Spacecraft formation attitude cooperative control method based on event triggering
By introducing event triggering mechanisms and adaptive control technologies into the spacecraft formation system, the flexibility and robustness problems in handling external perturbations and model uncertainties in the prior art are solved, and more efficient resource utilization and more stable attitude collaborative control are achieved.
Patent Information
- Application Number
- CN202211178812.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-27
- Publication Date
- 2025-03-14
- Estimated Expiration
- 2042-09-27
AI Technical Summary
The existing spacecraft formation attitude collaborative control algorithms lack flexibility and robustness in dealing with external perturbations and model uncertainties, and consume a lot of resources. Especially after the formation spacecraft attitudes tend to be consistent, continuous updating of the controller will only increase power consumption.
A spacecraft formation attitude coordinated control method based on event triggering is proposed. By establishing an attitude dynamic model that considers external perturbation and model uncertainty, setting a coordinated error auxiliary variable and measurement error variable, determining the event trigger attitude coordinated control law and conditions, and updating the controller only when specific conditions are met.
It improves the convergence accuracy and robustness of the control system, significantly reduces the energy, communication and computing resource consumption of the spacecraft formation system, and avoids unnecessary controller updates.
Smart Images
Figure CN115657698B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of spacecraft control technology, and in particular to a spacecraft formation attitude collaborative control method based on event triggering. Background Art
[0002] Since spacecraft formation flying can break through the limitations of the volume and mass of a single spacecraft, and has higher reliability, flexibility and stronger system performance, the spacecraft formation system has broad application prospects in the fields of earth monitoring, deep space exploration, space-based synthetic aperture radar, etc., and is the main direction of future aerospace technology development. The attitude cooperative control problem of formation spacecraft is one of the most critical and basic problems of spacecraft formation cooperative control. In actual spacecraft formation flight missions, the purpose of attitude cooperative control is to design a cooperative controller so that the attitudes of each formation spacecraft converge to the desired attitude.
[0003] At present, most attitude cooperative control algorithms designed for spacecraft formation cooperative control require continuous updates. However, the continuous update of attitude cooperative controllers consumes a large amount of energy, communication and computing resources of the formation spacecraft. Moreover, when the attitudes of the formation spacecraft tend to be consistent, the continuous update of attitude cooperative controllers will only increase power consumption. Since the energy, communication and computing resources on the formation spacecraft are limited and precious, the problem of limited spacecraft formation system resources must be taken into account when designing attitude cooperative controllers.
[0004] In order to save spacecraft formation system resources, the time-triggered method or event-triggered method is currently used to design attitude coordination control algorithms. Among them, the existing spacecraft formation attitude coordination control scheme based on time triggering allows the digital controller to periodically send control instructions through time triggering, and updates the controller based on the control instructions. The existing spacecraft formation attitude coordination control scheme based on event triggering saves resources by designing the response conditions of the control system. The controller is updated only when the response conditions are met.
[0005] However, in order to ensure the stability of the control system, the sampling frequency of the existing spacecraft formation attitude cooperative control scheme based on time triggering cannot be too low, which makes the cooperative controller calculate more times, occupies too many computing resources, lacks flexibility and scalability, and has low efficiency in saving resources. The existing spacecraft formation attitude cooperative control scheme based on event triggering does not consider external disturbances and model uncertainties. When the formation spacecraft is in orbit, it will inevitably be affected by disturbances and uncertainties. Failure to consider these factors will reduce the accuracy of the control system and may even cause the entire closed-loop system to become unstable. In addition, the trigger conditions considered require the real-time status information of adjacent formation spacecraft, which requires the formation spacecraft to communicate continuously with adjacent formation spacecraft, occupying too much communication bandwidth. Summary of the invention
[0006] In order to solve some or all of the technical problems existing in the above-mentioned prior art, the present invention provides a spacecraft formation attitude collaborative control method based on event triggering.
