Spacecraft cluster robust formation control method based on dynamic event triggering mechanism

Abstract

The invention discloses a spacecraft cluster robust formation control method based on a dynamic event trigger mechanism, which is applied to the technical field of spacecraft cluster formation control, and aims to solve the problem that the prior art still has certain limitations under the complex conditions of limited communication, unknown control input of a virtual leader, external disturbance and the like. The method comprises the following steps: firstly, constructing a six-degree-of-freedom attitude and orbit coupling spacecraft cluster system model influenced by external disturbance and model uncertainty; on the basis, a robust formation control scheme based on a dynamic event trigger communication mechanism is designed, and the scheme comprises three key components, the three mechanisms are respectively a self-adaptive second-order expansion system based on local discontinuous communication, a multi-spacecraft robust formation device based on neural network self-adaptive estimation and a unified dynamic event trigger communication mechanism.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft cluster formation control, and in particular relates to a spacecraft cluster robust formation control technology. Background Art

[0002] With the continuous advancement of aerospace technology, spacecraft swarm formation flight control technology has gradually become an important research direction in the aerospace field. Spacecraft swarm formation flight, due to its ability to perform a variety of complex tasks, has broad application prospects in distributed remote sensing, space exploration, satellite communications, and other fields. However, in practical applications, spacecraft swarm formation control faces many challenges, including limited communication, global unknowns in the virtual leader's control input, and external disturbances.

[0003] First, limited communication between spacecraft has always been a key factor hindering formation control performance. In actual missions, limited communication bandwidth, signal transmission delays, and communication interruptions are common, making traditional continuous communication control strategies difficult to implement effectively. Second, the global unknown control inputs of the virtual leader further complicate formation control, as spacecraft must achieve coordinated motion in the absence of global information. Furthermore, spacecraft are subject to both environmental disturbances and model uncertainty during operation, further exacerbating the complexity of formation control.

[0004] While existing research has proposed several solutions for spacecraft formation control, most approaches still face limitations under complex conditions such as limited communication, unknown virtual leader control inputs, and external disturbances. For example, some traditional control methods based on continuous communication can lead to excessive consumption of communication resources in communication-restricted environments. Meanwhile, some methods based on traditional control theory are less capable of handling the global unknowns of virtual leader control inputs and model uncertainty. Furthermore, while existing robust control methods based on neural networks can address model uncertainty and external disturbances to a certain extent, they still struggle with handling potential control input chatter and achieving asymptotic stability.

[0005] In summary, how to achieve robust formation control of spacecraft clusters under complex conditions such as limited communication, global unknown of virtual leader control input, and external disturbances, while eliminating control chatter and ensuring the asymptotic stability of the system, remains a key issue that needs to be urgently addressed in the current field of spacecraft formation control technology. Summary of the Invention

[0006] To address the aforementioned technical issues, this paper proposes a robust formation control method for spacecraft swarms based on a dynamic event-triggered communication mechanism. This method aims to address the formation control problem of spacecraft swarms under complex conditions such as limited communication, globally unknown virtual leader control inputs, and external disturbances. Furthermore, this paper provides rigorous theoretical proof of the asymptotic stability of the spacecraft swarm system and the absence of the Zeno phenomenon of the dynamic event-triggered communication mechanism.

[0007] The technical solution adopted by the present invention is: a spacecraft cluster robust formation control method based on dynamic event triggered communication mechanism,

[0008] Construct a six-degree-of-freedom attitude-orbit coupled spacecraft cluster system model affected by external disturbances and model uncertainties;

[0009] Based on the six-degree-of-freedom attitude-orbit coupled spacecraft cluster system model, a robust formation controller based on dynamic event-triggered communication mechanism is constructed; specifically:

[0010] According to the six-degree-of-freedom attitude-orbit coupled spacecraft cluster system model, an adaptive second-order expansion system based on local discontinuous communication is designed;

[0011] According to the adaptive second-order extended system, a distributed robust formation controller based on neural network fitting is designed;

[0012] Each spacecraft maintains its own adaptive second-order expansion system and distributed robust formation controller. The specific process is as follows:

[0013] Each spacecraft continuously monitors its own state. When the Euclidean norm of the measurement error associated with the state exceeds a specified threshold, the follower immediately broadcasts its current state to its neighbors and updates its own adaptive second-order expansion system and distributed robust formation controller. At the same time, the measurement error is immediately reset to 0. When a spacecraft receives the latest trigger state information from its neighbors, its own adaptive second-order expansion system and distributed robust formation controller are immediately updated.

