A cooperative control method for multi-rigid-body satellites under common attitude constraints

Abstract

This invention discloses a cooperative control method for multiple rigid-body satellites under common attitude constraints, comprising: constructing the attitude kinematics and dynamics of multiple rigid-body satellites based on attitude quaternions, and simplifying them to obtain a quaternion attitude model; describing the communication topology between satellites using graph theory, and designing a cooperative consistency control protocol for multiple satellites based on the quaternion attitude model constructed in step S1; designing a multi-satellite common attitude constraint protocol based on the quaternion attitude model and a barrier Lyapunov function; and generating a cooperative control protocol under common attitude constraints using the designed consistency control protocol and attitude constraint protocol to achieve cooperative control of multiple rigid-body satellites. This invention achieves stable attitude control under common attitude constraints through cooperative control among multiple satellites, ensuring high-precision attitude maintenance capability of multiple rigid-body satellites in complex space environments, and improving the robustness and reliability of the system.

Description

Technical Field

[0001] This invention belongs to the field of automatic control and relates to multi-rigid-body satellite cooperative control, specifically to a multi-rigid-body satellite cooperative control method under common attitude constraints. Background Technology

[0002] Multi-rigid-body satellite cooperative control systems are a key area of ​​research in current space missions, especially in the complex space environment. Achieving efficient cooperative control of multiple satellites while meeting attitude constraints has become a major research focus. In practical applications, precise attitude control of satellites is crucial for ensuring the effective operation of satellite constellations. This control involves not only traditional attitude-maintaining tasks, such as multi-satellite formation flying and space station docking, but also attitude constraint requirements under specific conditions, such as preventing sensitive equipment on satellites from being exposed to direct sunlight or other harmful radiation sources. These attitude constraints are significant for extending satellite lifespan, ensuring normal equipment operation, and improving the overall mission success rate.

[0003] Currently, the cooperative control technology for multi-rigid-body satellites mainly relies on independent attitude control systems. However, when meeting common action objectives, attitude constraints are often not completely unified, leading to attitude incoordination between satellites and affecting the overall mission accuracy and efficiency. 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 cooperative attitude constraint requirements in multi-satellite systems. When facing multi-satellite cooperative missions, these algorithms may lead to frequent attitude adjustments, increased fuel consumption, or even mission failure.

[0004] Furthermore, while some cooperative control schemes for multi-satellite systems have been proposed in the existing technology, most schemes exhibit certain limitations when dealing with complex attitude constraints. For example, some algorithms handle satellite attitude constraints in a relatively simple way, failing to effectively avoid violations of attitude constraints in dynamic environments; while other schemes, although able to take attitude constraints into account, involve a large computational load in the cooperative consistency control among multiple satellites, limiting the real-time performance and reliability of the system. Summary of the Invention

[0005] Objective: To overcome the shortcomings of existing technologies, this invention provides a cooperative control method for multiple rigid-body satellites under common attitude constraints, enabling consistent cooperative control of multiple satellites while meeting specific attitude limitations. Through cooperative control among multiple satellites, stable attitude control under common attitude constraints is achieved, ensuring high-precision attitude maintenance of multiple rigid-body satellites in complex space environments and improving the robustness and reliability of the system.

[0006] Technical Solution: To achieve the above objectives, this invention provides a multi-rigid-body satellite cooperative control method under common attitude constraints, comprising the following steps:

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

[0008] S2: Use graph theory to describe the communication topology between satellites, and design a multi-satellite cooperative consistency control protocol based on the quaternion attitude model constructed in step S1.

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

[0010] S4: Utilize the designed consistency control protocol and attitude constraint protocol to generate a cooperative control protocol under common attitude constraints, thereby realizing cooperative control of multi-rigid-body satellites.

