A Multi-Spacecraft Attitude Synchronization and Tracking Control Method Based on Event-Triggered Communication

Abstract

This invention discloses a multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication, relating to the field of multi-spacecraft attitude synchronization and tracking technology. The method includes the following steps: designing a distributed attitude filter for the spacecraft; designing event-triggered communication conditions for the spacecraft; and designing an adaptive tracking controller for the spacecraft based on the distributed attitude filter and the event-triggered communication conditions to complete the multi-spacecraft attitude synchronization and tracking control based on event-triggered communication. This invention solves the problems of degraded system performance caused by existing technologies and the lack of a control method for spacecraft attitude synchronization and tracking based on trigger communication.

Description

Technical Field

[0001] This invention relates to the field of attitude synchronization and tracking technology for multiple spacecraft, and in particular to a method for attitude synchronization and tracking control of multiple spacecraft based on event-triggered communication. Background Technology

[0002] In recent years, with the development of aerospace technology, multi-spacecraft formation flying has attracted great attention from experts and scholars due to its wide range of applications in multi-satellite coordination, Earth monitoring, and planetary observation. Attitude synchronization and tracking control is one of the fundamental research problems in this field, aiming to design an attitude synchronization and tracking method for spacecraft so that the attitudes of all spacecraft tend to be consistent and track the desired attitude.

[0003] Effective communication between spacecraft is a prerequisite for achieving attitude synchronization. Current spacecraft communication typically employs a constant-period communication method, meaning that information is exchanged between spacecraft at fixed time intervals. This method results in a significant amount of communication even when no information exchange is needed, thus wasting communication and computing resources. To address this issue, researchers have proposed event-triggered communication mechanisms, where spacecraft communicate only when a specific event occurs. Compared to constant-period communication, event-triggered communication significantly reduces the amount of communication and conserves communication resources.

[0004] Currently, most attitude synchronization and tracking methods are based on precisely known moments of inertia, which can easily lead to reduced system performance. At the same time, existing technologies lack control methods for spacecraft attitude synchronization and tracking based on trigger communication. Summary of the Invention

[0005] To address the aforementioned shortcomings in the prior art, this invention provides a multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication, which solves the problems of reduced system performance caused by the prior art and the lack of a control method for spacecraft attitude synchronization and tracking based on trigger communication.

[0006] To achieve the aforementioned objectives, the present invention employs the following technical solution: a method for multi-spacecraft attitude synchronization and tracking control based on event-triggered communication, comprising the following steps:

[0007] S1: Design a distributed attitude filter for spacecraft;

[0008] S2: Event-triggered communication conditions for designing spacecraft;

[0009] S3: Based on distributed attitude filters and event-triggered communication conditions, design an adaptive tracking controller for spacecraft to achieve multi-spacecraft attitude synchronization and tracking control based on event-triggered communication.

[0010] The beneficial effects of the above scheme are: by designing a distributed attitude filter and event-triggered communication conditions for the spacecraft, and then designing an adaptive tracking controller for the spacecraft, this invention makes full use of the advantages of event-triggered communication, greatly reduces the amount of communication, saves communication resources, and solves the problems of reduced system performance caused by existing technologies and the lack of control methods for spacecraft attitude synchronization and tracking based on trigger communication.

[0011] Furthermore, the distributed attitude filter in S1 is:

[0012]

[0013]

[0014]

[0015]

[0016] k i,2 =1+d i,2

[0017] Among them, F i,1 Let F be the first state of the distributed attitude filter of spacecraft i. i,2 For the second state of the distributed attitude filter of spacecraft i, F i,3 Let k be the third state of the distributed attitude filter of spacecraft i, where the superscript · denotes the derivative with respect to time t. i,1 k is the first coefficient. i,2 a is the second coefficient. ij Let i and j be the elements in the adjacency matrix, i and j be distinct spacecraft, N be the number of spacecraft, and F be the number of spacecraft. j,3 For the third state of the distributed attitude filter of spacecraft j, μ i The diagonal elements in the traction matrix, with the superscript "-" indicating the state of the attitude filter at the trigger moment, σ r For the desired attitude of the spacecraft, d i,1 d is the first positive parameter. i,2 It is the second positive parameter.

