynamics of a multi-rigid-body satellite based on an attitude quaternion, and carrying out the simplification processing of the attitude kinematics and dynamics, and obtaining a quaternion attitude model; s2, describing a communication topological structure between satellites by adopting a graph theory, and designing a cooperative consistency control protocol of multiple satellites based on the quaternion attitude model constructed in the step S1; based on the quaternion attitude model, designing a multi-satellite common attitude constraint protocol based on a barrier Lyapunov function; and generating a cooperative control protocol under the common attitude constraint by using the designed consistency control protocol and the attitude constraint protocol to realize cooperative control of the multi-rigid-body satellites. According to the invention, through cooperative control among multiple satellites, stable attitude control under a common attitude constraint condition is realized, the high-precision attitude keeping capability of the multiple rigid satellites in a complex space environment is ensured, and the robustness and reliability of the system are improved.

Description

Technical Field

[0001] The invention belongs to the field of automatic control, relates to the coordinated control of multiple rigid satellites, and specifically to a method for coordinated control of multiple rigid satellites under common attitude constraints. Background Art

[0002] The multi-rigid body satellite cooperative control system is one of the most concerned technical fields in current space missions. Especially in complex space environments, how to achieve efficient cooperative control of multiple satellites while meeting attitude constraints has become a research focus. In practical applications, precise control of satellite attitude is crucial to ensure the effective operation of satellite clusters. This control not only involves traditional attitude maintenance tasks, such as multi-satellite formation flying and space station docking, but also includes attitude constraint requirements under specific conditions, such as avoiding exposure of sensitive equipment on satellites to direct sunlight or other harmful radiation sources. These attitude constraints are of great significance for extending the service life of satellites, ensuring the normal operation of equipment, and improving the overall mission success rate.

[0003] At present, the coordinated control technology of multiple rigid satellites mainly relies on independent attitude control systems. However, when meeting common action goals, attitude constraints are often not completely unified, resulting in attitude incoordination between satellites, which in turn affects the accuracy and efficiency of the overall mission. Traditional attitude constraint control algorithms, such as [Feng Zhenxin, Guo Jianguo, Zhou Jun. Multi-constraint attitude maneuver planning method for microsatellites. Journal of Astronautics, 2019, 40(10): 1205-1211.], usually focus on the attitude constraint control of a single satellite, and do not fully consider the coordinated attitude constraint requirements in a multi-satellite system. When faced with multi-satellite collaborative missions, these algorithms may lead to frequent attitude adjustments, increased fuel consumption, and even mission failure.

[0004] In addition, in the existing technology, although some coordinated control schemes for multi-satellite systems have been proposed, most of them show certain limitations when dealing with complex attitude constraints. For example, some algorithms handle satellite attitude constraints in a simple way and cannot effectively avoid the violation of attitude constraints in a dynamic environment; while other schemes can take attitude constraints into account, but there is a large amount of calculation in the coordinated consistency control among multiple satellites, which limits the real-time performance and reliability of the system. Summary of the invention

[0005] Purpose of the invention: In order to overcome the deficiencies in the prior art, a method for cooperative control of multiple rigid satellites under common attitude constraints is provided, so that multiple satellites can achieve consistent cooperative control under the premise of meeting specific attitude constraints. Through cooperative control between multiple satellites, stable attitude control under common attitude constraints is achieved, ensuring the high-precision attitude maintenance capability of multiple rigid satellites in complex space environments, and improving the robustness and reliability of the system.

[0006] Technical solution: To achieve the above purpose, the present invention provides a method for cooperative control of multiple rigid body satellites under common attitude constraints, comprising the following steps:

[0007] S1: Construct the attitude kinematics and dynamics of multi-rigid body satellites based on attitude quaternions, and simplify them to obtain the quaternion attitude model;

[0008] S2: Use graph theory to describe the communication topology between satellites, and design a collaborative consistency control protocol for multiple satellites based on the quaternion attitude model constructed in step S1;

[0009] S3: Based on the quaternion attitude model obtained in step S1, a multi-satellite common attitude constraint protocol based on obstacle Lyapunov function is designed;

[0010] S4: Use the designed consistency control protocol and attitude constraint protocol to generate a collaborative control protocol under common attitude constraints to achieve collaborative control of multiple rigid body satellites.

