Spacecraft formation event-triggered cooperative attitude control method considering communication delay

Abstract

The application discloses a spacecraft formation event-triggered attitude coordination control method considering communication time delay, comprising the following steps: according to the communication topology structure of a spacecraft formation system, an attitude dynamics model of the spacecraft formation is established, which can consider external disturbance, model uncertainty and communication time delay; based on the attitude dynamics model, a nonlinear observer is constructed, which can observe the collective nonlinear term of the spacecraft formation system; based on the nonlinear observer, an event-triggered attitude coordination control law and an event-triggering mechanism are designed; according to the event-triggered attitude coordination control law, the attitude and angular velocity of the formation spacecraft are controlled, and according to the event-triggering mechanism, it is determined whether the corresponding event-triggered attitude coordination control law of the formation spacecraft needs to be updated and whether the state information of the formation spacecraft needs to be sent to the adjacent formation spacecraft. The application can consider the influence of disturbance, uncertainty and communication time delay, save the energy, communication and computing resources of the system while ensuring good control performance.

Description

Technical Field

[0001] This invention relates to the field of spacecraft control technology, and in particular to a spacecraft formation event-triggered attitude cooperative control method that takes into account communication latency. Background Technology

[0002] With the rapid development of aerospace microelectronics technology, the operational mode of a spacecraft formation flight system consisting of multiple small spacecraft has gradually become the main direction of spacecraft development. Compared with traditional single large spacecraft, spacecraft formation flight has stronger system performance, higher reliability, and better flexibility, and has great application value in fields such as Earth monitoring and deep space exploration. The attitude coordination control problem of spacecraft formation is one of the most critical and fundamental issues in spacecraft formation coordination control. In actual spacecraft formation flight missions, the goal of attitude coordination control is to design a coordination controller that enables the attitudes of each spacecraft in the formation to converge to the desired attitude.

[0003] However, small spacecraft are constrained by their size and mass, making their energy, communication, and computing resources extremely valuable. Continuous updates of the cooperative controller consume significant amounts of energy and computing resources from the formation spacecraft. Furthermore, information exchange between the formation spacecraft is fundamental to cooperative control; therefore, continuous updates of the cooperative controller require continuous communication between the formation spacecraft, which consumes considerable communication bandwidth. Thus, the resource constraints of the spacecraft formation system must be considered when designing a spacecraft formation attitude cooperative controller. To conserve spacecraft formation system resources, event-triggered attitude cooperative control methods are currently primarily used to design attitude cooperative controllers. These methods conserve resources by designing response conditions for the control system, and the cooperative controller only updates when these conditions are met.

[0004] During in-orbit operation, spacecraft formation systems are affected by disturbance torques such as aerodynamic torque and gravity gradient torque. Furthermore, as fuel is consumed, the moment of inertia of the formation spacecraft changes over time, leading to uncertainties in the attitude dynamics model. Simultaneously, due to the limited capacity of communication lines and the limited transmission power of communication equipment between formation spacecraft, communication delays are inevitable in information exchange. However, existing event-triggered attitude coordination control methods for spacecraft formations do not consider the impact of disturbances, uncertainties, and communication delays on the system, resulting in poor control performance, low operational stability of the event triggering mechanism, and a higher actual triggering frequency than the theoretical frequency, leading to significant resource consumption by the spacecraft formation system. Summary of the Invention

[0005] To address some or all of the technical problems existing in the prior art, the present invention provides a spacecraft formation event-triggered attitude cooperative control method that takes into account communication latency.

[0006] The technical solution of the present invention is as follows:

[0007] A spacecraft formation event-triggered attitude cooperative control method considering communication latency is provided, the method comprising:

[0008] Based on the communication topology of the spacecraft formation system, a spacecraft formation attitude dynamics model that can take into account external disturbances, model uncertainties, and communication delays is established.

[0009] Based on the spacecraft formation attitude dynamics model, a nonlinear observer capable of observing the lumped nonlinear terms of the spacecraft formation system is constructed.

[0010] Based on a nonlinear observer, an event-triggered attitude cooperative control law and an event-triggered mechanism are designed.

[0011] The attitude and angular velocity of the formation spacecraft are controlled according to the event-triggered attitude cooperative control law. The event-triggered mechanism determines whether it is necessary to update the event-triggered attitude cooperative control law corresponding to the formation spacecraft, and whether to send the status information of the formation spacecraft to its neighboring formation spacecraft.