[0014] A robust formation controller based on dynamic event-triggered communication mechanism is deployed in a spacecraft cluster system, thereby realizing robust formation control of spacecraft clusters in a communication-constrained environment.

[0015] Beneficial Effects of the Present Invention: This invention proposes a robust formation control method for spacecraft swarms based on a dynamic event-triggered communication mechanism. First, a model of a six-degree-of-freedom attitude-orbit coupled spacecraft swarm system subject to external disturbances and model uncertainty is constructed. Based on this, a robust formation control scheme based on the dynamic event-triggered communication mechanism is designed. The design process of this scheme consists of three key steps. First, an adaptive second-order expansion system based on local discontinuous communication is designed for the spacecraft to overcome the adverse effects of communication limitations and the global unknown of the virtual leader's control input on the spacecraft swarm system. Second, a robust formation controller based on neural network adaptive estimation is designed for the spacecraft by utilizing the composite uncertainties in the neural network fitting system. This controller introduces a robust term with adaptive parameters, which not only effectively eliminates the adverse effects of neural network fitting residuals on control performance but also avoids possible control input chatter, thereby further improving the control accuracy and robustness of the system. Finally, a unified dynamic event-triggered communication mechanism is designed for the spacecraft to adjust the communication frequency between spacecraft, reducing unnecessary information exchange between spacecraft and making the proposed scheme more suitable for environments with limited communication. The present invention focuses on the formation control problem of spacecraft cluster systems under complex conditions such as limited communication, global unknown of virtual leader control input and external disturbances, and proposes an effective robust formation control scheme, which significantly improves the robustness and reliability of the spacecraft cluster system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The present invention provides a flow chart of a spacecraft cluster formation control method using a dynamic event-triggered communication mechanism.

[0017] Figure 2 Schematic diagram of the communication topology relationship between a given spacecraft and a leader in an embodiment of the present invention.

[0018] Figure 3 Schematic diagram of the attitude and position tracking error changes of a given spacecraft in an embodiment of the present invention;

[0019] Among them, (a) is the attitude tracking error curve, and (b) is the position tracking error curve.

[0020] Figure 4 A schematic diagram of control input changes of a given spacecraft in an embodiment of the present invention;

[0021] Among them, (a) is the attitude control input change curve, and (b) is the position control input change curve.

[0022] Figure 5A schematic diagram of the F-norm variation of the neural network weight estimation value of a given spacecraft in an embodiment of the present invention and the motion trajectory of the spacecraft in the orbital coordinate system;

[0023] Among them, (a) is the change curve of the neural network weight F norm, and (b) is the motion trajectory of the spacecraft in the LVLH system.

[0024] Figure 6 Schematic diagram of the communication time interval of a given spacecraft in an embodiment of the present invention;

[0025] Among them, (a) is the communication time interval of spacecraft 1, (b) is the communication time interval of spacecraft 2, (c) is the communication time interval of spacecraft 3, and (d) is the communication time interval of spacecraft 4. DETAILED DESCRIPTION

[0026] To facilitate those skilled in the art to understand the technical content of the present invention, the present invention is further explained below with reference to the accompanying drawings.

[0027] like Figure 1 As shown, the method of the present invention comprises the following steps:

[0028] S1. Establish a disturbed six-degree-of-freedom attitude-orbit coupled spacecraft cluster system;

[0029] S2. Construct an adaptive second-order expansion system based on local discontinuous communication;

[0030] S3. Design a multi-spacecraft robust formation controller based on neural network adaptive estimation;

[0031] S4. Design a unified dynamic event-triggered communication mechanism;

[0032] S5. Based on S2-S4, a robust formation control scheme based on dynamic event-triggered communication mechanism is designed to complete multi-spacecraft formation control.

[0033] Furthermore, the step S1 is specifically as follows:

[0034] S11. Construct a six-degree-of-freedom spacecraft attitude-orbit coupling dynamics model.