[0011] Furthermore, the specific method for constructing the attitude kinematics and dynamics of the multi-rigid body satellite based on the attitude quaternion in step S1 is:

[0012] Consider a multi-satellite coordinated control system consisting of n satellites. Assume that the attitude quaternion part of the i-th satellite is [q i ,q i0 ] T , where q i =[q i1 ,q i2 ,q i3 ] T is the vector part of the quaternion; q i0 is the scalar part of the quaternion; based on the defined attitude quaternion, the attitude kinematics and dynamics of multiple satellites are obtained by the following formula:

[0013]

[0014] in, Q i The derivative with respect to time; ω i =[ω i1 ,ω i2 ,ωi3 ] T is the angular velocity of the ith satellite in the body coordinate system, ω i The derivative with respect to time; J i is the moment of inertia of the ith satellite, τ i =[τ i1 ,τ i2 ,τ i3 ] T is the control torque of the ith satellite; E i =0.5(S(q i )+q 0i I3), I3 is the third-order unit matrix, S(ω i ) represents the following matrix:

[0015]

[0016] S(q i ) represents the following matrix:

[0017]

[0018] Furthermore, in step S1, the attitude kinematics and dynamics of the multi-rigid body satellite are simplified by introducing new variables to obtain a quaternion attitude model, specifically:

[0019] Define a new variable v i =E i ω i =[v i1 ,v i2 ,v i3 ] T , then the simplified attitude kinematics and dynamics of the ith satellite are

[0020]

[0021] in, Yes i Derivative with respect to time; is the matrix E i The inverse matrix of is a matrix The transposed matrix of For E i The derivative with respect to time, S(v i ) represents the following matrix:

[0022]

[0023] Furthermore, the specific method of using graph theory to describe the communication topology structure between satellites in step S2 is:

[0024] The communication topology of n satellites is described by an undirected graph G = (s, ε, A), where s = {s1, ..., s n} represents a finite non-empty set of n satellites; ε∈(s×s) represents an edge set; A=[a ij ]∈R n×n represents the adjacency matrix of the graph G, and the symbol R represents the set of all real numbers;

[0025] If there is an edge from the i-th satellite to the j-th satellite (s i ,s j )∈ε, then a ij >0, otherwise a ij =0; therefore, satellite node s i The neighbor nodes of i ={j:(v i ,v j )∈ε}; On this basis, the degree of the i-th satellite node is defined as Then the degree matrix and Laplacian matrix of graph G are D=diag{d1,...,d n}∈R n×n and L = DA;

[0026] In addition, in order to describe the reception of the expected attitude signal by the satellite, the expected signal reception matrix is ​​defined as B = diag{b1,...,b n}, when satellite i can obtain the expected attitude signal, then b i >0, otherwise b i =0.

[0027] Furthermore, the design method of the multi-satellite collaborative consistency control protocol in step S2 is:

[0028] Based on the constructed quaternion attitude model, the following collaborative consistency control protocol for the i-th satellite is designed:

[0029]

[0030] Among them, k1>0 is the gain of the control protocol, q d is the expected attitude value that all satellites want to reach.

[0031] Furthermore, the design method of the multi-satellite common attitude constraint protocol in step S3 is:

[0032] A1: Define the common attitude constraints that satellites need to satisfy and the relative constraints that satellites need to satisfy;

[0033] A2: Based on the quaternion attitude model, common attitude constraint values ​​and relative constraint values, a common attitude constraint protocol based on obstacle Lyapunov function is designed.

[0034] Furthermore, the step A1 is specifically as follows:

[0035] The attitude constraint value of the i-th satellite in the satellite constellation is defined as M k =[M k1 ,M k2 ,M k3 ] T , where M k1 >0,M k2 >0,M k3 >0 is a normal number; that is, the i-th satellite is required to satisfy the following conditions during the control process:

[0036] |q i1 |<M k1 ,|q i2 |<M k2 ,|q i3 |<M k3 ,i=1,...,n

[0037] Define the relative attitude constraint value between the i-th satellite in the satellite cluster and its neighboring satellites as N k =[N k1 ,N k2 ,N k3 ] T , where N k1 >0,N k2 >0,N k3 >0 is a normal number; that is, the i-th satellite is required to satisfy the following conditions during the control process:

[0038] |q i1 -q j1 |<N k1 ,|q i2 -q j2 |<N k2 ,|q i3 -q j3 |<N k3 ,i=1,...,nj∈Γ i .