[0018] The beneficial effect of the above-mentioned further scheme is that, since only some spacecraft can acquire the desired attitude, a distributed attitude filter as described above is designed for each spacecraft.

[0019] Furthermore, the event-triggered communication conditions in S2 are as follows:

[0020]

[0021] in, Let inf{·} be the current moment when the event triggers the communication condition, and let inf{·} be the infimum of the set. To meet the preset event trigger communication conditions at the time, x i (t) is a clock-like scalar.

[0022] The beneficial effect of the above-mentioned further solution is that, through the above technical solution, for the distributed attitude filter, trigger conditions are designed to manage the data transmission of state.

[0023] Furthermore, the clock-like scalar x i The parameter update law for (t) is:

[0024]

[0025] Among them, D i k is a variable, the superscript ∧ represents the estimated value. i It is the third positive parameter;

[0026]

[0027] Where P is the first positive definite matrix, H is the regression matrix, I3 is the 3×3 identity matrix, Q is the second positive definite matrix, and λ min (·) is the smallest eigenvalue. Let denote the Kronecker product of two matrices, and ‖·‖ denote the matrix norm.

[0028] The beneficial effect of the above further scheme is that the above formula can be used to update clock-like scalars.

[0029] Furthermore, variable D i The parameter update law is:

[0030]

[0031]

[0032] in, for The derivative of r with respect to time t i ε is the fourth positive parameter. i To represent measurement error, the superscript T denotes the transpose of the matrix.

[0033] The beneficial effect of the above further scheme is that the above formula can be used to update variable D. i .

[0034] Furthermore, the design of the adaptive tracking controller for the spacecraft in S3 includes the following steps:

[0035] S3-1: Define tracking error and sliding mode error, and obtain the kinematic and dynamic models of the spacecraft according to the Euler-Lagrange equations, as follows:

[0036]

[0037] M i (σ i ) = G -T (σ i )J i G -1 (σ i )

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Among them, M i (·) is a symmetric positive definite matrix, σ i For the corrected Rodriguez parameter, s i For sliding mode error, C i (·) represents the first matrix function, H(·) represents the regression matrix function, and c i z is a positive constant. i To track the error, the superscript ".." represents the second derivative with respect to time t, and θ i To set parameters, G is the second matrix, u i Let G(·) be the control input for spacecraft i, and J be the second matrix function. i It is a symmetric positive definite inertial matrix, the superscript × indicates the cross product operator, and the superscript -1 indicates the inverse matrix;

[0044] S3-2: Based on the kinematic and dynamic models of the spacecraft, design the adaptive tracking controller for the spacecraft, using the following formula:

[0045]

[0046]

[0047] Among them, K i It is a 3×3 positive definite matrix.

[0048] The beneficial effect of the above-mentioned further scheme is that, through the above technical scheme, based on the Euler-Lagrange equation and the defined sliding mode error, the design of the spacecraft's adaptive attitude synchronization and tracking controller is completed.

[0049] Furthermore, in S3-2 The parameter update law is:

[0050]

[0051] Among them, Γ i It is a 6×6 positive definite matrix.

[0052] The beneficial effect of the above further solution is that the parameters used to update the design are obtained through the above formula. Attached Figure Description

[0053] Figure 1 This is a flowchart of a multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication.

[0054] Figure 2 This is a diagram of the communication topology of multiple spacecraft with a fixed navigator.

[0055] Figure 3 This is a simulation diagram of the attitude synchronization of multiple spacecraft.

[0056] Figure 4 This is a simulation diagram of angular velocity tracking for multiple spacecraft.

[0057] Figure 5 Simulation diagram of control inputs for multiple spacecraft.

[0058] Figure 6 This is a simulation diagram of the triggering time for multiple spacecraft. Detailed Implementation

[0059] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0060] like Figure 1 As shown, a method for multi-spacecraft attitude synchronization and tracking control based on event-triggered communication includes the following steps:

[0061] S1: Design a distributed attitude filter for spacecraft;

[0062] S2: Event-triggered communication conditions for designing spacecraft;

[0063] S3: Based on distributed attitude filters and event-triggered communication conditions, design an adaptive tracking controller for spacecraft to achieve multi-spacecraft attitude synchronization and tracking control based on event-triggered communication.