[0007] The technical solution of the present invention is as follows:
[0008] A spacecraft formation attitude collaborative control method based on event triggering is provided, the method comprising:
[0009] Establish the attitude dynamics model of the spacecraft formation system considering external disturbances and model uncertainties;
[0010] According to the attitude and angular velocity information of the formation spacecraft and the communication relationship between the formation spacecraft, setting auxiliary variables for representing the coordination error of the spacecraft formation system;
[0011] According to the collaborative error auxiliary variable, the measurement error variable is set;
[0012] According to the cooperative error auxiliary variable and the measurement error variable, the event-triggered attitude cooperative control law and the event triggering condition are determined;
[0013] The attitude and angular velocity of the formation spacecraft are controlled according to the event-triggered attitude cooperative control law, and it is determined whether the event triggering condition is met. If so, the event-triggered attitude cooperative control law corresponding to the formation spacecraft is updated, and the status information of the formation spacecraft is sent to the adjacent formation spacecraft.
[0014] In some possible implementations, the following attitude dynamics model of the spacecraft formation system considering external disturbances and model uncertainties is established:
[0015]
[0016] Where I3 represents the 3×3 dimensional identity matrix, represents the attitude of the ith formation spacecraft described by the modified Rodriguez parameters, Represents σ i The derivative of represents the angular velocity of the i-th formation spacecraft in the body coordinate system, Represents ω i The derivative of represents the inertia matrix of the i-th formation spacecraft, represents the control input of the i-th formation spacecraft, represents the generalized disturbance corresponding to the i-th formation spacecraft, including external disturbance and model uncertainty, ||·|| represents the 2-norm, and for the three-dimensional vector Represents the skew-symmetric matrix corresponding to x, defined as Represents the set of real numbers.
[0017] In some possible implementations, the following collaborative error auxiliary variables are set:
[0018]
[0019]
[0020]
[0021] s i =r1e 1i +e 2i
[0022]
[0023]
[0024]
[0025]
[0026] Among them, e 1i 、e 2i 、e 3i 、s i , χ 1i , χ 2i , χ 3i and are auxiliary variables of collaborative errors, n represents the number of spacecraft in the formation, σ j represents the attitude of the j-th formation spacecraft described by the modified Rodriguez parameters, Represents σ j The derivative of j represents the angular velocity of the j-th formation spacecraft in the body coordinate system, Represents ω j The derivative of r1 is a positive constant, σ d and ω d denote the desired attitude and angular velocity of the formation spacecraft, respectively. Represents σ d The derivative of ij represents the element in the i-th row and j-th column of the adjacency matrix A. The adjacency matrix A is used to represent the communication connectivity between the spacecraft in each formation. If the i-th formation spacecraft can receive the information of the j-th formation spacecraft, then a ij > 0, otherwise a ij =0, b i represents the i-th element of vector B. Vector B is used to describe whether each spacecraft in the formation can obtain the expected information. If the i-th spacecraft in the formation can obtain the expected information, then b i =1, otherwise b i =0, represents the current triggering time of the j-th formation spacecraft, Indicates that at the trigger time The attitude of the j-th formation spacecraft is described by the modified Rodriguez parameter under express The derivative of Indicates that at the trigger time The angular velocity of the j-th formation spacecraft in the body coordinate system.
[0027] In some possible implementations, the following measurement error variables are set:
[0028]
[0029]
[0030]
[0031]
[0032]
[0033]
[0034] in, and are all measurement error variables, represents the current triggering time of the i-th formation spacecraft, Indicates that at the trigger time The attitude of the i-th formation spacecraft is described by the modified Rodriguez parameter under Indicates that at the trigger time The angular velocity of the i-th formation spacecraft in the body coordinate system is, Indicates that at the trigger time The auxiliary variable of the coordinated error corresponding to the i-th formation spacecraft under Indicates that at the trigger time The auxiliary variable χ of the coordinated error corresponding to the i-th formation spacecraft under 3i ,
[0035] In some possible implementations, the event-triggered attitude cooperative control law is:
[0036]
[0037] in,
[0038]
[0039]
[0040]
[0041] k i =k0+r1||J i ||+n+1
[0042] β i =(n+1)(δ2||J i ||+ρ max )
[0043]
[0044] u i represents the control input of the i-th formation spacecraft, ε1, ε2, r2, r3, k0 and are all positive numbers, ρ max , δ2, δ3 and δ4 are the upper bounds of generalized disturbance, generalized angular acceleration, attitude measurement error, and angular velocity measurement error, respectively. and To adaptively update variables, and The initial value of is preset, and sgn(·) represents the standard sign function.