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

[0012] Consider a multi-satellite cooperative control system consisting of n satellites. Assume 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 The vector part of the quaternion; q i0 For the scalar part of the quaternion; based on the defined attitude quaternion, the attitude kinematics and dynamics of the multi-satellite are obtained by the following equation:

[0013]

[0014] in, For q i The derivative with respect to time; ω i =[ω i1 ,ω i2 ,ωi3 ] T Let be the angular velocity of the i-th satellite in the body coordinate system. For ω i The derivative with respect to time; J i Let τ be the moment of inertia of the i-th satellite. i =[τ i1 ,τ i2 ,τ i3 ] T E represents the control torque of the i-th satellite. i =0.5(S(q) i )+q 0i I3), where I3 is a third-order identity matrix, S(ω) i The matrix is ​​represented as follows:

[0015]

[0016] S(q i The matrix is ​​represented as follows:

[0017]

[0018] Furthermore, in step S1, a quaternion attitude model is obtained by simplifying the attitude kinematics and dynamics of the multi-rigid-body satellite by introducing new variables, 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 i-th satellite are as follows:

[0020]

[0021] in, It is v i The derivative with respect to time; It is matrix E i The inverse matrix, It is a matrix The transpose of the matrix; For E i The derivative with respect to time, S(v) i The matrix is ​​represented as follows:

[0022]

[0023] Furthermore, the specific method for describing the communication topology between satellites using graph theory in step S2 is as follows:

[0024] An undirected graph G = (s, ε, A) is used to describe the communication topology of n satellites; where s = {s1, ..., s2} n} represents a finite non-empty set of n satellites; ε∈(s×s) represents the edge set; A=[a ij ]∈R n×n Let R represent the adjacency matrix of graph G, and let R represent the set of all real numbers.

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

[0026] Furthermore, to describe the satellite's reception of the desired attitude signal, the desired signal reception matrix is ​​defined as B = diag{b1,...,b}. n When satellite i can acquire the desired attitude signal, then b i >0, otherwise b i =0.

[0027] Furthermore, the design method for the multi-satellite cooperative consensus control protocol in step S2 is as follows:

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

[0029]

[0030] Where k1 > 0 is the gain of the control protocol, q d This represents the desired attitude value that all satellites are expected to reach.

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

[0032] A1: Define the common attitude constraints that satellites must meet and the relative constraints that satellites must meet;

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

[0034] Further, step A1 specifically includes:

[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 , of which M k1 >0,M k2 >0,M k3 >0 represents a positive constant; that is, the i-th satellite is required to satisfy the following 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 constellation and its neighboring satellites as N. k =[N k1 N k2 N k3 ] T , where N k1 >0,N k2 >0,N k3 >0 represents a positive constant; that is, the i-th satellite is required to satisfy the following 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] Further, step A2 specifically includes:

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

[0041]

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

[0043] Further, step S4 specifically includes:

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

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

[0046] This invention addresses the problems of insufficient attitude constraint handling and low collaborative control efficiency in current multi-rigid-body satellite collaborative control systems by providing a novel control protocol and system capable of achieving efficient collaborative control under complex attitude constraints. This novel control method and system not only ensures the collaborative consistency of satellite swarms under shared attitude constraints but also improves control accuracy and mission success rate in the variable space environment, further promoting the practical application of multi-satellite collaborative missions.

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

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

[0049] 2. The cooperative attitude constraint controller provided by this invention has a simple structure, is easy to implement, and is relatively friendly to the hardware environment used. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the control method of the present invention;

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

[0052] Figure 3 These are the attitude response curves of the four rigid body satellites in this embodiment;

[0053] Figure 4 The following are the angular velocity response curves of the four rigid body satellites in this embodiment;

[0054] Figure 5 The control torque response curves for the four rigid body satellites in this embodiment are shown. Detailed Implementation

[0055] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0056] like Figure 1 As shown, this invention provides a multi-rigid-body satellite cooperative control method under common attitude constraints, comprising the following steps:

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

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

[0059] Consider a multi-satellite cooperative control system consisting of n satellites. Assume 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 The vector part of the quaternion; q i0 For the scalar part of the quaternion; based on the defined attitude quaternion, the attitude kinematics and dynamics of the multi-satellite are obtained by the following equation:

[0060]

[0061] in, For q i The derivative with respect to time; ω i =[ω i1 ,ω i2 ,ω i3 ] T Let be the angular velocity of the i-th satellite in the body coordinate system. For ω i The derivative with respect to time; J iLet τ be the moment of inertia of the i-th satellite. i =[τ i1 ,τ i2 ,τ i3 ] T E represents the control torque of the i-th satellite. i =0.5(S(q) i )+q 0i I3), where I3 is a third-order identity matrix, S(ω) i The matrix is ​​represented as follows:

[0062]

[0063] S(q i The matrix is ​​represented as follows:

[0064]

[0065] By introducing new variables to simplify the attitude kinematics and dynamics of a multi-rigid-body satellite, a quaternion attitude model is obtained, 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 i-th satellite are as follows:

[0067]

[0068] in, It is v i The derivative with respect to time; It is matrix E i The inverse matrix, It is a matrix The transpose of the matrix; For E i The derivative with respect to time, S(v) i The matrix is ​​represented as follows:

[0069]

[0070] S2: Use graph theory to describe the communication topology between satellites, and design a multi-satellite cooperative consistency control protocol based on the quaternion attitude model constructed in step S1.

[0071] An undirected graph G = (s, ε, A) is used to describe the communication topology of n satellites; where s = {s1, ..., s2} n} represents a finite non-empty set of n satellites; ε∈(s×s) represents the edge set; A=[a ij ]∈R n＝n Let R represent the adjacency matrix of graph G, and let R represent the set of all real numbers.

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

[0073] Furthermore, to describe the satellite's reception of the desired attitude signal, the desired signal reception matrix is ​​defined as B = diag{b1,...,b}. n When satellite i can acquire the desired attitude signal, then b i >0, otherwise b i =0.

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

[0075]

[0076] Where k1>0 is the gain of the control protocol, q d This represents the desired attitude value that all satellites are expected to reach.

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

[0078] A1: Define the common attitude constraints that satellites must meet and the relative constraints that satellites must meet;

[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 , of which M k1 >0,M k2 >0,Mk3 >0 represents a positive constant; that is, the i-th satellite is required to satisfy the following during the control process:

[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 constellation and its neighboring satellites as N. k =[N k1 N k2 N k3 ] T , where N k1 >0,N k2 >0,N k3 >0 represents a positive constant; that is, the i-th satellite is required to satisfy the following 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 values, and relative constraint values, design a common attitude constraint protocol based on the obstacle Lyapunov function;

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

[0085]

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

[0087] S4: Utilize the designed consistency control protocol and attitude constraint protocol to generate a cooperative control protocol under common attitude constraints, thereby realizing cooperative control of multi-rigid-body satellites;

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

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

[0090] To verify the effectiveness and impact of the present invention, this embodiment employs simulation experiments and analysis, as detailed below:

[0091] In this embodiment, MATLAB 2023b is used as the simulation software to simulate the attitude control of four identical satellites, and their inertia matrices are as follows:

[0092]

[0093] The communication topology diagram of the four satellites is as follows: Figure 2 As shown, where a 12 =a 13 =a 34 =1. Furthermore, only the first satellite can receive the reference desired attitude command signal, i.e., b1 = 1. Assume 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 for the four satellites is selected as M. k =[0.6,0.65,0.7] T The relative attitude constraint is N. k=[1,1,1] T The reference expectation signal for the four satellites is q. d =[0,0,0] T .

[0095] Figure 3 Attitude response curves based on quaternions for four satellites are presented. Figure 3 It can be seen from this that the attitudes of all four satellites can reach the desired attitude q. d Furthermore, during satellite control, the attitudes of all four satellites can satisfy a common attitude constraint M. k .

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

[0097] Figure 5 The response curves of the control torque for four satellites are presented. Figure 5 It can be seen that the control torque of the four satellites can achieve the control of the four satellites.

[0098] The simulation results above clearly show that the multi-rigid-body satellite cooperative control protocol and system under common attitude constraints proposed in this invention can quickly track the desired attitude signal. Furthermore, during the control process, the attitude is strictly limited to the set common constraints.

[0099] In summary, the multi-rigid-body satellite cooperative control method under common attitude constraints provided by this invention is fast, robust, and can achieve consistent control of multiple satellites under attitude constraints.