[0035] Considering a spacecraft cluster system consisting of n spacecraft, the modified Rodrigues parameters (MRPs) and CW (Clohessy-Wiltshire) equations are used to describe the attitude change of spacecraft i in the Earth-centered inertial coordinate system (ECI) and the relative motion in the orbital coordinate system (Local Vertical / Local Horizontal, LVLH), respectively. First, define σ i =[σ i1 ,σ i2 ,σ i3 ] T and ρ i =[ρ i1 ,ρ i2 ,ρ i3 ] T They represent the attitude of spacecraft i in the ECI coordinate system and the relative position in the LVLH coordinate system respectively. The index of spacecraft i belongs to Then the attitude dynamics equation and relative orbital kinematics equation of the i-th spacecraft are shown in equations (1) and (2):

[0036]

[0037] in Respectively represent ρ i The second and first derivatives of ω i =[ω i1 ,ω i2 ,ω i3 ] T It represents the projection of the angular velocity of the body coordinate system of spacecraft i relative to the ECI system in this system, represents the angular velocity of the reference point in the LVLH coordinate system rotating around the earth (the reference point is the origin of the LVLH coordinate system), J i ∈R 3×3 ,m i ∈R represent the moment of inertia and mass of spacecraft i, τ i ,τ di ∈R 3×1 They represent the projections of the control torque and interference torque acting on spacecraft i in the system, F bi ,f di ∈R 3×1 They represent the projection of the control force of spacecraft i on the system and the external interference it receives. In the present invention, R represents a real number set, and the matrix G(σ i )∈R 3×3 is represented as:

[0038]

[0039] In the present invention, for vector x=[x1,x2,x3] T , the superscript T means taking the transpose of a matrix or vector, [x] × It is expressed as follows

[0040] That is, vector σ i =[σ i1 ,σ i2 ,σ i3 ] T ,

[0041] Matrix R lbi ∈R 3×3 Represents the rotation matrix of spacecraft i to the LVLH coordinate system, and satisfies the following relationship

[0042]

[0043] R le ,R bei ∈R 3×3 They represent the rotation matrices from the ECI coordinate system to the LVLH coordinate system and from the spacecraft i system to the ECI coordinate system, R le It can be calculated by the position and velocity of the reference point. From formula (4), we can see that the matrix R lbi The value of is mainly determined by the attitude σ of spacecraft i i Then combined with formula (2), we can see that R lbi It is also used as the control input gain matrix in the relative motion model of spacecraft i. In summary, the coupling of attitude and position in the six-degree-of-freedom spacecraft attitude-orbit coupling dynamics model proposed in this invention is mainly reflected in the matrix R lbi middle.

[0044] Definition G i =G(σ i ), and then rewrite Equation (1) into the Euler-Lagrange form:

[0045]

[0046] in

[0047] Considering the order of magnitude difference between the spacecraft position state and attitude state, the position state can be normalized. The state variable of spacecraft i is defined as where ρ maxRepresents the maximum distance between the spacecraft and the reference point, which is an artificially set constant. Then, by combining equations (2) and (5), we can obtain the attitude-orbit coupling dynamic model of spacecraft i:

[0048]

[0049] in, represents the rate of change of the state variables of spacecraft i, For i The derivative of

[0050] This invention mainly considers the situation where the spacecraft is subject to bounded but unknown disturbances in the space environment, which means that ||F di || has an upper bound. Moreover, due to factors such as fuel loss and sensor noise, the mass m of the spacecraft is i and moment of inertia J i Cannot be accurately obtained.

[0051] S12. Determine the communication constraint relationship between spacecraft.

[0052] In the research of this invention, the spacecraft cluster system can realize distributed collaborative control behavior through local network communication, and the communication structure between spacecraft can be described by the following graph theory knowledge.

[0053] Assume that the spacecraft cluster system contains n spacecraft, and the communication topology between spacecraft is a fixed connected undirected topology in represents a point set, where represents the node of spacecraft i in the topology, represents the edge set, represents the adjacency matrix. If Then a ij >0, which means that spacecraft i can receive the information sent by spacecraft j. Then a ij = 0. At the same time, the neighbor set of spacecraft i can be defined as represents the degree matrix, where So we can get the topology The Laplace matrix of Used in the following text Represents matrices respectively The element in row i and column j of .

[0054] S13. Clarify the problem of robust formation control of spacecraft clusters

[0055] In order to facilitate the design of robust formation control scheme, a virtual leader is introduced for the multi-spacecraft system, and its dynamic model is as follows:

[0056]

[0057] where ξ l , Represent the leader’s state and state change rate respectively, represents the control input of the leader, which is unknown and bounded for all spacecraft, i.e. in represents a positive constant. At the same time, for the sake of convenience, f l replace

[0058] At the same time, the virtual leader is used as a node Using directed graphs Describe the communication relationship between the spacecraft and the virtual leader. Let As the adjacency matrix between the virtual leader and the spacecraft, if b i >0, then spacecraft i can directly obtain the information of the virtual leader ξ l , Otherwise b i = 0. Define the matrix Considering the topological connectivity, the matrix It is positive.