[0064] In one embodiment of the present invention, the communication topology between N spacecraft is a fixed directed graph. It means that, among them, Represents a set of nodes. Let N represent the set of edges. If two spacecraft satisfy (i,j)∈ε, it means that spacecraft j can receive information from spacecraft i, but the converse is not necessarily true. In this case, spacecraft i is called an in-degree neighbor of spacecraft j, and spacecraft j is called an out-degree neighbor of spacecraft i. Let N be the set of in-degree neighbors of spacecraft i. i Directed graph The adjacency matrix is ​​defined as A = [a ij ]∈R N×N And all its elements are non-negative: if (j,i)∈ε, then a ij =1; otherwise a ij =0. In this scheme, the existence of... Therefore, the diagonal elements of the adjacency matrix A are all 0, i.e., a ii =0. Define the in-degree matrix as Δ, and its diagonal elements are... Accordingly, the Laplace matrix is ​​defined as L = Δ - A.

[0065] The control objective of this invention is to design a fully distributed adaptive attitude synchronization and tracking method for N spacecraft based on event-triggered communication, such that: (1) all closed-loop signals are globally consistent and bounded, and each spacecraft excludes Zeno behavior; (2) for the attitude synchronization and tracking of a static navigator, all spacecraft can progressively track the navigator's attitude σ. r ∈R 3 That is, for satisfy 03 represents a 3×1 column vector consisting entirely of 0 elements.

[0066] In order to achieve the above control objectives, without loss of generality, it is assumed that only some spacecraft can acquire the desired attitude σ. r If spacecraft i can obtain the desired attitude σ r Then use μ i =1 indicates that otherwise, μ i =0. Assume a directed communication topology between N spacecraft. It contains a spanning tree, meaning that any other node can be accessed from the root node of this communication topology, and the spacecraft located at the root node can obtain the desired attitude. Define B = diag{μ1,...,μ N Let} be the traction matrix. Under the above assumptions, it can be known that matrix H = L + B is a non-singular matrix, defined as [P1,…,P...]. N ] T =H -T [1,…,1]T And P = diag{P1,…,P N}, then P and Q = PH + H T P are all positive definite matrices.

[0067] Because this control method employs an event-triggered communication mechanism to control data transmission between spacecraft, for spacecraft i, This indicates the triggering time of the triggering condition. At these times, spacecraft i sends its distributed attitude observer status to its out-degree neighbors and updates its attitude observer information.

[0068] Since only some spacecraft can acquire the desired attitude, a distributed attitude filter is designed for each spacecraft as follows:

[0069] The distributed attitude filter in S1 is:

[0070]

[0071]

[0072]

[0073]

[0074] k i,2 =1+d i,2

[0075] Among them, F i,1 Let F be the first state of the distributed attitude filter of spacecraft i. i,2 For the second state of the distributed attitude filter of spacecraft i, F i,3 Let k be the third state of the distributed attitude filter of spacecraft i, where the superscript · denotes the derivative with respect to time t. i,1 k is the first coefficient. i,2 a is the second coefficient. ij Let i and j be the elements in the adjacency matrix, i and j be distinct spacecraft, N be the number of spacecraft, and F be the number of spacecraft. j,3 For the third state of the distributed attitude filter of spacecraft j, μ i The diagonal elements in the traction matrix, with the superscript "-" indicating the state of the attitude filter at the trigger moment, σ r For the desired attitude of the spacecraft, d i,1 d is the first positive parameter. i,2 It is the second positive parameter.

[0076] The event-triggered communication conditions in S2 are:

[0077]

[0078] in, Let inf{·} be the current moment when the event triggers the communication condition, and let inf{·} be the infimum of the set. To meet the preset event trigger communication conditions at the time, x i (t) is a clock-like scalar.