[0045] In some possible implementations,
[0046] The event trigger conditions are:
[0047] F i ≥0
[0048] in,
[0049] The main advantages of the technical solution of the present invention are as follows:
[0050] The event-triggered spacecraft formation attitude cooperative control method of the present invention utilizes adaptive control and sliding mode control technology to deal with the disturbance and uncertainty of the formation spacecraft, which can improve the convergence accuracy and robustness of the control system; at the same time, attitude cooperative control only needs to use the state information of adjacent formation spacecraft at their triggering moment, which can avoid continuous communication between formation spacecraft, effectively save the communication resources of the spacecraft formation system, and reduce the communication burden of the formation system; and, the formation spacecraft updates its own controller only when the triggering condition is met, which can significantly reduce the update frequency of the controller. BRIEF DESCRIPTION OF THE DRAWINGS
[0051] The drawings described herein are used to provide a further understanding of the embodiments of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:
[0052] Figure 1 This is a flow chart of a spacecraft formation attitude cooperative control method based on event triggering according to an embodiment of the present invention;
[0053] Figure 2 This is a schematic diagram of the communication topology structure of the spacecraft formation system in Example 1 of the present invention;
[0054] Figure 3 This is a schematic diagram of the simulation results of the attitude errors of the formation spacecraft in Example 1 of the present invention;
[0055] Figure 4 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;
[0056] Figure 5a , Figure 5b , Figure 5c ,and Figure 5d They are respectively schematic diagrams of control inputs for the first to fourth formation spacecraft in Example 1 of the present invention;
[0057] Figure 6a , Figure 6b , Figure 6c ,and Figure 6d They are respectively schematic diagrams of the triggering intervals of the 1st to 4th formation spacecraft in Example 1 of the present invention. DETAILED DESCRIPTION
[0058] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.
[0059] The technical solution provided by the embodiments of the present invention is described in detail below with reference to the accompanying drawings.
[0060] refer to Figure 1 An embodiment of the present invention provides a spacecraft formation attitude cooperative control method based on event triggering, the method comprising the following steps S1-S5:
[0061] Step S1, establishing a spacecraft formation system attitude dynamics model taking into account external disturbances and model uncertainties;
[0062] In one embodiment of the present invention, for the i-th formation spacecraft in the spacecraft formation, the following attitude dynamics model of the spacecraft formation system considering external disturbances and model uncertainties is established:
[0063]
[0064] Where I3 represents the 3×3 dimensional identity matrix, represents the attitude of the i-th formation spacecraft described by the modified Rodriguez parameter, σ ix ,σ iy ,σ iz Respectively represent σ i The components of the coordinate system under the x-axis, y-axis and z-axis, Represents σ i The derivative of represents the angular velocity of the i-th formation spacecraft in the body coordinate system, ω ix ,ω iy ,ω iz Respectively represent ω i The components of the coordinate system under the x-axis, y-axis and z-axis, Represents ω i The derivative of represents the inertia matrix of the i-th formation spacecraft, represents the control input of the i-th formation spacecraft, represents the generalized disturbance corresponding to the i-th formation spacecraft, including external disturbance and model uncertainty, ||·|| represents the 2-norm, and for the three-dimensional vector Represents the skew-symmetric matrix corresponding to x, defined as Represents the set of real numbers.
[0065] With reference to the spacecraft formation system attitude dynamics model corresponding to the i-th formation spacecraft established above, a corresponding spacecraft formation system attitude dynamics model can be established for each formation spacecraft in the spacecraft formation.