[0059] Based on the above analysis, the present invention aims to solve the problem of robust formation control of a six-degree-of-freedom attitude-orbit coupled spacecraft cluster system under communication constraints and external interference conditions. Specifically, the communication between spacecraft is determined by the topology The communication between the spacecraft and the leader is described by the topology Description. Status information in leader l , In the case of local knowledge, all spacecraft can track the trajectory of the virtual leader in a certain attitude and formation configuration through local discontinuous communication, and rely on dynamic event-triggered communication mechanism to reduce the communication frequency between spacecraft, that is, the following conditions are met.

[0060]

[0061] where d li Denotes the expected state deviation vector of spacecraft i relative to the leader. In the present invention, we consider it to be an internal parameter of spacecraft i, so it does not need to be obtained through communication.

[0062] The step S2 is specifically as follows:

[0063] S21. Given the challenges of limited communication and global unknowns in the virtual leader's control input, in order to effectively solve this problem, it is necessary to construct an adaptive second-order expansion system based on local discontinuous communication for spacecraft i. First, the following two auxiliary variables φ are designed for spacecraft i. i and

[0064]

[0065] in They represent the output of the second-order expansion system respectively. Furthermore, the compact form of Equation (9) can be expressed as:

[0066]

[0067] in It can be seen from formula (9) that the two auxiliary variables φ of spacecraft i i , The output of the extended second-order system of the neighboring spacecraft is used in both, which means that real-time information exchange is required between spacecraft. However, considering the limited communication resources, it is necessary to introduce an event trigger mechanism to reduce the communication frequency between spacecraft, so as to achieve the purpose of saving communication resources. Under the event trigger mechanism, each spacecraft broadcasts its own observation value to the neighbor only when the event trigger condition is met. Therefore, the spacecraft can only obtain the information broadcast by the neighbor at the time of event triggering. So we can use the variable represents the information broadcast by spacecraft i to its neighbors for the kith time, represents the time when spacecraft i broadcasts information to its neighbors for the kith time. Since spacecraft i can only receive information broadcast by neighbor j for the kjth time, equation (9) can be transformed into:

[0068]

[0069] Formula (9) and formula (10) are mainly used for the stability analysis of the system in the following text. Represents two auxiliary variables under the event trigger mechanism, which are mainly used to build an adaptive extended second-order system. The following transformations can be performed between the two:

[0070]

[0071] in represents the measurement error between the trigger moment and the current moment, ξi express With φ i difference, express and The difference, Ξξi , It is mainly used for the stability analysis of the system in the following text.

[0072] S22, considering the control input f of the virtual leader l It is unknown for all spacecraft, but combined with f l , we can use f l Upper bound estimate Therefore, the present invention designs the following adaptive extended second-order system for spacecraft i:

[0073]

[0074] Where β1,β2>0, Represents spacecraft i The estimated value of , its adaptive update rate is designed as follows:

[0075]

[0076] Where γ1>0.

[0077] Furthermore, the step S3 is specifically as follows:

[0078] S31. Use neural network to fit composite uncertainties. First, design the following auxiliary variables for spacecraft i:

[0079]

[0080] where k p ,k d >0. Substituting equation (15) into equation (6) yields the following new kinetic equation:

[0081]

[0082] Among them D i =k d B i .

[0083] Considering that the spacecraft dynamics model is difficult to be accurately modeled and the spacecraft is subject to external disturbances, the present invention uses radial basis function neural networks (RBFNNs) to fit the composite uncertainty term r i , so we can get the following equation:

[0084]

[0085] Where W i ∈R p×6 represents the ideal neural network weight, δ i ∈R 6×1Represents the neural network fitting residual, which has an unknown upper bound δ mi , for the radial basis function h(s i )∈R p×1 It is designed as a Gaussian function:

[0086]

[0087] where μ k ∈R 6×1 ,c k ∈R,k∈{1,2,…,p}.

[0088] Thus, we can get the estimated value of the composite uncertainty:

[0089]

[0090] in It represents the estimated value of the ideal weight of the neural network, and its update rate is designed to be as follows:

[0091]

[0092] Where γ2>0.

[0093] S32. Based on step S31, this step designs a robust term with adaptive parameters for spacecraft i to eliminate the adverse effects of the neural network fitting residual on the control performance of the spacecraft system and to avoid possible control input chatter. The specific form is as follows:

[0094]

[0095] in Represents the upper bound of the residual error of the neural network fitting δ mi The estimated value of Indicates that an adaptive parameter satisfies At the same time, their update rates are designed to be as follows:

[0096]

[0097] Among them, γ3,γ4>0.