[0079] clock-like scalar x i The parameter update law for (t) is:

[0080]

[0081] Among them, D i k is a variable, the superscript ∧ represents the estimated value. i It is the third positive parameter;

[0082]

[0083] Where P is the first positive definite matrix, H is the regression matrix, I3 is the 3×3 identity matrix, Q is the second positive definite matrix, and λ min (·) is the smallest eigenvalue. Let ||·|| denote the Kronecker product of two matrices, and ||·|| denote the matrix norm.

[0084] Variable D i The parameter update law is:

[0085]

[0086]

[0087] in, for The derivative of r with respect to time t i ε is the fourth positive parameter. i To represent measurement error, the superscript T denotes the transpose of the matrix.

[0088] Without loss of generality, it is assumed that the states used in the controller design are appropriately represented in the same coordinate system. The tracking error z is defined as follows. i and sliding mode error s i And according to the Euler-Lagrange equation, we can obtain:

[0089] The design of an adaptive tracking controller for a spacecraft in S3 includes the following steps:

[0090] S3-1: Define tracking error and sliding mode error, and obtain the kinematic and dynamic models of the spacecraft according to the Euler-Lagrange equations, as follows:

[0091]

[0092] M i (σ i ) = G -T (σ i )J i G -1 (σ i )

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] Among them, M i (·) is a symmetric positive definite matrix, σ i For the corrected Rodriguez parameter, s i For sliding mode error, C i (·) represents the first matrix function, H(·) represents the regression matrix function, and c i z is a positive constant. i To track the error, the superscript ".." represents the second derivative with respect to time t, and θ i To set parameters, G is the second matrix, u i Let G(·) be the control input for spacecraft i, and J be the second matrix function. i It is a symmetric positive definite inertial matrix, the superscript × indicates the cross product operator, and the superscript -1 indicates the inverse matrix;

[0099] S3-2: Based on the kinematic and dynamic models of the spacecraft, design the adaptive tracking controller for the spacecraft, using the following formula:

[0100]

[0101]

[0102] Among them, K i It is a 3×3 positive definite matrix.

[0103] S3-2 The parameter update law is:

[0104]

[0105] Among them, Γ i It is a 6×6 positive definite matrix.

[0106] In summary, considering the dynamics and kinematics of multi-rigid spacecraft, under the reasonable assumptions described above, the distributed attitude filter, event triggering conditions, adaptive attitude synchronization and tracking controller, and parameter update law designed in this scheme can guarantee that all closed-loop signals are uniformly bounded, and that the attitude of all spacecraft can track the desired attitude σ. r ,Right now

[0107] In one embodiment of the present invention, to verify the effectiveness of the proposed multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication, the method was simulated using Matlab / Simulink. In the simulation, a case with four spacecraft was considered, and the unknown rotational inertia matrices J1 = [10,1,1; 1,10,1; 1,1,9] kg·m for each of the four spacecraft were given. 2 , J2=[15,2,1;2,9,3;1,3,9]kg·m 2 , J3=[9,1,3;1,8,2;3,2,8]kg·m 2 , J4=[12,3,2; 3,10,3; 2,3,10]kg·m 2 Set the desired attitude of the fixed navigator as σ. r =[0.5,0.3,1] T The communication topology between the four spacecraft is as follows: Figure 2 As shown, only spacecraft 1 can obtain the navigator's attitude information σ. r The initial attitude and filter initial state are set as follows: σ1(0) = F 1,1 (0)=F 1,2 (0)=F 1,3 (0) = [0.5, 0.6, 0.7] T σ2(0)=F 2,1 (0)=F 2,2 (0)=F 2,3 (0) = [0.4, 0.3, 0.2] T , σ3(0)=F 3,1 (0)=F 3,2 (0)=F 3,3 (0) = [0.3, 0.4, 0.5] T , σ4(0)=F 4,1 (0)=F 4,2 (0)=F 4,3 (0) = [0.6, 0.7, 0.8] T Set the initial angular velocity to ω. i (0) = [0,0,0] T Parameter estimation initial value initial value Other parameters are set to: d i,1 =5,d i,2 =5,c i =1,k i =0.1, K i =50I3,Γ i =I6, i=1,2,3,4.