[0012] In some possible implementations, the following spacecraft formation attitude dynamics model is established, taking into account external disturbances, model uncertainties, and communication delays:

[0013]

[0014] Among them, g i =J i T -1 (σ i )

[0015]

[0016]

[0017] e i The derivative, e i =αe 1i +e 2i , α represents a positive constant, n represents the number of spacecraft in the formation, and σ i This represents the attitude of the i-th formation spacecraft described by the modified Rodriguez parameters. σ i The derivative of σ jThis represents the attitude of the j-th formation spacecraft described by the modified Rodriguez parameters. σ j The derivative of , where t represents the time variable, T ij σ represents the communication delay between the j-th formation spacecraft and the i-th formation spacecraft. d Indicates the desired attitude of the formation of spacecraft. σ d The derivative of T i Let a represent the communication delay caused by the i-th formation spacecraft receiving the desired information. ij Let a represent the element in the i-th row and j-th column of the adjacency matrix A. Adjacency matrix A represents the communication connectivity between spacecraft in each formation. If the i-th spacecraft in a formation can receive information from the j-th spacecraft in a formation, then a... ij >0, otherwise a ij =0, b i Let b represent the i-th element of vector B. Vector B describes whether each formation spacecraft can obtain the desired information. If the i-th formation spacecraft can obtain the desired information, then b... i >0, otherwise b i =0, This represents the control input for the i-th spacecraft in the formation. Let T represent the inertial matrix of the i-th formation spacecraft. -1 (σ i ) represents T(σ i The inverse matrix of ) I3 represents a 3×3 identity matrix. σ i The transpose of ||·|| denotes the 2-norm for a three-dimensional vector. Let x be the skew-symmetric matrix, defined as follows: H represents the set of real numbers. i This represents the lumped nonlinear term of the spacecraft formation system. σ j The second derivative, σ d The second derivative, T(σ) i The derivative of ) This represents the combined disturbance of external disturbances and model uncertainties experienced by the i-th formation spacecraft.

[0018] In some possible implementations, the nonlinear observer is constructed as follows:

[0019]

[0020] in, express The derivative, Represents the nonlinear term h i The estimate, where r represents a positive constant. This indicates the current trigger time of the i-th formation spacecraft;

[0021] Defined as:

[0022]

[0023] express Moment e 1i The derivative, express Moment e 2i The derivative, express Moment express Moment express Moment express Moment σ i The second derivative, express Moment express Moment Indicates the time of triggering the i-th formation spacecraft. The moment when the latest status information of the j-th spacecraft has been received. Indicates the time of triggering the i-th formation spacecraft. The moment when the latest expected information has been received;

[0024] Defined as:

[0025]

[0026] Defined as:

[0027]

[0028] express and The upper bound of time t, This represents the m-th trigger time of the j-th formation spacecraft. express The communication delay between the j-th formation spacecraft and the i-th formation spacecraft at time j. express The communication delay caused by the i-th formation spacecraft receiving the desired information at time i.

[0029] In some possible implementations, the event-triggered attitude cooperative control law is:

[0030]

[0031] Where k represents a positive constant, express e of time i , express Moment

[0032] In some possible implementations, the event triggering conditions for the event triggering mechanism are designed as follows:

[0033]

[0034] Where δ represents a positive constant;

[0035] Defined as:

[0036]

[0037]

[0038] Defined as:

[0039]

[0040] express σ at time j , express σ at time d .

[0041] In some possible implementations, the event triggering mechanism is as follows:

[0042]

[0043] in, This indicates the next trigger time for the i-th formation spacecraft. express and The lower bound of time t.

[0044] In some possible implementations, the need to update the event-triggered cooperative control law corresponding to the formation spacecraft and whether to send the state information of the formation spacecraft to its neighboring formation spacecraft are determined based on the event triggering mechanism, including:

[0045] Determine if the event triggering condition is met. If so, update the event triggering attitude cooperative control law corresponding to the formation spacecraft and send the state information of the formation spacecraft to its neighboring formation spacecraft.