[0066] Step S2, setting a cooperative error auxiliary variable for representing the spacecraft formation system according to the attitude and angular velocity information of the formation spacecraft and the communication relationship between the formation spacecraft;
[0067] In one embodiment of the present invention, for the i-th formation spacecraft in the spacecraft formation, according to the attitude and angular velocity information of the formation spacecraft, and the communication relationship between the formation spacecraft, the following auxiliary variables for representing the coordinated error of the spacecraft formation system can be set:
[0068]
[0069]
[0070]
[0071] s i =r1e 1i +e 2i
[0072]
[0073]
[0074]
[0075]
[0076] Among them, e 1i 、e 2i 、e 3i 、s i , χ 1i , χ 2i , χ 3i and represents the auxiliary variable of the collaborative error corresponding to the i-th formation spacecraft, n represents the number of formation spacecraft, σ j represents the attitude of the j-th formation spacecraft described by the modified Rodriguez parameters, Represents σ j The derivative of j represents the angular velocity of the j-th formation spacecraft in the body coordinate system, Represents ω j The derivative of r1 is a positive constant, σ dand ω d denote the desired attitude and angular velocity of the formation spacecraft, respectively. Represents σ d The derivative of ij represents the element in the i-th row and j-th column of the adjacency matrix A, b i represents the i-th element of vector B, represents the current triggering time of the j-th formation spacecraft, Indicates that at the trigger time The attitude of the j-th formation spacecraft is described by the modified Rodriguez parameter under express The derivative of Indicates that at the trigger time The angular velocity of the j-th formation spacecraft in the body coordinate system.
[0077] In one embodiment of the present invention, the adjacency matrix A is determined according to the communication connectivity relationship between the spacecraft in the spacecraft formation, and is used to represent the communication connectivity of each spacecraft in the formation. If the i-th spacecraft in the formation can receive the information of the j-th spacecraft in the formation, then a ij > 0, otherwise a ij = 0. The vector B is determined based on whether each spacecraft in the spacecraft formation can obtain the expected information including the expected attitude and / or the expected angular velocity, and is used to describe whether each spacecraft in the formation can obtain the expected information. If the i-th spacecraft in the formation can obtain the expected information, then b i =1, otherwise b i =0.
[0078] With reference to the above-set coordination error auxiliary variable corresponding to the i-th formation spacecraft, a corresponding coordination error auxiliary variable may be set for each formation spacecraft in the spacecraft formation.
[0079] Step S3, setting the measurement error variable according to the collaborative error auxiliary variable;
[0080] In one embodiment of the present invention, for the i-th formation spacecraft in the spacecraft formation, based on the above-mentioned specifically set collaborative error auxiliary variables, the following measurement error variables are set:
[0081]
[0082]
[0083]
[0084]
[0085]
[0086]
[0087] in, and represents the measurement error variable corresponding to the i-th formation spacecraft, represents the current triggering time of the i-th formation spacecraft, Indicates that at the trigger time The attitude of the i-th formation spacecraft is described by the modified Rodriguez parameter under Indicates that at the trigger time The angular velocity of the i-th formation spacecraft in the body coordinate system is, Indicates that at the trigger time The auxiliary variable of the coordinated error corresponding to the i-th formation spacecraft under Indicates that at the trigger time The auxiliary variable χ of the coordinated error corresponding to the i-th formation spacecraft under 3i ,
[0088] With reference to the measurement error variable corresponding to the i-th formation spacecraft set above, a corresponding measurement error variable may be set for each formation spacecraft in the spacecraft formation.
