Fault-tolerant control method, system and device for unmanned aerial vehicle cluster and medium

Abstract

The invention relates to the technical field of unmanned aerial vehicle control, and discloses a fault-tolerant control method, system and device for an unmanned aerial vehicle cluster and a medium. The method comprises the following steps: establishing a first dynamic model of a leader and a second dynamic model of each follower; designing a distributed expansion observer, and estimating state information of each follower and lumped interference formed by external disturbance of the follower and an actuator fault by using relative state information between each follower and a neighbor follower; determining the state information of the leader, and designing an event triggering mechanism according to a first error between the state information of each follower and the state information of the leader and a second error between the state information of each follower; and when the first error is greater than a first preset threshold value or the second error is greater than a second preset threshold value, determining a triggering event triggering mechanism, and controlling each follower in the unmanned aerial vehicle cluster according to the relative state information between the followers and the estimated lumped interference.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, and in particular to a fault-tolerant control method, system, device, and medium for UAV swarms. Background Technology

[0002] Unmanned aerial vehicle (UAV) swarm systems, with their inherent flexibility, robustness, and efficiency, have become a hot research topic, especially when facing complex tasks, where they demonstrate excellent fault tolerance and coordination advantages. However, as the complexity of the tasks increases, problems such as actuator failures and communication interruptions become more frequent. These situations can potentially lead to a collapse in swarm coordination, thereby affecting the successful completion of the task. Therefore, researching corresponding fault-tolerant control strategies for actuator failures is crucial for improving the robustness of the swarm.

[0003] However, most existing fault-tolerant control methods are based on ideal communication assumptions or single failure mode designs, making it difficult to cope with complex scenarios where compound faults (such as partial actuator failure, bias faults, etc.) are coupled with external disturbances. Furthermore, traditional centralized observers rely on global state information, and when communication resources are limited, data packet loss may occur, leading to a decrease in estimation accuracy. Summary of the Invention

[0004] The purpose of this invention is to provide a fault-tolerant control method, system, device and medium for unmanned aerial vehicle (UAV) swarms, which can solve the problems that existing fault-tolerant control methods cannot cope with complex scenarios coupled with compound faults and external disturbances, and the problem of insufficient estimation accuracy when communication resources are limited.

[0005] To address the aforementioned technical problems, embodiments of the present invention provide a fault-tolerant control method for unmanned aerial vehicle (UAV) swarms, comprising the following steps: For a drone swarm with one leader and multiple followers, establish a first dynamics model for the leader and a second dynamics model for each follower; Based on the second dynamics model of multiple followers, a distributed extended observer is designed. By using the distributed extended observer, the relative state information between each follower and its neighboring followers is used to estimate the state information of each follower and the lumped disturbances consisting of external disturbances and actuator failures of the followers. Based on the first dynamic model, the leader's state information is determined, and an event triggering mechanism is designed based on the first error between the state information of each follower and the leader's state information, as well as the second error between the state information of each follower. When the first error is greater than the first preset threshold or the second error is greater than the second preset threshold, the trigger event mechanism is determined, and after the trigger event mechanism is determined, each follower in the drone swarm is controlled according to the relative state information between each follower and the estimated lumped interference.

[0006] Furthermore, the distributed extended observer is: ; In the formula, , , All values ​​greater than 0 indicate the observer gain. The elements of the adjacency matrix represent the communication weights from j to i. This represents the connection weight between the follower and the leader, where i is the follower index and t is the time. The estimated position of follower i; The estimated velocity of follower i; For the lumped disturbance estimate of follower i; The actual location of neighbor follower j; The actual position of the leader; This is the control input for follower i; Let i be the set of neighbors of follower i.

[0007] Furthermore, the following formula is used to determine whether the event triggering mechanism is triggered: ; In the formula, It is a drone Measurement error, and They represent followers respectively. The position and velocity at the moment of triggering, and These are the estimated position and estimated velocity of the follower at the current moment, respectively.

[0008] Furthermore, both the first preset threshold and the second preset threshold are updated in real time using the following formula: ; In the formula, in the formula, >0 represents the dynamic threshold for event triggering of follower i; For η i (t) is the first derivative with respect to time t; α>0 is the threshold attenuation coefficient; β>0 is the threshold amplification coefficient; x̃ j (t)=x j (t)−x̂ j (t) represents the position estimation error of neighbor j; Error in estimating the leader's position; x̂ i (t) represents the estimated position of follower i; ||·|| represents the Euclidean norm.