[0046] The main advantages of the technical solution of this invention are as follows:

[0047] The spacecraft formation event-triggered attitude cooperative control method of the present invention, which considers communication delay, can take into account the impact of disturbances, uncertainties and communication delays on the spacecraft formation system, and can improve the control performance, convergence accuracy and robustness of the control system. The implementation of the nonlinear observer and the event-triggered attitude cooperative control law does not require continuous communication between the formation spacecraft, which can save a lot of communication resources of the formation spacecraft. Furthermore, the formation spacecraft only updates its own controller when the triggering condition is met, which can significantly reduce the update frequency of the controller and save the energy and computing resources of the formation spacecraft. Attached Figure Description

[0048] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and constitute a part of this invention, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0049] Figure 1 This is a flowchart of a spacecraft formation event-triggered attitude cooperative control method considering communication latency, according to an embodiment of the present invention.

[0050] Figure 2 This is a schematic diagram of the communication topology of the spacecraft formation system in Example 1 of the present invention;

[0051] Figure 3 This is a schematic diagram of the simulation results of the observation error of the nonlinear term of the formation spacecraft in Example 1 of the present invention;

[0052] Figure 4 This is a schematic diagram of the attitude error simulation results of the formation spacecraft in Example 1 of the present invention;

[0053] Figure 5 This is a schematic diagram of the simulation results of the angular velocity error of the formation spacecraft in Example 1 of the present invention;

[0054] Figure 6 This is a schematic diagram of the control inputs for the formation spacecraft in Example 1 of the present invention;

[0055] Figure 7This is a schematic diagram of the trigger interval of the formation spacecraft in Example 1 of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0057] The technical solutions provided by the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0058] refer to Figure 1 An embodiment of the present invention provides a spacecraft formation event-triggered attitude cooperative control method considering communication latency, the method comprising the following steps S1-S4:

[0059] Step S1: Based on the communication topology of the spacecraft formation system, establish a spacecraft formation attitude dynamics model that can take into account external disturbances, model uncertainties, and communication delays.

[0060] In one embodiment of the present invention, taking the i-th formation spacecraft in a spacecraft formation system as an example, considering external disturbances and model uncertainties, the following attitude dynamics model is established:

[0061]

[0062] Where I3 represents a 3×3 identity matrix, σ represents the attitude of the i-th formation spacecraft described by the modified Rodriguez parameters. ix ,σ iy ,σ iz σ i Components along the x, y, and z axes of the body coordinate system σ i The derivative, σ i transpose, Let ω represent the angular velocity of the i-th formation spacecraft in the body coordinate system. ix ,ω iy ,ω iz They represent ω respectively i Components along the x, y, and z axes of the body coordinate system Represents ω i The derivative, Let represent the inertial matrix of the i-th formation spacecraft. This represents the control input for the i-th spacecraft in the formation. Let ||·|| denote the composite perturbation experienced by the i-th formation spacecraft, consisting of external disturbances and model uncertainties, and let ||·|| denote the 2-norm for a three-dimensional vector. Let x be the skew-symmetric matrix, defined as follows: It represents the set of real numbers.

[0063] σ i This can be expressed as:

[0064]

[0065] E i and θ i These represent the Euler axis and Euler angles, respectively.

[0066] Furthermore, based on the attitude dynamics model established above, the attitude dynamics model can be restated as follows:

[0067]

[0068] in, σ i The second derivative, For T(σ) i The derivative of ) For J i The inverse matrix.

[0069] Since coordinated attitude control of spacecraft formations requires information exchange between the spacecraft, in one embodiment of the present invention, for a spacecraft formation system comprising n spacecraft, a directed graph G = {V, E, A} is used to describe the communication topology of the spacecraft formation system. Where V = {v1, v2, ..., v...} n} represents the set of all nodes. Let v represent the set of all edges, where v is the edge(v). i ,v j ) represents node v i Able to send to node v j Transmitting information; This represents a weighted adjacency matrix, where adjacency matrix A is used to represent the communication connectivity between spacecraft in each formation. Let a be the value of a. ii =0, a ij Let represent the element in the i-th row and j-th column of the adjacency matrix A. If the i-th formation spacecraft can receive information from the j-th formation spacecraft, i.e., (v j ,v i If )∈E, then a ij >0, otherwise a ij =0. From node v i to node v jThe path can be represented as a series of paths of the form {(v i ,v k ),(v k ,v l ),…,(v m ,v j If G is an ordered tree with ordered edges, then if G has a directed spanning tree, there exists a node to which there is at least one directed path, called the root node.