[0089] Step S4, determining the event-triggered attitude collaborative control law and the event triggering condition according to the collaborative error auxiliary variable and the measurement error variable;
[0090] In one embodiment of the present invention, for the i-th formation spacecraft in the spacecraft formation, based on the above-mentioned specific settings of the collaborative error auxiliary variable and the measurement error variable, the event-triggered attitude collaborative control law is designed as follows:
[0091]
[0092] in,
[0093]
[0094]
[0095]
[0096] k i =k0+r1||J i ||+n+1
[0097] β i =(n+1)(δ2||J i ||+ρ max )
[0098]
[0099] u i represents the control input of the i-th formation spacecraft, ε1, ε2, r2, r3, k0 and are all positive numbers, ρ max , δ2, δ3 and δ4 are the generalized disturbance (ρ), generalized angular acceleration ( and ), attitude measurement error ( ), and angular velocity measurement error ( and ), and To adaptively update variables, and The initial value of is pre-set, sgn(·) represents the standard sign function, for any vector
[0100] With reference to the event-triggered attitude cooperative control law corresponding to the i-th formation spacecraft determined above, the event-triggered attitude cooperative control law corresponding to each formation spacecraft in the spacecraft formation can be determined.
[0101] Furthermore, in one embodiment of the present invention, for the i-th formation spacecraft in the spacecraft formation, the event triggering condition is set as:
[0102] F i ≥0
[0103] in,
[0104] Furthermore, based on the event trigger conditions set above, the next triggering moment of the i-th formation spacecraft can be determined using the following event triggering function:
[0105]
[0106] in, Indicates F i ≥0 and The lower bound of time t.
[0107] With reference to the event triggering condition and event triggering function corresponding to the i-th formation spacecraft determined above, the event triggering condition and event triggering function corresponding to each formation spacecraft in the spacecraft formation may be determined.
[0108] Step S5, controlling the attitude and angular velocity of the formation spacecraft according to the event-triggered attitude cooperative control law, and judging whether the event triggering condition is met, if so, updating the event-triggered attitude cooperative control law corresponding to the formation spacecraft, and sending the status information of the formation spacecraft to the adjacent formation spacecraft.
[0109] Specifically, a corresponding attitude cooperative control law is designed according to the determined event-triggered attitude cooperative control law, and the attitude cooperative controller is used to control the attitude and angular velocity of the formation spacecraft in real time, and to judge in real time whether the event triggering condition is met, that is, whether the next triggering moment is reached. If so, the event-triggered attitude cooperative control law corresponding to the formation spacecraft is updated, that is, the corresponding attitude cooperative controller is updated, and the real-time status information of the formation spacecraft is sent to the adjacent formation spacecraft.
[0110] Among them, each formation spacecraft in the spacecraft formation is controlled using the above method.
[0111] The event-triggered spacecraft formation attitude cooperative control method provided by an embodiment of the present invention utilizes adaptive control and sliding mode control technology to process the disturbances and uncertainties suffered by formation spacecraft, which can improve the convergence accuracy and robustness of the control system; at the same time, attitude cooperative control only needs to use the state information of adjacent formation spacecraft at their triggering moments, which can avoid continuous communication between formation spacecraft, effectively save the communication resources of the spacecraft formation system, and reduce the communication burden of the formation system; and, the formation spacecraft updates its own controller only when the triggering conditions are met, which can significantly reduce the update frequency of the controller.
[0112] The beneficial effects of the event-triggered spacecraft formation attitude collaborative control method provided by an embodiment of the present invention are described below in conjunction with specific examples.