[0098] S33 designs a distributed robust formation controller based on neural network fitting. First, define the consistent formation error of spacecraft i:

[0099]

[0100] Taking into account the discontinuous communication between spacecraft, Equation (24) can be rewritten as follows:

[0101]

[0102] in It represents the information broadcast by spacecraft j to neighboring spacecraft for the kjth time, so the measurement error can be defined as It is worth noting that Then Equation (25) can be written in a compact form:

[0103]

[0104] in

[0105] Based on the above analysis, combined with equations (21), (22) and (25), the following controller can be designed for spacecraft i:

[0106]

[0107] where k s >0.

[0108] Furthermore, the step S4 is specifically as follows:

[0109] S41. First, design an adaptive parameter χ for spacecraft i. ki , and its update rate is as follows:

[0110]

[0111] where α ki ,χ ki (0),κ ki ,η ki >0 is a parameter that can be set manually. It is a parameter determined by the stability of the spacecraft system. The specific value selection method will be given in step S5.

[0112] S42: To reduce unnecessary information transmission between adjacent spacecraft and alleviate the burden on the communication network, a unified dynamic event-triggered communication mechanism is designed to adjust the communication frequency between spacecraft. For spacecraft i, the dynamic event-triggered mechanism is designed as follows:

[0113]

[0114] in represents a time series, i.e. in

[0115] The dynamic event trigger function Designed as follows:

[0116]

[0117] where τ ki >0. Under the proposed unified dynamic event-triggered communication mechanism, each spacecraft only needs to continuously monitor its own status ξ i , and s i , and estimated and Without considering any real-time information from neighbors. When the Euclidean norm of exceeds the specified threshold (i.e. ), follower i will immediately broadcast its current state to its neighbors and update its second-order expansion system (13) and controller (27). At the same time, the measurement error will be immediately reset to 0. On the other hand, when spacecraft i receives the latest trigger state information from its neighbors, its own second-order expansion system and controller will also be updated immediately. It is worth noting that there is no communication between adjacent spacecraft between two consecutive trigger moments.

[0118] S43. Based on equations (29) and (30), for Both have χ ki >0 and the following inequality holds

[0119]

[0120] Next we will prove that the above equation holds. When t = 0, we have χ ki (0)>0. Then according to equations (29) and (30), we can obtain the following inequality:

[0121]

[0122] So far, we have proved Equation (31). Next, we will prove that ki >0. Because τ ki >0, formula (32) can be rewritten as:

[0123]

[0124] Then, combining equations (28) and (33), we can obtain:

[0125]

[0126] According to formula (34), we can get

[0127] Furthermore, the specific content of step S5 is as follows:

[0128] S51. In S2-S4, design a robust formation control scheme based on dynamic event-triggered communication mechanism.

[0129] The robust formation control scheme based on dynamic event-triggered communication mechanism designed in the present invention mainly consists of three key components: an adaptive second-order expansion system based on local discontinuous communication (13), a multi-spacecraft robust formation controller based on neural network adaptive estimation (27), and a unified dynamic event-triggered communication mechanism (29).

[0130] S52. By using the robust formation control scheme based on the dynamic event-triggered communication mechanism designed by the present invention, robust formation control of a spacecraft cluster can be achieved.

[0131] Consider the Lyapunov function of the following closed-loop system:

[0132]

[0133] in Represents spacecraft i The estimation error of represents the tracking error, represents the neural network weight estimation error, Represents the upper bound estimation error of the neural network fitting residual, p i >0∈R. Because the matrix is a positive definite matrix, so we can get the Lyapunov function V is positive definite. Then take the time derivative of V to get:

[0134]

[0135] in They are expressed as follows:

[0136]

[0137] First analyze According to formula (10) and formula (13), formula (37) can be simplified as:

[0138]

[0139] Substituting Equation (12) into the above equation and using Young's inequality, Equation (39) can be simplified to:

[0140]

[0141] in, ε1>0. Then according to f l Substituting Equation (14) into Equation (40) yields the following:

[0142]

[0143] Continuing to analyze We first give the following important inequalities:

[0144]

[0145] Similarly, we can get:

[0146]

[0147] Then, we can substitute inequalities (42) and (43) into equation (41) to obtain:

[0148]

[0149] The parameters are:

[0150]

[0151] By properly designing the parameters, θ1>0 can be achieved.

[0152] Then analyze Substituting equations (16), (21), (23) and (27) into equation (38), we can obtain:

[0153]

[0154] For the Euler-Lagrangian system, we have Substituting equations (13), (15), (18) and (25) into equation (45) yields:

[0155]

[0156] in, By reasonably designing the parameters, the parameters θ3,θ5 can be made greater than 0.