[0070] Furthermore, define vector B = [b1, b2, ..., b n ] T This describes whether each formation of spacecraft can obtain the desired information. If the i-th formation of spacecraft can obtain the desired information, then b i >0, otherwise b i =0. Simultaneously, it is assumed that the directed graph G has a directed spanning tree, and the formation spacecraft corresponding to the root node can access the desired information.

[0071] Furthermore, the following auxiliary variable is constructed to represent the cooperative error of the spacecraft formation system:

[0072]

[0073]

[0074] e i =αe 1i +e 2i

[0075] Where α represents a positive constant, n represents the number of spacecraft in the formation, and σ j This represents the attitude of the j-th formation spacecraft described by the modified Rodriguez parameters. σ j The derivative of , where t represents the time variable, T ij σ represents the communication delay between the j-th formation spacecraft and the i-th formation spacecraft. d Indicates the desired attitude of the formation of spacecraft. σ d The derivative of T i This represents the communication delay caused by the i-th formation spacecraft receiving the desired information.

[0076] Combining the aforementioned auxiliary variables and the restated attitude dynamics model, the following spacecraft formation attitude dynamics model considering external disturbances, model uncertainties, and communication delays is established:

[0077]

[0078] Among them, g i =Ji T -1 (σ i )

[0079]

[0080]

[0081] e i The derivative of h i T represents the lumped nonlinear term of the spacecraft formation system. -1 (σ i ) represents T(σ i The inverse matrix of ) σ j The second derivative, σ d The second derivative of .

[0082] Step S2: Based on the spacecraft formation attitude dynamics model, construct a nonlinear observer capable of observing the lumped nonlinear terms of the spacecraft formation system.

[0083] In one embodiment of the present invention, based on the spacecraft formation attitude dynamics model established above that considers external disturbances, model uncertainties, and communication delays, the following nonlinear observer for observing the lumped nonlinear term of the spacecraft formation system is constructed:

[0084]

[0085] in, express The derivative, Represents the nonlinear term h i The estimate, where r represents a positive constant. This indicates the current trigger time of the i-th formation spacecraft;

[0086] Defined as:

[0087]

[0088] express Moment e 1i The derivative, express Moment e 2i The derivative, express Moment express Moment express Moment express Moment express Moment express Moment Indicates the time of triggering the i-th formation spacecraft. The moment when the latest status information of the j-th spacecraft has been received. Indicates the time of triggering the i-th formation spacecraft. The moment when the latest expected information has been received;

[0089] Defined as:

[0090]

[0091] Defined as:

[0092]

[0093] express and The upper bound of time t, This represents the m-th trigger time of the j-th formation spacecraft. express The communication delay between the j-th formation spacecraft and the i-th formation spacecraft at time j. express The communication delay caused by the i-th formation spacecraft receiving the desired information at time i.

[0094] In one embodiment of the present invention, an auxiliary triggering time is defined. and It can transform event-triggered control problems with communication delays into regular event-triggered control problems.

[0095] Step S3: Based on the nonlinear observer, design the event-triggered attitude cooperative control law and event triggering mechanism.

[0096] In one embodiment of the present invention, taking the i-th spacecraft in a spacecraft formation system as an example, based on the aforementioned specifically defined spacecraft formation attitude dynamics model and nonlinear observer, the event-triggered attitude cooperative control law is designed as follows:

[0097]

[0098] Where k represents a positive constant, express e of time i , express Moment

[0099] Referring to the event-triggered attitude cooperative control law corresponding to the i-th formation spacecraft determined above, the corresponding event-triggered attitude cooperative control law can be determined for each formation spacecraft in the spacecraft formation.

[0100] In one embodiment of the present invention, neither the nonlinear observer nor the event-triggered attitude cooperative control law designed above requires the use of the current state information and expected information of the adjacent formation spacecraft. The implementation of the nonlinear observer and the event-triggered attitude cooperative control law does not require continuous communication between the formation spacecraft, which can save a lot of communication resources of the formation spacecraft.