[0009] Furthermore, each follower in the drone swarm is controlled using the following formula: ; In the formula, It is the control gain matrix. The lumped disturbance, x, is estimated using a distributed extended observer. j (t) and x i (t) represents the actual positions of neighbor j and follower i, respectively.

[0010] Embodiments of the present invention also provide a fault-tolerant control system for unmanned aerial vehicle (UAV) swarms, comprising: The model building module is used to build a first dynamics model of the leader and a second dynamics model of each follower for a leader and multiple followers in a drone swarm. The state estimation module is used to design a distributed extended observer based on the second dynamic model of multiple followers, and to estimate the state information of each follower and the lumped disturbances consisting of external disturbances and actuator failures of the followers by using the relative state information between each follower and its neighboring followers through the distributed extended observer. The trigger design module is used to determine the leader's state information based on the first dynamic model, and to design an event triggering mechanism based on the first error between the state information of each follower and the leader's state information and the second error between the state information of each follower. The fault-tolerant control module is used to determine the trigger event triggering mechanism when the first error is greater than the first preset threshold or the second error is greater than the second preset threshold, and after the trigger event triggering mechanism is triggered, to control each follower in the drone swarm based on the relative state information between each follower and the estimated lumped interference.

[0011] Embodiments of the present invention also provide a computer device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute the above-described fault-tolerant control method for unmanned aerial vehicle (UAV) swarms.

[0012] Embodiments of the present invention also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described fault-tolerant control method for unmanned aerial vehicle (UAV) swarms.

[0013] The fault-tolerant control method for UAV swarms provided by this invention has at least the following beneficial effects: To address system uncertainties caused by actuator failures (e.g., malfunctions, bias faults) and external disturbances, this invention designs a distributed extended observer. This extended observer treats all system uncertainties (including changes in internal parameters, unmodeled dynamics, external disturbances, and actuator failures) as a completely new state, expanding the system state variables to predict all system states (including lumped disturbances and unmeasurable states) in real time. The distributed design avoids the reliance on global state information for unified calculations found in traditional centralized observers. Each follower is an independent decision-making unit; therefore, by leveraging the relative state information between each follower and its neighbors, it achieves high-precision estimation of unmeasurable state information and lumped disturbances caused by follower actuator failures and external disturbances. Simultaneously, an event-triggered mechanism is designed, which reduces unnecessary communication data by adjusting trigger conditions in real time.

[0014] In summary, this invention combines a distributed extended observer and an event-triggered mechanism to control each follower in a drone swarm. Under conditions of limited communication resources, it compensates for the aggregated interference of each follower in the drone swarm, ensuring consistent leader-follower control of the system under faults and disturbances. Attached Figure Description

[0015] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0016] Figure 1 This is a flowchart illustrating a fault-tolerant control method for a drone swarm provided by the present invention. Detailed Implementation

[0017] 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. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0018] Currently, with the increasing complexity of missions and environmental uncertainties, UAV swarm systems are facing numerous technical challenges. Firstly, the actuator is the core component of the UAV's power system, and its reliability directly affects the stability of the swarm. In complex electromagnetic environments or under conditions such as mechanical fatigue, actuators may experience partial failure, jamming, or even complete malfunction. For example, in a multi-UAV collaborative forest fire monitoring mission, a sudden power drop in one UAV's motor caused the formation's trajectory to deviate, ultimately leading to mission interruption. Such cases demonstrate that a single node failure can propagate to the entire swarm through the communication link, causing a "snowball effect." Secondly, the limited communication resources inherent in UAV swarms are particularly prominent. Traditional periodic control strategies often require high-frequency information exchange, which can easily lead to communication congestion or even data loss in scenarios with limited bandwidth or interference. Furthermore, external disturbances such as wind shear and electromagnetic interference, coupled with the uncertainties inherent in the model, further increase the design difficulty of the control system.