[0039] Furthermore, the step A2 is specifically as follows:

[0040] Based on the simplified quaternion attitude model, the following common attitude constraint protocol is designed for the i-th satellite:

[0041]

[0042] Among them, k2, k3>0; 3 / 4<α<1 is the ratio of two positive odd numbers; Represents v i 1 / (2α-1)th power; represent 1 / (2α-1)th power; Represents σ i 2α-1 power.

[0043] Furthermore, the step S4 is specifically as follows:

[0044] According to the designed consistency control protocol and common attitude constraint protocol, the following cooperative control protocol under common attitude constraint is generated for the i-th satellite:

[0045] τ i =S(ω i )J i ω i +ρ i +u i .

[0046] The present invention aims at the problems of insufficient attitude constraint processing and low efficiency of collaborative control in the current collaborative control of multiple rigid satellites, and provides a new control protocol and system that can achieve efficient collaborative control under complex attitude constraint conditions. This new control method and system can not only ensure the collaborative consistency of the satellite group under common attitude constraints, but also improve the control accuracy and mission success rate in a changeable space environment, and further promote the practical application of multi-satellite collaborative tasks.

[0047] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0048] 1. The present invention can achieve attitude consistency control of multiple satellites within a limited time by designing a collaborative attitude constraint control protocol. By introducing advanced control algorithms, the present invention ensures that the multi-satellite system can quickly and accurately adjust its attitude in a complex environment to meet the common attitude constraint requirements. This capability greatly improves the response speed and overall coordination of the multi-satellite system when performing collaborative tasks, and significantly improves the control accuracy and mission success rate.

[0049] 2. The collaborative attitude constraint controller provided by the present invention has a simple structure, is easy to implement, and is relatively friendly to the hardware environment used. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic flow chart of the control method of the present invention;

[0051] Figure 2 : is a communication topology diagram of four rigid satellites in this embodiment;

[0052] Figure 3 is the attitude response curve of the four rigid satellites in this embodiment;

[0053] Figure 4 is the angular velocity response curve of the four rigid satellites in this embodiment;

[0054] Figure 5 ] are the control torque response curves of the four rigid satellites in this embodiment. DETAILED DESCRIPTION

[0055] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0056] like Figure 1 As shown, the present invention provides a method for cooperative control of multiple rigid body satellites under common attitude constraints, comprising the following steps:

[0057] S1: Construct the attitude kinematics and dynamics of multi-rigid body satellites based on attitude quaternions, and simplify them to obtain the quaternion attitude model;

[0058] The specific method of constructing attitude kinematics and dynamics of multi-rigid body satellites based on attitude quaternions is:

[0059] Consider a multi-satellite coordinated control system consisting of n satellites. Assume that the attitude quaternion part of the i-th satellite is [q i ,q i0 ] T , where q i =[q i1 ,q i2 ,q i3 ] T is the vector part of the quaternion; q i0 is the scalar part of the quaternion; based on the defined attitude quaternion, the attitude kinematics and dynamics of multiple satellites are obtained by the following formula:

[0060]

[0061] in, for q i The derivative with respect to time; ω i =[ω i1 ,ω i2 ,ω i3 ] T is the angular velocity of the ith satellite in the body coordinate system, ω i The derivative with respect to time; J iis the moment of inertia of the ith satellite, τ i =[τ i1 ,τ i2 ,τ i3 ] T is the control torque of the ith satellite; E i =0.5(S(q i )+q 0i I3), I3 is the third-order unit matrix, S(ω i ) represents the following matrix:

[0062]

[0063] S(q i ) represents the following matrix:

[0064]

[0065] The quaternion attitude model is obtained by introducing new variables to simplify the attitude kinematics and dynamics of the multi-rigid body satellite, specifically:

[0066] Define a new variable v i =E i ω i =[v i1 ,v i2 ,v i3 ] T , then the simplified attitude kinematics and dynamics of the ith satellite are

[0067]

[0068] in, Yes i Derivative with respect to time; is the matrix E i The inverse matrix of is a matrix The transposed matrix of For E i The derivative with respect to time, S(v i ) represents the following matrix:

[0069]

[0070] S2: Use graph theory to describe the communication topology between satellites, and design a collaborative consistency control protocol for multiple satellites based on the quaternion attitude model constructed in step S1;

[0071] The communication topology of n satellites is described by an undirected graph G = (s, ε, A), where s = {s1, ..., s n} represents a finite non-empty set of n satellites; ε∈(s×s) represents an edge set; A=[a ij ]∈R n＝n represents the adjacency matrix of the graph G, and the symbol R represents the set of all real numbers;

[0072] If there is an edge from the i-th satellite to the j-th satellite (s i ,s j )∈ε, then a ij >0, otherwise a ij =0; therefore, satellite node s i The neighbor nodes of i ={j:(v i ,v j )∈ε}; On this basis, the degree of the i-th satellite node is defined as Then the degree matrix and Laplacian matrix of graph G are D=diag{d1,...,d n}∈R n×n and L = DA;

[0073] In addition, in order to describe the reception of the expected attitude signal by the satellite, the expected signal reception matrix is ​​defined as B = diag{b1,...,b n}, when satellite i can obtain the expected attitude signal, then b i >0, otherwise b i =0.

[0074] Based on the constructed quaternion attitude model, the following collaborative consistency control protocol for the i-th satellite is designed:

[0075]

[0076] Among them, k1>0 is the gain of the control protocol, q d is the expected attitude value that all satellites want to reach.

[0077] S3: Based on the quaternion attitude model obtained in step S1, a multi-satellite common attitude constraint protocol based on the obstacle Lyapunov function is designed, which specifically includes:

[0078] A1: Define the common attitude constraints that satellites need to satisfy and the relative constraints that satellites need to satisfy;

[0079] The attitude constraint value of the i-th satellite in the satellite constellation is defined as M k =[M k1 ,M k2 ,M k3 ] T , where M k1 >0,M k2 >0,Mk3 >0 is a normal number; that is, the i-th satellite is required to satisfy the following conditions during control:

[0080] |q i1 |<M k1 ,|q i2 |<M k2 ,|q i3 |<M k3 ,i=1,...,n

[0081] Define the relative attitude constraint value between the i-th satellite in the satellite cluster and its neighboring satellites as N k =[N k1 ,N k2 ,N k3 ] T , where N k1 >0,N k2 >0,N k3 >0 is a normal number; that is, the i-th satellite is required to satisfy the following conditions during the control process:

[0082] |q i1 -q j1 |<N k1 ,|q i2 -q j2 |<N k2 ,|q i3 -q j3 |<N k3 ,i=1,...,nj∈Γ i

[0083] A2: Based on the quaternion attitude model, common attitude constraint value and relative constraint value, a common attitude constraint protocol based on obstacle Lyapunov function is designed;

[0084] Based on the simplified quaternion attitude model, the following common attitude constraint protocol is designed for the i-th satellite:

[0085]

[0086] Among them, k2, k3>0; 3 / 4<α<1 is the ratio of two positive odd numbers; Represents v i 1 / (2α-1)th power; represent 1 / (2α-1)th power; Represents σ i 2α-1 power.

[0087] S4: Use the designed consistency control protocol and attitude constraint protocol to generate a cooperative control protocol under common attitude constraints to achieve cooperative control of multiple rigid body satellites;

[0088] According to the designed consistency control protocol and common attitude constraint protocol, the following cooperative control protocol under common attitude constraint is generated for the i-th satellite:

[0089] τ i =S(ω i )J i ω i +ρ i +u i .