[0108] Simulation results are as follows Figures 3 to 6 As shown, where, Figure 3 This demonstrates the spacecraft's progressive tracking of the desired attitude of a fixed navigator; Figure 4 This shows that the spacecraft's angular velocity converges to 0; by Figure 5 It can be seen that the control inputs of each spacecraft are bounded and free of chattering; in addition, Figure 6 The simulation results show that the event trigger time and minimum event interval for each spacecraft are calculated to be 0.112s, 0.216s, 0.233s, and 0.105s, respectively, which also means that Zeno behavior will not occur. Therefore, the simulation results above demonstrate that the multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication proposed in this invention is effective.

[0109] This invention solves the problem of attitude synchronization and tracking control of multiple spacecraft under event-triggered communication conditions, without requiring known rotational inertia parameters of the spacecraft. This invention designs event-triggered communication conditions and ensures the existence of a positive lower bound for the triggering time interval, effectively reducing the amount of communication between spacecraft, saving communication resources, and improving control performance.

[0110] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the invention.

Claims

1. A method for multi-spacecraft attitude synchronization and tracking control based on event-triggered communication, characterized in that, Includes the following steps: S1: Design a distributed attitude filter for spacecraft; S2: Event-triggered communication conditions for designing spacecraft; S3: Based on distributed attitude filters and event-triggered communication conditions, design an adaptive tracking controller for spacecraft to achieve multi-spacecraft attitude synchronization and tracking control based on event-triggered communication; The adaptive tracking controller for the spacecraft designed in S3 includes the following steps: S3-1: Define tracking error and sliding mode error, and obtain the kinematic and dynamic models of the spacecraft according to the Euler-Lagrange equations, as follows: in, It is a symmetric positive definite matrix. For the corrected Rodriguez parameters, For sliding mode error, For the first matrix function, For regression matrix functions, For positive integers, To track errors, superscript Indicates time The first derivative, superscript For time The second derivative, For spacecraft The first state of the distributed attitude filter, For spacecraft The second state of the distributed attitude filter, For spacecraft The third state of the distributed attitude filter, As the first coefficient, As the second coefficient, To set parameters, For the second matrix, For spacecraft The control input, For the second matrix function, The inertial matrix is ​​a symmetric positive definite matrix, with superscript... For cross product operators, superscript It is the inverse matrix. for The identity matrix, superscript This is the transpose of the matrix; S3-2: Based on the kinematic and dynamic models of the spacecraft, design the adaptive tracking controller for the spacecraft, using the following formula: in, for Positive definite matrix, superscript Indicates the state of the attitude filter at the trigger moment, superscript This is an estimated value.

2. The multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication according to claim 1, characterized in that, The distributed attitude filter in S1 is: in, For spacecraft The first state of the distributed attitude filter, For spacecraft The second state of the distributed attitude filter, For spacecraft The third state of the distributed attitude filter, superscript Indicates time The derivative, As the first coefficient, As the second coefficient, These are elements in the adjacency matrix. and For different spacecraft, For the number of spacecraft, For spacecraft The third state of the distributed attitude filter, The diagonal elements in the traction matrix, with superscripts This indicates the state of the attitude filter at the trigger moment. For the desired attitude of the spacecraft, As the first positive parameter, It is the second positive parameter.

3. The multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication according to claim 2, characterized in that, The event-triggered communication conditions in S2 are as follows: in, The current moment when the event triggers the communication conditions. Let the infimum of the set be... To meet the preset event trigger communication conditions at the time, It is a clock-like scalar.

4. The multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication according to claim 3, characterized in that, The clock-like scalar The parameter update law is: in, For variables, superscript This is an estimated value. It is the third positive parameter; in, It is the first positive definite matrix. For the regression matrix, for The identity matrix, It is the second positive definite matrix. It is the smallest eigenvalue. Denotes the Kronecker product of two matrices. Represents the matrix norm.

5. The multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication according to claim 4, characterized in that, The variable The parameter update law is: in, for Regarding time The derivative, It is the fourth positive parameter. To account for measurement error, superscript This is the transpose of the matrix.

6. The multi-spacecraft attitude synchronization and tracking control method based on event-triggered communication according to claim 5, characterized in that, In S3-2 The parameter update law is: in, for A positive definite matrix.

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