[0019] Against this backdrop, researching fault-tolerant control strategies under actuator failure conditions is crucial. Theoretically, fault-tolerant control, through real-time fault diagnosis and dynamic compensation mechanisms, ensures the system maintains stability even when some components fail, providing a novel methodology for robustness research in multi-agent systems. Specifically, designing distributed observers to accurately estimate complex faults and disturbances, constructing adaptive event-triggered mechanisms to optimize communication resources, and achieving fault isolation and task reconfiguration through hierarchical control architectures are all cutting-edge topics in control theory. From an application perspective, reliable fault-tolerant control technology can significantly improve the survivability of UAV swarms in harsh environments. For example, during border patrol missions, UAV swarms need to maintain formation even under strong electromagnetic interference and with some nodes damaged; while in agricultural plant protection, multi-aircraft systems need to adapt to changing airflow disturbances and skillfully avoid sudden obstacles.

[0020] Against this backdrop, researching fault-tolerant control strategies under actuator failures has significant theoretical and practical value. From a practical standpoint, drone swarms performing high-risk missions such as border patrols and disaster relief require high autonomy and anti-interference capabilities. However, most existing fault-tolerant control methods are based on ideal communication assumptions or single-failure-mode designs, making it difficult to handle complex scenarios involving compound failures (such as partial actuator failure coupled with communication delays) and dynamic disturbances. For example, traditional centralized observers rely on global state information, and when communication resources are limited, data loss can occur, leading to decreased estimation accuracy. Static event-triggered mechanisms often lag in response to sudden failures, making it difficult to achieve a balance between control performance and communication efficiency. The technical challenges lie in: how to achieve distributed state estimation to reduce communication overhead, how to design adaptive mechanisms to dynamically adjust control strategies, and how to ensure system stability under fault propagation.

[0021] This invention aims to overcome the limitations of existing methods by integrating distributed observation and dynamic triggering technologies, thereby providing strong theoretical support for the reliable operation of UAV swarms in complex environments and promoting the advancement of UAV swarm fault-tolerant control theory towards engineering applications.

[0022] Specifically, for UAV swarm systems where actuator composite failures (partial failure, complete failure, and intermittent failure) coexist with limited communication resources, an adaptive event-triggered fault-tolerant control strategy based on a distributed extended state observer (ESO) is proposed.

[0023] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0024] One embodiment of the present invention relates to a fault-tolerant control method for unmanned aerial vehicle (UAV) swarms. The specific flow of the fault-tolerant control method for UAV swarms in this embodiment can be as follows: Figure 1 As shown, it includes: Step 101: For a leader and multiple followers in a drone swarm, establish a first dynamic model for the leader and a second dynamic model for each follower.

[0025] Step 102: Based on the second dynamic model of multiple followers, design a distributed extended observer, and through the distributed extended observer, use the relative state information between each follower and its neighboring followers to estimate the state information of each follower and the lumped disturbances consisting of external disturbances and actuator failures of the followers.

[0026] Step 103: Based on the first dynamic model, determine the leader's state information, and design an event triggering mechanism based on the first error between the state information of each follower and the leader's state information, as well as the second error between the state information of each follower.

[0027] Step 104: When the first error is greater than the first preset threshold or the second error is greater than the second preset threshold, determine the trigger event triggering mechanism, and after the trigger event triggering mechanism is triggered, control each follower in the drone cluster according to the relative state information between each follower and the estimated lumped interference.

[0028] The following is a detailed description of the implementation details of the fault-tolerant control of the drone swarm in this embodiment. The following content is only for the convenience of understanding and is not necessary for implementing this solution.

[0029] First, a six-DOF (Degree of Freedom) UAV nonlinear dynamic model is established based on the Newton-Euler equations, defining actuator failure modules (exponential decay failure, step bias, and intermittent failure). Addressing the insufficient adaptability of existing graph theory methods to dynamic topologies, an augmented Laplace matrix modeling method for leader-follower communication topologies is proposed. The design principles of ESO (Executable Switched Oscillator) and the mathematical framework of event-triggered control are systematically explained, with a focus on analyzing the limitations of traditional static threshold mechanisms, laying the foundation for the subsequent design of dynamic threshold adaptive strategies.

[0030] Define the communication topology graph: The communication topology of the UAV swarm system is a weighted directed graph. It means that, among them: ={1,2,…,N} is a set of nodes, and each node corresponds to a drone. ⊆V×V ​​is the set of edges, where edge (i,j)∈ This indicates that drone i can transmit information to drone j.

[0031] =[ ] Let be an adjacency matrix, satisfying: ; Define the Laplacian matrix: The Laplacian matrix L of graph G = Defined as: ; It has the following properties: Row sum equals zero: L1 N =0, where 1 N It is a vector consisting entirely of 1s.