[0113] refer to Figure 2 , taking a spacecraft formation system consisting of four spacecraft as an example, according to Figure 2 The communication relationship between the formation spacecraft is shown. The adjacency matrix A and vector B corresponding to the spacecraft formation system can be:
[0114]
[0115] Further, in this example, the corresponding parameters are set as follows:
[0116] The inertia matrix is set to:
[0117] J1=[10.2,0.1,0.1;0.1,10.3,0.2;0.1,0.2,9.8]kg·m 2
[0118] J2=[8.9,0.2,0.1;0.2,9.4,0.2;0.1,0.2,10]kg·m 2
[0119] J3=[9.9,0.2,0.2;0.2,9.8,0.1;0.2,0.1,10.5]kg·m 2
[0120] J4=[8.8,0.1,0.2;0.1,9.6,0.1;0.2,0.1,10.1]kg·m 2
[0121] The equivalent disturbance torque is set as:
[0122] ρ1=[2sin(0.1t),2sin(0.2t),cos(0.2t)] T ×10 -3 Nm
[0123] ρ2=[3sin(0.2t),2cos(0.3t),2sin(0.1t)] T ×10 -3 Nm
[0124] ρ3=[cos(0.2t),2cos(0.1t),sin(0.1t)] T ×10 -3 Nm
[0125] ρ4=[2cos(0.1t),sin(0.2t),sin(0.2t)] T ×10 -3 Nm
[0126] The desired posture is set to:
[0127] σ d =0.001×[3sin(0.2t),2sin(0.1t),-cos(0.1t)] T
[0128] t is the time variable;
[0129] The initial state of the spacecraft formation system is σ1(0) = [0.3, -0.1, 0.2] T ,σ2(0)=[0.1,0.2,0.3] T ,σ3(0)=[0.3,-0.2,-0.1] T ,σ4(0)=[0.1,0.4,-0.3] T ,ω1(0)=[0.05,0.1,0.05] Trad / s, ω2(0)=[-0.03,0.04,0.04] T rad / s, ω3(0)=[-0.05,0.03,0.02] T rad / s, ω4(0)=[0.03,-0.04,-0.04] T rad / s;
[0130] The control torque amplitude is set to: |u ij |≤0.2Nm, where j=x,y,z;
[0131] The parameters of the event-triggered attitude cooperative controller are set as: k0 = 1, r1 = 0.7, r2 = 0.5, r3 = 0.05, ε1 = 0.5, ε2 = 0.1, δ2 = 0.1, δ3 = 1, δ4 = 1, ρ max =0.1 and
[0132] The initial values of the adaptive update variables are set to: and
[0133] In addition, to avoid chattering, the saturation function sat(·) is used to replace the above sign function sgn(·), where the saturation function is defined as follows:
[0134]
[0135] In the simulation, ψ=1.
[0136] Furthermore, a simulation test is performed based on the above-set spacecraft formation system, parameters and simulation conditions to obtain corresponding simulation results.
[0137] In this example, the final simulation curves of attitude error and angular velocity error are as follows: Figure 3 and Figure 4 As shown, according to the simulation results shown in the accompanying drawings, it can be seen that under the action of the event-triggered attitude collaborative controller designed by the present invention, the system state error can converge collaboratively to the vicinity of the origin within 40 seconds.
[0138] Furthermore, the control input curves of the four formation spacecraft are as follows: Figure 5a-5d As shown in the figure, the triggering time and triggering interval of the four formation spacecraft are as follows: Figure 6a-6d As shown in the figure, it can be seen that the event-triggered attitude coordination controller is updated quickly in the initial stage to achieve attitude coordination. When the control system is stable, the controller is updated slowly to save formation system resources.
[0139] Among them, the details of the trigger interval after the control system is stable are shown in the following Table 1. Compared with the corresponding time-triggered controller with a fixed frequency of 10 Hz, the event-triggered gesture collaborative controller designed by the present invention can save more than 90% of communication resources.
[0140] Table 1 Trigger interval (40-200s)
[0141] Spacecraft 1 Spacecraft 2 Spacecraft 3 Spacecraft 4 Trigger times 123 95 130 97 Minimum trigger interval 0.01s 0.42s 0.11s 0.20s Average trigger interval 1.30s 1.69s 1.23s 1.62s Maximum trigger interval 7.41s 16.10s 9.87s 9.59s Reduction rate 92.3％ 94.1％ 91.9％ 93.9％
[0142] It can be seen that the event-triggered spacecraft formation attitude collaborative control method provided by an embodiment of the present invention can significantly save the energy, communication and computing resources of the formation system while ensuring that the formation system has good control performance.
[0143] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In addition, "front", "back", "left", "right", "upper" and "lower" in this article are all referenced to the placement state shown in the accompanying drawings.