Claims

1. A multi-rigid-body satellite cooperative control method under common attitude constraints, characterized in that, Includes the following steps: S1: Construct the attitude kinematics and dynamics of a multi-rigid-body satellite based on attitude quaternions, and simplify them to obtain a quaternion attitude model; S2: Use graph theory to describe the communication topology between satellites, and design a multi-satellite cooperative consistency control protocol based on the quaternion attitude model constructed in step S1. S3: Based on the quaternion attitude model obtained in step S1, design a multi-satellite common attitude constraint protocol based on the obstacle Lyapunov function; S4: Utilize the designed consistency control protocol and attitude constraint protocol to generate a cooperative control protocol under common attitude constraints, thereby realizing cooperative control of multi-rigid-body satellites; The design method for the multi-satellite cooperative consensus control protocol in step S2 is as follows: Based on the constructed quaternion attitude model, the following cooperative consensus control protocol for the i-th satellite is designed: Where k1 > 0 is the gain of the control protocol, q d The desired attitude values ​​that all satellites are expected to reach; The design method for the multi-satellite common attitude constraint protocol in step S3 is as follows: A1: Define the common attitude constraints that satellites must meet and the relative constraints that satellites must meet; A2: Based on the quaternion attitude model, common attitude constraint values, and relative constraint values, design a common attitude constraint protocol based on the obstacle Lyapunov function; Step A1 is 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 , of which M k1 >0,M k2 >0,M k3 >0 represents a positive constant; that is, the i-th satellite is required to satisfy the following 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 constellation and its neighboring satellites as N. k =[N k1 N k2 N k3 ] T , where N k1 >0,N k2 >0,N k3 >0 represents a positive constant; that is, the i-th satellite is required to satisfy the following 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 ; Step A2 is as follows: Based on the simplified quaternion attitude model, the following common attitude constraint protocol is designed for the i-th satellite: Where k2, k3 > 0; 3 / 4 < α < 1 is the ratio of two positive odd numbers; Represents v i 1 / (2α-1) power; represent 1 / (2α-1) power; Represents σ i 2α-1; Step S4 is as follows: Based on the designed consistency control protocol and common attitude constraint protocol, the following cooperative control protocol under common attitude constraints is generated for the i-th satellite: t i =S(ω i )J i oh i +r i +u i 。 2. The multi-rigid-body satellite cooperative control method under common attitude constraints according to claim 1, characterized in that, The specific method for constructing the attitude kinematics and dynamics of a multi-rigid-body satellite based on attitude quaternions in step S1 is as follows: Consider a multi-satellite cooperative control system consisting of n satellites. Assume 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 The vector part of the quaternion; q i0 For the scalar part of the quaternion; based on the defined attitude quaternion, the attitude kinematics and dynamics of the multi-satellite are obtained by the following equation: in, For q i The derivative with respect to time; ω i =[ω i1 ,ω i2 ,ω i3 ] T Let be the angular velocity of the i-th satellite in the body coordinate system. For ω i The derivative with respect to time; J i Let τ be the moment of inertia of the i-th satellite. i =[τ i1 ,τ i2 ,τ i3 ] T E represents the control torque of the i-th satellite. i =0.5(S(q) i )+q 0i I3), where I3 is a third-order identity matrix, S(ω) i ) represents the following matrix: S(q i The matrix is ​​represented as follows:

3. The multi-rigid-body satellite cooperative control method under common attitude constraints according to claim 2, characterized in that, In step S1, a quaternion attitude model is obtained by simplifying the attitude kinematics and dynamics of the multi-rigid-body satellite by introducing new variables. 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 i-th satellite are as follows: in, It is v i The derivative with respect to time; It is matrix E i The inverse matrix, It is a matrix The transpose of the matrix; For E i The derivative with respect to time, S(v) i ) represents the following matrix:

4. The multi-rigid-body satellite cooperative control method under common attitude constraints according to claim 1, characterized in that, The specific method for describing the communication topology between satellites using graph theory in step S2 is as follows: 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 the edge set; A=[a ij ]∈R n×n Let R represent the adjacency matrix of graph G, and let R represent the set of all real numbers. If there exists an edge (s) connecting the i-th satellite to the j-th satellite. i ,s j If )∈ε, then a ij >0, otherwise a ij =0; therefore, satellite node s i The neighbor nodes are represented as Γ i ={j:(v i ,v j Based on this, the degree of the i-th satellite node is defined as )∈ε}; Then the degree matrix and Laplacian matrix of graph G are respectively D=diag{d1,...,d n }∈R n×n With L=DA; Define the desired signal reception matrix as B = diag{b1,...,b} n When satellite i can acquire the desired attitude signal, then b i >0, otherwise b i =0.

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