[0032] Positive semidefiniteness: for any nonzero vector ,have .

[0033] Define a leader-follower communication topology: The system consists of one leader (node ​​0) and N followers. (Additional graph) The adjacency matrix is:

[0034] ; Where B = diag(b1,…,b) N This indicates the connection between followers and leaders (b) i >0 indicates a connection.

[0035] Matrix theory and stability analysis: Schur's complement lemma: For a block matrix If R > 0, then M < 0 if and only if ; Lyapunov stability: Consider the system =f(x), if there exists a positive definite function V(x) satisfying: ; The system then becomes asymptotically stable at the origin.

[0036] Extended State Observer (ESO) Design Principles: Expansion state: Treating the system perturbation w(t) as an additional state, we construct an extended system: ; Where h(t) is the derivative of the disturbance (assuming it is bounded).

[0037] Observer design: Design an extended state observer: ; Gains l1, l2, and l3 are required to dynamically stabilize the observer error. Among these, For position estimation, u is the control input. To estimate the speed, f(x, ) is an estimate of the lumped disturbance. ) is a nonlinear function describing the dynamics of the system; x is the actual position, e(t) is the measurement error, representing the difference between the estimated position and the actual position at the current time t; x(tk) is the actual position at the trigger time; x(t) is the actual position at the current time t.

[0038] Basics of event triggering control: Event triggering conditions: Control input update time t k It is determined by the trigger function Γ(e(t),t)≥0, where e(t)=x(t) kLet )−x(t) represent the measurement error. Common conditions include:

[0039] Static trigger: ; Where ||e(t)|| is the Euclidean norm of the measurement error, representing the magnitude of the error; η is a constant threshold, representing the threshold of the triggering mechanism, which triggers control when the error exceeds this value.

[0040] Dynamic triggering: ; in, α is the first derivative of the threshold η(t) with respect to time t; α>0 is the threshold decay coefficient, which controls the rate at which the threshold decreases; β>0 is the threshold amplification coefficient, which controls the rate at which the threshold increases.

[0041] No Zeno behavior: If the triggering function satisfies ||e(t)||≤μ||x(t)|| and μ is appropriately chosen, then there exists a minimum triggering interval τ>0 such that Basic framework of fault-tolerant control: Actuator Fault Model: Actuator failures can be categorized as follows: Partial failure: (t)=(1−ρ i (t))u i (t), where 0 < ρ i (t)≤1.

[0042] Bias fault: (t)=u i (t)+Δ i (t), where Δ i (t) represents the unknown bias.

[0043] Fault tolerance control objective: The controller is designed so that the closed-loop system still satisfies the following in the event of a fault: .

[0044] The above forms the theoretical foundation for fault-tolerant control of UAV swarms. First, based on graph theory, the adjacency matrix and Laplace matrix of the communication topology are defined, clarifying the mathematical description method of the leader-follower structure. Second, Schur's complement lemma and Lyapunov stability criterion in matrix theory are introduced, providing tools for subsequent stability analysis. The design principle of the Extended State Observer (ESO) and its application in lumped disturbance estimation are further elaborated, and the basic framework of event-triggered control and the Zeno-free behavior condition are analyzed. Finally, typical actuator failure models for fault-tolerant control are outlined. These theoretical tools lay the mathematical foundation for the design of the following distributed fault-tolerant control strategies.

[0045] Then, addressing the issue of traditional fault-tolerant control relying on global information, a distributed ESO design method is proposed: unmeasurable velocity and lumped disturbances (including faults and perturbations) are jointly estimated using the relative state information of neighboring nodes, and exponential convergence of observation errors is achieved through gain optimization. Furthermore, to address the lag in response of static event-triggered mechanisms under sudden faults, a dynamic threshold adaptive triggering condition is designed, combined with a hierarchical fault-tolerant architecture to achieve fault isolation and task reconfiguration. In addition, based on Lyapunov stability theory, the asymptotic convergence of the closed-loop system is rigorously proven, and the explicit expression of the control gain matrix is ​​derived.

[0046] Specifically, this paper addresses the event-triggered fault-tolerant consistency control problem in UAV swarm systems under the influence of actuator failure, unmeasurable speed, and external disturbances. Considering the limited communication resources in UAV swarm systems, a fault-tolerant control method based on an event-triggered mechanism is proposed to optimize the use of communication resources by reducing unnecessary information transmission.