[0101] Furthermore, in one embodiment of the present invention, taking the i-th formation spacecraft in a spacecraft formation system as an example, the event triggering condition in the event triggering mechanism is designed as follows:

[0102]

[0103] Where δ represents a positive constant;

[0104] Defined as:

[0105]

[0106]

[0107] Defined as:

[0108]

[0109] express σ at time j , express σ at time d .

[0110] Furthermore, based on the event triggering conditions designed above, the event triggering mechanism is designed as follows:

[0111]

[0112] in, This indicates the next trigger time for the i-th formation spacecraft. express and The lower bound of time t.

[0113] Referring to the event triggering conditions and event triggering mechanisms corresponding to the i-th formation spacecraft as determined above, the corresponding event triggering conditions and event triggering mechanisms can be determined for each formation spacecraft in the spacecraft formation system, and the triggering time of the formation spacecraft is determined using the aforementioned event triggering mechanisms.

[0114] Step S4: Control the attitude and angular velocity of the formation spacecraft according to the event-triggered attitude cooperative control law, determine whether it is necessary to update the event-triggered attitude cooperative control law corresponding to the formation spacecraft, and whether to send the status information of the formation spacecraft to its neighboring formation spacecraft according to the event triggering mechanism.

[0115] Specifically, a corresponding attitude coordination controller is designed based on the determined event-triggered attitude coordination control law. The attitude coordination controller is used to control the attitude and angular velocity of the formation spacecraft in real time. The event-triggered mechanism determines whether the event-triggered attitude coordination control law corresponding to the formation spacecraft needs to be updated. If so, the event-triggered attitude coordination control law corresponding to the formation spacecraft is updated. The attitude and angular velocity of the formation spacecraft are controlled based on the updated event-triggered attitude coordination control law, and the state information of the formation spacecraft, including attitude and angular velocity, is sent to its neighboring formation spacecraft.

[0116] In one embodiment of the present invention, determining whether to update the event-triggered attitude cooperative control law corresponding to the formation spacecraft, and whether to send the state information of the formation spacecraft to its neighboring formation spacecraft, based on the event triggering mechanism, includes:

[0117] Determine if the event triggering condition is met. If so, update the event triggering attitude cooperative control law corresponding to the formation spacecraft and send the state information of the formation spacecraft to its neighboring formation spacecraft.

[0118] Specifically, it determines whether the event triggering condition is met, i.e. whether the next triggering moment has been reached. If so, it updates the event triggering attitude coordination control law corresponding to the formation spacecraft, i.e., updates the corresponding attitude coordination controller.

[0119] The above method is used to control each spacecraft in the spacecraft formation system.

[0120] The spacecraft formation event-triggered attitude cooperative control method provided in one embodiment of the present invention, which considers communication delay, can take into account the impact of disturbances, uncertainties and communication delays on the spacecraft formation system, and can improve the control performance, convergence accuracy and robustness of the control system. The implementation of the nonlinear observer and the event-triggered attitude cooperative control law does not require continuous communication between the formation spacecraft, which can save a lot of communication resources of the formation spacecraft. Furthermore, the formation spacecraft only updates its own controller when the triggering condition is met, which can significantly reduce the update frequency of the controller and save the energy and computing resources of the formation spacecraft.

[0121] The following examples illustrate the beneficial effects of a spacecraft formation event-triggered attitude cooperative control method considering communication latency provided by an embodiment of the present invention.

[0122] refer to Figure 2 Taking a spacecraft formation system consisting of 5 spacecraft as an example, according to Figure 2 The communication relationships between the spacecraft in the formation shown can be represented by the adjacency matrix A and vector B corresponding to this spacecraft formation system:

[0123]

[0124] Furthermore, in this example, the corresponding parameter settings are as follows:

[0125] The inertia matrix is ​​set as follows:

[0126] J1=[13.1,0,0;0,12.8,0;0,0,13]kg·m 2

[0127] J2=[12.9,0,0;0,13.4,0;0,0,13.2]kg·m 2

[0128] J3=[12.7,0,0;0,12.8,0;0,0,13.3]kg·m 2

[0129] J4=[12.8,0,0;0,13.3,0;0,0,13.2]kg·m 2

[0130] J5=[13.3,0,0;0,13,0;0,0,13.1]kg·m 2

[0131] The combined disturbance moment is set as follows:

[0132] ρ1=[2+sin(0.1t),2cos(0.3t),1+cos(0.1t)] T ×10 -3 N·m

[0133] ρ2=[cos(0.1t),2+cos(0.2t),2sin(0.2t)] T ×10 -3 N·m

[0134] ρ3=[2cos(0.2t),2+sin(0.1t),sin(0.2t)] T ×10 -3N·m

[0135] ρ4=[1+cos(0.1t),sin(0.1t),cos(0.2t)] T ×10 -3 N·m

[0136] ρ5=[sin(0.3t),2sin(0.1t),2+2sin(0.1t)] T ×10 -3 N·m

[0137] The initial attitude and angular velocity of the formation spacecraft are set as follows:

[0138] σ1(0)=[0.2,0.3,0.1] T

[0139] σ²(0) = [0.1, 0.3, -0.1] T

[0140] σ3(0)=[-0.2,0.1,-0.1] T

[0141] σ4(0)=[0.4,-0.2,0.1] T

[0142] σ5(0)=[-0.1,0.2,0.2] T

[0143] ω1(0)=[0.1,0.2,0.1] T rad / s

[0144] ω2(0)=[0.2,-0.3,0.1] T rad / s

[0145] ω3(0)=[0.2,0.1,-0.2] T rad / s

[0146] ω4(0)=[-0.3,0.1,0.2] T rad / s

[0147] ω5(0)=[0.3,-0.1,-0.2] T rad / s

[0148] Communication delay is set to:

[0149] T 14 =0.1+sin(0.02t)

[0150] T 21 =0.2+cos(0.01t)

[0151] T 32 =0.1+cos(0.02t)

[0152] T 43 =0.2+sin(0.03t)

[0153] T 45 =0.3+sin(0.01t)

[0154] T 54 =0.2+cos(0.02t)

[0155] T1 = 0.1 + cos(0.03t)

[0156] Desired attitude is set as follows:

[0157] σ d =[0,0,0] T

[0158] The parameters of the event-triggered attitude cooperative controller and the nonlinear observer are set as follows:

[0159] α=0.05, r=0.4, δ=0.001, k0=1, β=25, g dmax =20, i = 1, 2, 3, 4, 5.

[0160] Control inputs satisfy:

[0161] |u ij |≤0.5N·m, where j=x,y,z.

[0162] Furthermore, simulation experiments were conducted based on the spacecraft formation system, parameters, and simulation conditions set above, and the corresponding simulation results were obtained.

[0163] In this example, the observation error of the nonlinear observer is as follows: Figure 3 As shown, from Figure 3 As can be seen from the simulation, the observation error converges quickly and with high accuracy. The simulation curves of the attitude error and angular velocity error of the formation spacecraft are shown below. Figure 4 and Figure 5 As shown in the attached figure, the simulation results indicate that the attitude and angular velocity can converge to the vicinity of the origin within 100s.

[0164] Furthermore, the control input response curves of the five spacecraft formations are as follows: Figure 6 As shown in the attached figure, the simulation results indicate that the control input is very small once the system stabilizes.

[0165] The trigger intervals of the five formation spacecraft are as follows Figure 7As shown in Tables 1 and 2, the trigger counts of the event-driven controller and the time-driven controller with a fixed frequency of 10Hz are as follows. It can be seen that when the system is stable, the event-triggered attitude coordination controller designed in one embodiment of the present invention can effectively reduce the number of controller triggers by more than 80%.

[0166] Table 1. Number of triggers (0-200s)

[0167]

[0168] Table 2: Number of triggers (200-2000s)

[0169]

[0170] As can be seen, the spacecraft formation event-triggered attitude cooperative control method considering communication delay provided by an embodiment of the present invention can take into account the effects of disturbances, uncertainties and communication delays, and can significantly save energy, communication and computing resources of the formation system while ensuring good control performance.

[0171] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Additionally, the terms "front," "back," "left," "right," "upper," and "lower" in this document refer to the placement shown in the accompanying drawings.