[0157] Then we can combine equation (44) and equation (46)

[0158]

[0159] Then substitute formula (28) into the above formula to obtain:

[0160]

[0161] parameter Take (θ0-θ6), and according to χ ki >0, then formula (48) can be simplified to the following form:

[0162]

[0163] Then, integrating both sides of equation (49) yields:

[0164]

[0165] From formula (50), we can see that the Lyapunov function V is bounded, and then combined with formula (35), we can know that are all bounded. Combining equations (10) and (13) and The boundedness of Further, we can get Taking into account The boundedness of ξ can be obtained i ∈L ∞ Combining with formula (15), we can get Further Taking into account The boundedness of Then, combining equations (18) and (27), we can get u i ,r i ∈L ∞ , further, combined with formula (16), we can get Summarizing the above results, we can get

[0166] Then from formula (50) we can see intuitively that By using Babarlet's Lemma, we can get that when t→∞, Combined with formula (10), because So there is When t→∞. Combined with formula (15), because So there is When t→∞. Combining the above analysis, we can get Therefore, the designed scheme can realize the formation control of multiple space vehicles.

[0167] S53. The designed unified dynamic event-triggered communication mechanism will not cause Zeno phenomenon.

[0168] First of all, Taking the time derivative yields the following equation:

[0169]

[0170] Since the stability proof of the closed-loop system has been completed in step S52, it can be obtained are all bounded. Therefore There is also an upper bound, so we have:

[0171]

[0172] where Z ki >0. In the time domain Integrating both sides of equation (52) yields:

[0173]

[0174] Because in There is always Then combined with formula (53), we can get The following inequality exists at all times:

[0175]

[0176] Then, combined with the designed dynamic event triggering mechanism (29) and (30), The moments are:

[0177]

[0178] Furthermore, combining equations (54) and (55), we can obtain:

[0179]

[0180] From formula (56), we can see that the value of T is always positive, so the designed dynamic event-triggered communication mechanism will not exhibit Zeno behavior.

[0181] S54. By deploying the robust formation control scheme based on the dynamic event-triggered communication mechanism proposed in S51 into the spacecraft cluster system, robust formation control of the spacecraft cluster in a communication-restricted environment can be achieved.

[0182] In this example, four spacecraft are considered. The control objective is to estimate the information of the virtual leader directly or indirectly, so that the spacecraft can form a tetrahedron formation and track the trajectory of the leader through discontinuous local interactions. Moreover, the attitude of all spacecraft must be consistent with the attitude of the virtual leader. However, only the first and second spacecraft can directly obtain the information of the virtual leader, and the remaining spacecraft can only communicate and interact with their neighbors. At the same time, the parameters of each spacecraft are m = 50kg, J = diag (27, 25, 40) kg·m 2 .

[0183] The initial position of the leader is at the reference point, assuming that the orbital eccentricity of the reference point is 0, the right ascension of the ascending node is 45 degrees, and the orbital radius is R c =6678140m. Define ω l =0.002rad / s, the leader's state is:

[0184] ζ l =[0.2cos(ω l t),0.2cos(ω l t),0.2sin(ω l t), 50cos(ω l t),50sin(ω l t),50sin(ω l t)] T

[0185] The initial position and velocity of the follower spacecraft are:

[0186] ρ1(0)=[-20,-25,-25] T ,ρ2(0)=[-20,-30,95] T ,ρ3(0)=[20,-35,20] T

[0187] ρ4(0)=[-40,-35,20] T (m),v i =[0,0,0] T (m / s)

[0188] The initial values of the attitude and angular velocity of the follower spacecraft are:

[0189] σ1(0)=[0.25,0.01,0.08] T ,σ2(0)=[0.05,0.1,0.1] T ,σ3(0)=[0.03,0.36,0.04] T

[0190] σ1(0)=[0.3,0.01,0.0015] T ,ω i =[0,0,0] T (rad / s)

[0191] The expected state deviation vector of the follower spacecraft and the virtual leader is:

[0192] d l1 =[0,0,0,0,-75,0] T ,d 2l =[0,0,0,25,0,35] T

[0193] d l3 =[0,0,0,25,0,-35] T ,d l4=[0,0,0,-50,0,0] T

[0194] Taking into account the saturation of control input, the maximum control force of all spacecraft is 50N and the maximum control torque is 0.05Nm.