[0047] System Model and Problem Description: Consider a drone swarm system consisting of one leader and N followers, with the goal of achieving leader-follower consensus control. Each drone in the system has a state including position and velocity, and each drone follows a second-order dynamics model. The problem is how to achieve system consensus while considering actuator failures, unpredictable states, external disturbances, and limited communication resources.

[0048] The dynamics of leaders: The leader described a freely moving drone with the following dynamic equations: ; ; in, It is an inherent nonlinear function of the leader system, often used to simulate external disturbances or inherent nonlinear behaviors. The leader's position and velocity are known, and it is assumed that the leader will not be affected by actuator failures during this process. Thus, the leader's behavior is entirely determined by its own internal dynamic system.

[0049] The dynamics model of followers: Each follower The state of the system is also composed of position and velocity, and the dynamic equations of the system are as follows: ; ; in, and They represent followers respectively. Position and velocity, To control the input, External disturbances. The presence of actuator malfunctions affects the control input. Affected. Typically, actuator failure occurs via a failure factor. To model this, its value is between 0 and 1, representing the degree of decay of the control input. Therefore, the follower's control input... Revised to:

[0050] ; in, For the ideal control input, and The change reflects the degree of actuator failure. For example, =0 indicates that the actuator is normal. =1 indicates that the executor has completely failed.

[0051] In summary, actuator failures and external disturbances are combined into a single lumped disturbance term. Its expression is: ; Therefore, the state equation of the follower can be expressed as: .

[0052] Communication topology and adjacency matrix: To ensure that drones in a drone swarm system can communicate with each other and achieve consistent control, a communication topology needs to be defined. In this study, it is assumed that the system's communication topology is static and undirected, meaning that each drone can only exchange information with its neighbors. Adjacency matrix. The element a in the matrix is ​​used to represent the connection relationships between various drones. ijIndicate whether drone i and drone j are connected. If a ij If the value is greater than 0, it indicates that there is a communication connection between drone i and drone j.

[0053] An effective communication topology must ensure that all UAVs achieve consistent control through information exchange. This study employs a fixed adjacency matrix to ensure that followers can communicate with the leader as well as with other followers.

[0054] Actuator Fault Model: Common fault models can be categorized into the following types: Actuator failure: This is the most common type of failure, indicating complete or partial failure of the actuator. In the control input, actuator failure is represented by a decay factor. Modeling is performed, which in turn affects the effectiveness of control inputs.

[0055] Actuator bias fault: In addition to failure, actuators may also suffer from bias faults, which manifest as a constant offset in the control input. Bias faults are detected by a fixed bias value. This usually causes followers to deviate from the expected trajectory.

[0056] In this embodiment, the interference and fault conditions are assumed to be: Boundedness of external disturbances: External disturbance d i (t) satisfies And its first derivative Bounded, that is ; Actuator Fault Model: Actuator Fault Including partial failure, bias fault, and intermittent fault, satisfying And the rate of change of fault Bounded, that is ; Definition of lumped interference: Define lumped interference Its derivative satisfies ,in = .

[0057] Event triggering mechanism and control strategy design During the control operations of a drone swarm system, the effective utilization of communication resources is a crucial factor in achieving efficient system operation. Traditional control strategies often employ periodic updates, specifically updating the control input at regular time intervals. While simple and easy to implement, this approach can easily result in the transmission of a large amount of useless information, thus wasting valuable communication bandwidth. In practical applications, especially under conditions of limited communication resources, adopting an event-triggered mechanism to reduce unnecessary information transmission becomes an effective solution. This research proposes a fault-tolerant and consistent control strategy based on an event-triggered mechanism, which optimizes the use of communication resources while ensuring system stability and consistency.

[0058] Design of Distributed Extended State Observer (ESO): Observer dynamics: For follower dynamics models: ; Design a distributed ESO to estimate the unmeasurable velocity using relative state information of neighbors. and centralized interference : ; in, , , >0 represents the observer gain. For adjacency matrix elements, This represents the connection weight between followers and leaders, where i is the follower index and t is the time. (t) represents the estimated position of follower i; (t) represents the estimated speed of follower i; (t) represents the lumped disturbance estimate for follower i; (t) represents the actual position of neighbor follower j; (t) represents the leader's actual position; (t) represents the control input for follower i. N i Let i be the set of neighbors of follower i.