[0090] In order to verify the effectiveness and effect of the solution of the present invention, the present embodiment is verified by simulation experiments and analysis, as follows:

[0091] In this embodiment, MATLAB 2023b is used as the simulation software to simulate four satellites of the same type for attitude control, and the inertia matrix is ​​as follows:

[0092]

[0093] The communication topology of the four satellites is shown in the figure below: Figure 2 As shown, where a 12 =a 13 =a 34 =1. In addition, only the first satellite can know the reference expected attitude command signal, that is, b1 = 1. Assume that the initial states of the four satellites are: Satellite 1: q1(0) = [0.371, 0.384, 0.353] T ,ω1(0)=[-0.21,-0.23,-0.25] T rad / s, Satellite 2: q2(0) = [0.502, 0.54, 0.576] T ,ω2(0)=[0.13,0.32,0.34] T rad / s, Satellite 3: q3(0) = [0.572, 0.456, 0.668] T ,ω3(0)=[-0.1,-0.13,-0.14] T rad / s, Satellite 4: q4(0) = [0.556, 0.593, 0.528] T ,ω4(0)=[0.23,0.31,0.22] T rad / s.

[0094] In the simulation environment, the controller parameters are selected as follows: k1 = 12.3, k2 = 6, k3 = 3.4, α = 17 / 19. The common attitude constraint of the four satellites is selected as M k =[0.6,0.65,0.7] T , the relative posture constraint is N k=[1,1,1] T , the reference expected signals of the four satellites are q d =[0,0,0] T .

[0095] Figure 3 The attitude response curves of four satellites based on quaternions are given. Figure 3 It can be seen that the attitudes of the four satellites can reach the expected attitude q d In addition, during the satellite control process, the attitudes of the four satellites can satisfy the common attitude constraint M k .

[0096] Figure 4 The angular velocity response curves of the four satellites are given. Figure 4 It can be seen that the angular velocities of the four satellites can be stabilized.

[0097] Figure 5 The response curves of the control torques of the four satellites are given. Figure 5 It can be seen that the control torque of four satellites can realize the control of four satellites.

[0098] It can be clearly seen from the above simulation results that the multi-rigid body satellite collaborative control protocol and system under common attitude constraints proposed in the present invention can quickly track the desired attitude signal. In addition, during the control process, the attitude will be strictly limited to the set common constraints.

[0099] In summary, the method for collaborative control of multiple rigid body satellites under common attitude constraints provided by the present invention is fast and robust, and can achieve consistent control of multiple satellites under attitude constraints.

Claims

1. A method for cooperative control of multiple rigid body satellites under common attitude constraints, characterized in that: The steps include: S1: Construct the attitude kinematics and dynamics of multi-rigid body satellites based on attitude quaternions, and simplify them to obtain the quaternion attitude model; S2: Use graph theory to describe the communication topology between satellites, and design a collaborative consistency control protocol for multiple satellites based on the quaternion attitude model constructed in step S1; S3: Based on the quaternion attitude model obtained in step S1, a multi-satellite common attitude constraint protocol based on obstacle Lyapunov function is designed; S4: Use the designed consistency control protocol and attitude constraint protocol to generate a collaborative control protocol under common attitude constraints to achieve collaborative control of multiple rigid body satellites.

2. The method for cooperative control of multiple rigid body satellites under common attitude constraints according to claim 1, characterized in that: The specific method for constructing the attitude kinematics and dynamics of the multi-rigid body satellite based on the attitude quaternion in step S1 is: Consider a multi-satellite coordinated control system consisting of n satellites. Assume that the attitude quaternion part of the i-th satellite is [q i ,q i0 ] T , where q i =[q i1 ,q i2 ,q i3 ] T is the vector part of the quaternion; q i0 is the scalar part of the quaternion; based on the defined attitude quaternion, the attitude kinematics and dynamics of multiple satellites are obtained by the following formula: in, Q i The derivative with respect to time; ω i =[ω i1 ,ω i2 ,ω i3 ] T is the angular velocity of the ith satellite in the body coordinate system, ω i The derivative with respect to time; J i is the moment of inertia of the ith satellite, τ i =[τ i1 ,τ i2 ,τ i3 ] T is the control torque of the ith satellite; E i =0.5(S(q i )+q 0i I3), I3 is the third-order unit matrix, S(ω i ) represents the following matrix: S(q i ) represents the following matrix:

3. The method for cooperative control of multiple rigid body satellites under common attitude constraints according to claim 2, characterized in that: In step S1, the attitude kinematics and dynamics of the multi-rigid body satellite are simplified by introducing new variables to obtain a quaternion attitude model, specifically: Define a new variable v i =E i ω i =[v i1 ,v i2 ,v i3 ] T , then the simplified attitude kinematics and dynamics of the ith satellite are in, Yes i Derivative with respect to time; is the matrix E i The inverse matrix of is a matrix The transposed matrix of For E i The derivative with respect to time, S(v i ) represents the following matrix:

4. The method for cooperative control of multiple rigid body satellites under common attitude constraints according to claim 1, characterized in that: The specific method of using graph theory to describe the communication topology structure between satellites in step S2 is: An undirected graph G = (s, ε, A) is used to describe the communication topology of n satellites; Where s={s1,...,s n } represents a finite non-empty set of n satellites; ε∈(s×s) represents an edge set; A=[a ij ]∈R n×n represents the adjacency matrix of the graph G, and the symbol R represents the set of all real numbers; If there is an edge from the i-th satellite to the j-th satellite (s i ,s j )∈ε, then a ij >0, otherwise a ij =0; therefore, satellite node s i The neighbor nodes of i ={j:(v i ,v j )∈ε}; On this basis, the degree of the i-th satellite node is defined as Then the degree matrix and Laplacian matrix of graph G are D=diag{d1,...,d n }∈R n×n and L = DA; Define the expected signal receiving matrix as B = diag{b1,...,b n }, when satellite i can obtain the expected attitude signal, then b i >0, otherwise b i =0.

5. The method for cooperative control of multiple rigid body satellites under common attitude constraints according to claim 4, characterized in that: The design method of the multi-satellite collaborative consistency control protocol in step S2 is: Based on the constructed quaternion attitude model, the following collaborative consistency control protocol for the i-th satellite is designed: Among them, k1>0 is the gain of the control protocol, q d is the expected attitude value that all satellites want to reach.

6. The method for cooperative control of multiple rigid body satellites under common attitude constraints according to claim 3, characterized in that: The design method of the multi-satellite common attitude constraint protocol in step S3 is: A1: Define the common attitude constraints that satellites need to satisfy and the relative constraints that satellites need to satisfy; A2: Based on the quaternion attitude model, common attitude constraint values ​​and relative constraint values, a common attitude constraint protocol based on obstacle Lyapunov function is designed.

7. The method for cooperative control of multiple rigid body satellites under common attitude constraints according to claim 6, characterized in that: The step A1 is specifically as follows: The attitude constraint value of the i-th satellite in the satellite constellation is defined as M k =[M k1 ,M k2 ,M k3 ] T , where M k1 >0,M k2 >0,M k3 >0 is a normal number; that is, the i-th satellite is required to satisfy the following conditions during the control process: |q i1 |<M k1 ,|q i2 |<M k2 ,|q i3 |<M k3 ,i=1,...,n Define the relative attitude constraint value between the i-th satellite in the satellite cluster and its neighboring satellites as N k =[N k1 ,N k2 ,N k3 ] T , where N k1 >0,N k2 >0,N k3 >0 is a normal number; that is, the i-th satellite is required to satisfy the following conditions during the control process: |q i1 -q j1 |<N k1 ,|q i2 -q j2 |<N k2 ,|q i3 -q j3 |<N k3 ,i=1,...,n.j∈Γ i 。 8. The method for cooperative control of multiple rigid body satellites under common attitude constraints according to claim 7, characterized in that: The step A2 is specifically as follows: Based on the simplified quaternion attitude model, the following common attitude constraint protocol is designed for the i-th satellite: Among them, k2, k3v0; 3 / 4<α<1 is the ratio of two positive odd numbers; Represents v i 1 / (2α-1)th power; represent 1 / (2α-1)th power; Represents σ i 2α-1 power.

9. The method for cooperative control of multiple rigid body satellites under common attitude constraints according to claim 8, characterized in that: The step S4 is specifically as follows: According to the designed consistency control protocol and common attitude constraint protocol, the following cooperative control protocol under common attitude constraint is generated for the i-th satellite: t i =S(ω i )J i oh i +r i +u i 。

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