[0195] Reasonable parameter design enables the designed neural adaptive multi-spacecraft leader-follower formation control method to complete the robust formation control task of multiple spacecraft. The parameters are shown in Table 1:

[0196] Table 1 Numerical simulation parameters

[0197]

[0198]

[0199] For neural networks, the Gaussian function has a variance of c k =1, select p = 25 neural network nodes, the basis function center is μ k = uniformly selected from [-1, 1]. At the same time, the external interference to the spacecraft is considered as follows:

[0200] f di =10 -3 [3cos(0.5t)+10sin(0.1t)+15sin(0.05t)]·13(N)

[0201] τ di =10 -4 [sin(0.1t)+cos(0.01t)+sin(0.05t)]·13(Nm)

[0202] The example results are in Figure 2-Figure 6 given. Figure 3 The attitude tracking error and position tracking error of the spacecraft are shown. Figure 3 As can be seen from the figure, the tracking errors of attitude and position converge within 200s, and the tracking steady-state errors are less than 5×10 -3 (MRPs) and 0.2(m). Figure 4 The control input torque and control force of the spacecraft are shown. Figure 4 It can be seen that both the control torque and the control force meet the control saturation constraints, and the control input changes relatively smoothly without obvious vibration. This also shows to a certain extent that the control scheme designed by the present invention is suitable for practical applications. Figure 5 (a) shows the changing trend of the F-norm of the weight estimates of the neural network of all spacecraft. It can be seen that after 500 seconds, its change gradually stabilizes, indicating that the neural network has fitted the external disturbances and uncertainties of the system. Figure 5 (b) shows the motion trajectories of all spacecraft in the LVLH coordinate system. It can be seen that all spacecraft eventually form a tetrahedron formation, which also proves that the control scheme designed in this invention can solve the robust formation control problem of spacecraft clusters. Figure 6 The data shows the communication time intervals of all spacecraft under the inter-machine communication mechanism based on the event-triggered mechanism. It can be seen that in most time periods, the communication intervals between spacecraft are greater than 0.2s, which is significantly reduced compared with the time-triggered communication mechanism (communication period is 0.05s).

[0203] In summary, this paper proposes a robust formation control method for spacecraft swarms based on a dynamic event-triggered communication mechanism. First, a model of a six-degree-of-freedom attitude-orbit coupled spacecraft swarm system subject to external disturbances and model uncertainty is constructed. Based on this, a robust formation control scheme based on the dynamic event-triggered communication mechanism is designed. The design process of this scheme consists of three key steps. First, an adaptive second-order expansion system based on local discontinuous communication is designed for the spacecraft to overcome the adverse effects of communication limitations and the global unknown of the virtual leader's control input on the spacecraft swarm system. Second, a robust formation controller based on neural network adaptive estimation is designed for the spacecraft, utilizing the compound uncertainties in the neural network fitting system. This controller introduces a robust term with adaptive parameters, which not only effectively eliminates the adverse effects of neural network fitting residuals on control performance but also avoids possible control input chatter, thereby further improving the control accuracy and robustness of the system. Finally, a unified dynamic event-triggered communication mechanism is designed for the spacecraft to adjust the communication frequency between spacecraft, reducing unnecessary information exchange between spacecraft and making the proposed scheme more suitable for environments with limited communication. The present invention focuses on the formation control problem of spacecraft cluster systems under complex conditions such as limited communication, global unknown of virtual leader control input and external disturbances, and proposes an effective robust formation control scheme, which significantly improves the robustness and reliability of the spacecraft cluster system.

[0204] Those skilled in the art will appreciate that the embodiments described herein are intended to aid the reader in understanding the principles of the present invention, and it should be understood that the scope of the present invention is not limited to such specific descriptions and embodiments. Various modifications and variations are readily apparent to those skilled in the art. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are intended to be included within the scope of the claims.