[0059] ESO convergence, under the aforementioned assumed disturbance and fault conditions, if the observer gain satisfies Then the estimation error , It is globally asymptotically convergent and has positive constants. Make: .

[0060] in, (t) represents the position estimation error; (t) represents the velocity estimation error; (t) represents the lumped disturbance estimation error; (t), (t) represents the actual position and actual speed of follower i, respectively; (t) represents the actual lumped disturbance of follower i; ||·|| is the Euclidean norm; γ>0 is the error bound constant; λ>0 is the exponential convergence rate.

[0061] prove: Error dynamic equation: Based on the observer equations and follower dynamics, the error dynamics are: ; Where i is the follower index; t is the time; (t) represents the position estimation error; (t) represents the velocity estimation error; (t) represents the lumped disturbance estimation error.

[0062] Lyapunov function construction: selection In the formula, V(t) is the Lyapunov function (error energy scalar); N is the number of followers; (t), (t), (t) represents the position, velocity, and lumped disturbance estimation error of the i-th follower, respectively.

[0063] Differentiating, we get: ; Stability analysis: Substitute the error dynamic equation and rearrange: ; Based on the above-mentioned assumed interference and fault conditions Combining Young's inequality: ; Choose ϵ= ,but: ; When the gain satisfies At that time, there exists Make Therefore, the error exponent converges.

[0064] The convergence of ESO guarantees the exponential convergence of the ESO estimation error.

[0065] Adaptive event triggering mechanism design: The core idea of ​​the event-triggered mechanism is to update the control input only when the system state change exceeds a set threshold, rather than updating it at fixed time intervals. Each UAV triggers a controller update only when its state or observation error exceeds a predetermined threshold, thus avoiding unnecessary control input calculations and information transmissions. Specifically, the event triggering condition is based on the state error between the follower and the leader, as well as the relative state error among the followers.

[0066] The event triggering determination is based on the following conditions: ; in, It is a drone Measurement error, and They represent followers respectively. The position and velocity at the moment of triggering, and These are the estimated position and estimated velocity of the follower at the current moment. The event trigger condition is to trigger an update of the control input when the measurement error exceeds a preset threshold.

[0067] To further improve the flexibility and robustness of the control strategy, a dynamically adjusted threshold mechanism is introduced. This threshold is dynamically adjusted based on an adaptive control method, aiming to adjust the triggering conditions in real time according to the actual operating conditions of the system. This prevents excessively frequent triggering while ensuring the system can respond quickly to faults or disturbances. Specifically, the triggering threshold is defined by the following formula:

[0068] ; in, It is an error term based on neighbor state information and leader state information. These are adaptive parameters. The dynamic adjustment mechanism of adaptive parameters will be explained further later.

[0069] Triggering conditions and threshold updates: Defining state error The triggering condition is: ; Dynamic threshold η i The update law for (t) is: ; in >0 represents the dynamic threshold for event triggering of follower i; for The first derivative with respect to time t; α>0 is the threshold attenuation coefficient; β>0 is the threshold amplification coefficient; N iLet a be the set of neighbors of follower i; ij These are elements of the adjacency matrix; The position estimation error of neighbor j; b i ≥0 represents the connection weight between follower i and the leader; The error in estimating the leader's position; ||·|| is the Euclidean norm.

[0070] To optimize the performance of the control strategy and ensure system adaptability, an adaptive event-triggered mechanism was introduced. The key feature of this mechanism is its ability to reduce unnecessary control update operations by adjusting the event trigger threshold, and it can also respond quickly when the system state undergoes significant changes. The adaptive parameter controls the dynamic adjustment of the threshold, and its update follows the formula:

[0071] ; in, >0 represents the adaptive threshold weight parameter for follower i; d / dt α i (t) is α i (t) is the first derivative of (t) with respect to time t; Let || be the measurement error vector of the i-th follower; ||For The Euclidean norm, These are adaptive parameters that control the rate of adaptive adjustment. In this way, the drone can adjust the triggering frequency in real time according to changes in the current state, thereby avoiding over-updates or excessively long update delays.

[0072] Control strategy design: The control strategy in this embodiment is based on a leader-follower consistency control framework, aiming to drive each follower to follow the leader's trajectory through control inputs. The controller design considers the effects of actuator failures and external disturbances. The formula for calculating the control inputs is:

[0073] ; Among them, u i (t) represents the control input of follower i; K is the control gain matrix. The elements of the adjacency matrix represent the communication connections between drones. Followers The set of neighbors, x j (t), x i (t) represents the actual positions of neighbor j and follower i, respectively. The total disturbance is estimated through the extended state observer.