[0144] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A spacecraft formation attitude collaborative control method based on event triggering, characterized in that: include: Establish the attitude dynamics model of the spacecraft formation system considering external disturbances and model uncertainties; According to the attitude and angular velocity information of the formation spacecraft and the communication relationship between the formation spacecraft, setting auxiliary variables for representing the coordination error of the spacecraft formation system; According to the collaborative error auxiliary variable, the measurement error variable is set; According to the cooperative error auxiliary variable and the measurement error variable, the event-triggered attitude cooperative control law and the event triggering condition are determined; Control the attitude and angular velocity of the formation spacecraft according to the event-triggered attitude cooperative control law, and determine whether the event triggering condition is met. If so, update the event-triggered attitude cooperative control law corresponding to the formation spacecraft, and send the status information of the formation spacecraft to the adjacent formation spacecraft; The following attitude dynamics model of the spacecraft formation system considering external disturbances and model uncertainties is established: Where I3 represents the 3×3 dimensional identity matrix, represents the attitude of the ith formation spacecraft described by the modified Rodriguez parameters, Represents σ i The derivative of represents the angular velocity of the i-th formation spacecraft in the body coordinate system, Represents ω i The derivative of represents the inertia matrix of the i-th formation spacecraft, represents the control input of the i-th formation spacecraft, represents the generalized disturbance corresponding to the i-th formation spacecraft, including external disturbance and model uncertainty, ||·|| represents the 2-norm, and for the three-dimensional vector Represents the skew-symmetric matrix corresponding to x, defined as represents the set of real numbers; Set the following collaborative error auxiliary variables: s i =r1e 1i +e 2i Among them, e 1i 、e 2i 、e 3i 、s i , χ 1i , χ 2i , χ 3i and are auxiliary variables of collaborative errors, n represents the number of spacecraft in the formation, σ j represents the attitude of the j-th formation spacecraft described by the modified Rodriguez parameters, Represents σ j The derivative of j represents the angular velocity of the j-th formation spacecraft in the body coordinate system, Represents ω j The derivative of r1 is a positive constant, σ d and ω d denote the desired attitude and angular velocity of the formation spacecraft, respectively. Represents σ d The derivative of ij represents the element in the i-th row and j-th column of the adjacency matrix A. The adjacency matrix A is used to represent the communication connectivity between the spacecraft in each formation. If the i-th formation spacecraft can receive the information of the j-th formation spacecraft, then a ij > 0, otherwise a ij =0, b i represents the i-th element of vector B. Vector B is used to describe whether each spacecraft in the formation can obtain the expected information. If the i-th spacecraft in the formation can obtain the expected information, then b i =1, otherwise b i =0, represents the current triggering time of the j-th formation spacecraft, Indicates that at the trigger time The attitude of the j-th formation spacecraft is described by the modified Rodriguez parameter under express The derivative of Indicates that at the trigger time The angular velocity of the j-th formation spacecraft in the body coordinate system; Set the measurement error variables as follows: in, and are all measurement error variables, represents the current triggering time of the i-th formation spacecraft, Indicates that at the trigger time The attitude of the i-th formation spacecraft is described by the modified Rodriguez parameter under Indicates that at the trigger time The angular velocity of the i-th formation spacecraft in the body coordinate system is, Indicates that at the trigger time The auxiliary variable of the coordinated error corresponding to the i-th formation spacecraft under Indicates that at the trigger time The auxiliary variable χ of the coordinated error corresponding to the i-th formation spacecraft under 3i , f(ω i )=ω i × J i ω i .
2. The event-triggered spacecraft formation attitude collaborative control method according to claim 1, characterized in that: The event-triggered attitude cooperative control law is: in, k i =k0+r1||J i ||+n+1 b i =(n+1)(δ2||J i ||+r max ) u i represents the control input of the i-th formation spacecraft, ε1, ε2, r2, r3, k0 and are all positive numbers, ρ max , δ2, δ3 and δ4 are the upper bounds of generalized disturbance, generalized angular acceleration, attitude measurement error, and angular velocity measurement error, respectively. and To adaptively update variables, and The initial value of is preset, and sgn(·) represents the standard sign function.
3. The event-triggered spacecraft formation attitude collaborative control method according to claim 2, characterized in that: The event trigger conditions are: F i ≥0 in,