[0172] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A spacecraft formation event-triggered attitude cooperative control method considering communication latency, characterized in that, include: Based on the communication topology of the spacecraft formation system, a spacecraft formation attitude dynamics model that can take into account external disturbances, model uncertainties, and communication delays is established. Based on the spacecraft formation attitude dynamics model, a nonlinear observer capable of observing the lumped nonlinear terms of the spacecraft formation system is constructed. Based on a nonlinear observer, an event-triggered attitude cooperative control law and an event-triggered mechanism are designed. The attitude and angular velocity of the formation spacecraft are controlled according to the event-triggered attitude cooperative control law. The event-triggered mechanism determines whether it is necessary to update the event-triggered attitude cooperative control law corresponding to the formation spacecraft, and whether to send the status information of the formation spacecraft to its neighboring formation spacecraft. The following spacecraft formation attitude dynamics model is established, taking into account external disturbances, model uncertainties, and communication delays: ； in, ; ； ； express The derivative, , , , Represents positive numbers. Indicates the number of spacecraft in the formation. This represents the attitude of the i-th formation spacecraft described by the modified Rodriguez parameters. express The derivative, This represents the attitude of the j-th formation spacecraft described by the modified Rodriguez parameters. express The derivative, Represents a time variable. This represents the communication delay between the j-th formation spacecraft and the i-th formation spacecraft. Indicates the desired attitude of the formation of spacecraft. express The derivative, This represents the communication delay caused by the i-th spacecraft in the formation receiving the desired information. Representing the adjacency matrix The elements in the i-th row and j-th column, the adjacency matrix This is used to indicate the communication connectivity between spacecraft in each formation. If the i-th formation spacecraft can receive information from the j-th formation spacecraft, then... ,otherwise , Representing vectors The i-th element of the vector This describes whether each formation of spacecraft can obtain the desired information. If the i-th formation of spacecraft can obtain the desired information, then... ,otherwise , This represents the control input for the i-th spacecraft in the formation. Let represent the inertial matrix of the i-th formation spacecraft. express The inverse matrix, , express 3D identity matrix express transpose, Represents the 2-norm for a three-dimensional vector. , express The corresponding skew-symmetric matrix is ​​defined as follows: , Represents the set of real numbers. This represents the lumped nonlinear term of the spacecraft formation system. express The second derivative, express The second derivative, express The derivative, This represents the combined disturbance of external disturbances and model uncertainties experienced by the i-th formation spacecraft.

2. The spacecraft formation event-triggered attitude cooperative control method considering communication latency according to claim 1, characterized in that, Construct the following nonlinear observer: ； in, express The derivative, Represents nonlinear terms The estimate, Represents positive numbers. This indicates the current trigger time of the i-th formation spacecraft; Defined as: ； express Moment , express The derivative, express Moment , express The derivative, express Moment , express Moment , express Moment , express Moment , express The second derivative, express Moment , express Moment , Indicates the time of triggering the i-th formation spacecraft. The moment when the latest status information of the j-th spacecraft has been received. Indicates the time of triggering the i-th formation spacecraft. The moment when the latest expected information has been received; Defined as: ； Defined as: ； express and The upper bound of time t, This represents the m-th trigger time of the j-th formation spacecraft. express The communication delay between the j-th formation spacecraft and the i-th formation spacecraft at time j. express The communication delay caused by the i-th formation spacecraft receiving the desired information at time i.

3. The spacecraft formation event-triggered attitude cooperative control method considering communication latency according to claim 2, characterized in that, The event-triggered attitude cooperative control law is: ； in, Represents positive numbers. express Moment , express Moment .

4. The spacecraft formation event-triggered attitude cooperative control method considering communication delay according to claim 3, characterized in that, The event triggering mechanism is designed with the following event triggering conditions: ； in, Represents positive integers; Defined as: ； ； Defined as: ； express Moment , express Moment .

5. The spacecraft formation event-triggered attitude cooperative control method considering communication latency according to claim 4, characterized in that, The event triggering mechanism is as follows: ； in, This indicates the next trigger time for the i-th formation spacecraft. express and The lower bound of time t.

6. The spacecraft formation event-triggered attitude cooperative control method considering communication latency according to claim 5, characterized in that, The event-triggered mechanism determines whether the event-triggered cooperative control law corresponding to the formation spacecraft needs to be updated, and whether the status information of the formation spacecraft should be sent to its neighboring formation spacecraft, including: Determine if the event triggering condition is met. If so, update the event triggering attitude cooperative control law corresponding to the formation spacecraft and send the state information of the formation spacecraft to its neighboring formation spacecraft.

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