Claims

1. A robust formation control method for spacecraft clusters based on a dynamic event-triggered communication mechanism, characterized in that: Application scenarios include: multiple spacecraft and a virtual leader, each spacecraft tracks the trajectory of the virtual leader; the virtual leader is used as a node Using directed graph Describe the communication relationship between the spacecraft and the virtual leader, The point set elements in include and treating each spacecraft as a node, The edge set elements in include whether there is a communication connection between the spacecraft and the virtual leader, The adjacency matrix elements in include information about whether the spacecraft can acquire the virtual leader; Use a fixed connected undirected topology Describe the communication topology between spacecraft, The point set elements in include each spacecraft as a node, The edge set elements in include the existing communication links between spacecraft, The adjacency matrix elements in include whether the two spacecraft can receive the information sent by each other; The formation control method specifically includes: Construct a six-degree-of-freedom attitude-orbit coupled spacecraft cluster system model affected by external disturbances and model uncertainties; Based on the six-degree-of-freedom attitude-orbit coupled spacecraft cluster system model, a robust formation controller based on dynamic event-triggered communication mechanism is constructed; specifically: According to the six-degree-of-freedom attitude-orbit coupled spacecraft cluster system model, an adaptive second-order expansion system based on local discontinuous communication is designed; According to the adaptive second-order extended system, a distributed robust formation controller based on neural network fitting is designed; Each spacecraft maintains its own adaptive second-order expansion system and distributed robust formation controller. The specific process is as follows: Each spacecraft continuously monitors its own state. When the dynamic event trigger function related to the state meets the dynamic event trigger mechanism, the follower immediately broadcasts its current state to its neighbors and updates its own adaptive second-order expansion system and distributed robust formation controller. At the same time, the measurement error is immediately reset to 0. When a spacecraft receives the latest trigger state information from its neighbors, its own adaptive second-order expansion system and distributed robust formation controller are immediately updated. A robust formation controller based on dynamic event-triggered communication mechanism is deployed in a spacecraft cluster system, thereby realizing robust formation control of spacecraft clusters in a communication-constrained environment.

2. The method for robust formation control of a spacecraft cluster based on a dynamic event-triggered communication mechanism according to claim 1, characterized in that: The six-degree-of-freedom attitude-orbit coupling spacecraft cluster system model is expressed as: in, Represents the state variable ξ of spacecraft i i The rate of change of express The first derivative of σ i represents the attitude of spacecraft i in the ECI coordinate system, I3 represents the 3D unit matrix, τ di represents the projection of the disturbance torque acting on spacecraft i in this system, f di represents the external interference to spacecraft i, ρ max represents the maximum distance between the spacecraft and the reference point, τ i represents the control torque acting on spacecraft i, F bi represents the projection of the control force of spacecraft i on this system, R lbi represents the rotation matrix from the spacecraft i system to the LVLH coordinate system, 3. The method for robust formation control of a spacecraft cluster based on a dynamic event-triggered communication mechanism according to claim 2, characterized in that: The adaptive second-order expansion system is expressed as: Among them, β1,β2>0, Represents spacecraft i The estimated value of Ξ ξi express With φ i difference, express and The difference, φ i and is an auxiliary variable, a ij express The elements of the adjacency matrix in , and Indicates the measurement error between the trigger moment and the current moment, b i express The elements of the adjacency matrix in .

4. The method for robust formation control of a spacecraft cluster based on a dynamic event-triggered communication mechanism according to claim 3, characterized in that: The distributed robust formation controller is expressed as: in, represents a column vector, Indicates the trigger time The corresponding s i , k p ,k d >0, is the output of the adaptive second-order expansion system of spacecraft i itself, Indicates the trigger time The corresponding s j , represents the state variable ξ of spacecraft j j The rate of change, is the output of the adaptive second-order expansion system of spacecraft j itself, Λ i represents a robust term with adaptive parameters, represents the estimated value of the composite uncertainty term in the six-degree-of-freedom attitude-orbit coupled spacecraft cluster system model, The Laplace matrix represents the communication topology between spacecraft, I represents the 1-dimensional identity matrix, I6 represents the 6-dimensional identity matrix, k s >0.

5. The method for robust formation control of a spacecraft cluster based on a dynamic event-triggered communication mechanism according to claim 4, characterized in that: Use radial basis function neural network to fit composite uncertainties.

6. The method for robust formation control of a spacecraft cluster based on a dynamic event-triggered communication mechanism according to claim 5, characterized in that: The status monitored by each spacecraft includes: i , and s i .

7. The method for robust formation control of a spacecraft cluster based on a dynamic event-triggered communication mechanism according to claim 6, characterized in that: The dynamic event triggering function related to the state is expressed as: Among them, χ ki is the adaptive parameter, is χ ki The update rate, α ki ,χ ki (0),κ ki ,η ki >0 is a parameter that can be set manually. ,θ2,θ4,λ 1i ,λ 2i ,λ 3i ,λ 4i is a parameter determined by the stability of the spacecraft system. ,θ2,θ4,λ 1i ,λ 2i ,λ 3i ,λ 4i >0.

8. The method for robust formation control of a spacecraft cluster based on a dynamic event-triggered communication mechanism according to claim 7, characterized in that: The dynamic event triggering mechanism is designed as follows: Where t represents the current time.

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