[0074] Stability analysis of closed-loop system: Communication topology assumptions: Communication topology diagram It contains a spanning tree with the leader as the root node, and the subgraph G is undirected.

[0075] The boundedness assumption of nonlinear functions: There exists a constant. , >0, such that for any agent i, its nonlinear function satisfies: ; Closed-loop system stability: Under the above assumptions, if the control gain K satisfies: ; Where H = L + B is the augmented Laplace matrix, the closed-loop system is asymptotically stable under the action of the adaptive event-triggered fault-tolerant controller. H is the augmented Laplace matrix; L is the Laplace matrix; B = diag(b1,…,bN) is the leader connection weight matrix; b i ≥0 represents a weight element; K is the speed channel control gain matrix; λ min (H) is the smallest eigenvalue of H; , It is a nonlinear bounded constant.

[0076] prove: Define the Lyapunov function: ; in V is a Lyapunov function used to prove the stability of the system; The position estimation error for the i-th follower; Let be the velocity estimation error of the i-th follower; N is the number of followers in the system.

[0077] Differentiate and substitute into the dynamic model: ; Application controller design: ; ; Among them, u i The control input for the i-th follower is K; K is the control gain matrix, which adjusts the control strength; a ij For each element of the adjacency matrix, N represents the communication weight from the j-th follower to the i-th follower. i Let i be the set of neighbors of the i-th follower; is the derivative of the Lyapunov function, representing the rate of change of energy; The velocity estimation error of the i-th follower; ρ1 and ρ2 are constants used to adjust the control strategy; , The Euclidean norm is the error in the position and velocity estimation.

[0078] Using matrix inequalities: ; when The system is asymptotically stable.

[0079] To ensure the system maintains a stable state under event-triggered conditions, a detailed stability analysis was conducted. This involved introducing Lyapunov functions and integrating the system's dynamic model with the control input design. This demonstrated that under an adaptive event-triggered mechanism, the system's state error gradually converges until it reaches zero. Furthermore, simulations validated the proposed event-triggered control strategy, showing that it effectively ensures system consistency even under actuator failures and external disturbances.

[0080] Proof of no Zeno behavior: No Zeno behavior: If the threshold parameter η is triggered i (t) satisfies the dynamic update law: ; If α and β > 0, then there exists a minimum triggering interval τ > 0 such that any two triggering times satisfy the following condition. η i (t) is the adaptive threshold for the i-th follower; a ij For each element of the adjacency matrix, the communication weight is represented from follower j to follower i. The position estimation error for the j-th follower; The connection weight between follower i and leader; Error in estimating the leader's position.

[0081] prove: Step 1: Trigger Error Definition and Dynamic Analysis: The trigger error is defined as the state change between adjacent trigger times: ; Among them, e i (t) represents the measurement error of the i-th follower; x i (t k ) represents the i-th follower at the last trigger time t. k Position; x i (t) represents the position of the i-th follower at the current time t; t k ,t k+1These are two consecutive trigger moments.

[0082] Its derivative is: ; Combining follower dynamics and control law We can obtain: ; Step 2: Proof of the boundedness of the error derivative: By the assumption of boundedness of disturbance and the convergence of ESO, there exists a constant M > 0 such that: ; in, Let H be the norm of the rate of change of the velocity of the i-th follower; K is the control gain matrix; ||H|| is the norm of the augmented Laplace matrix; The Euclidean norm of the position estimation error for the i-th follower; For the lumped disturbance estimate of the i-th follower; w i (t) represents the actual lumped disturbance of the i-th follower, γ>0 is the attenuation coefficient, and λ>0 is the attenuation rate; This serves as the boundary for external disturbances.

[0083] Furthermore, within a limited time interval Within this bound, there exists a unified upper bound: ; Step 3: Trigger threshold and error growth constraint: Triggering conditions and threshold dynamics We can obtain: ; Where, η i (t) is the dynamic threshold of the i-th follower; η i (t k ) represents the i-th follower at time t k The threshold; α>0 is the threshold decay coefficient; t k The trigger time.

[0084] At the same time, the trigger error growth rate satisfies: ; Among them, ||v i (t)|| is the Euclidean norm of the velocity of the i-th follower; For the i-th follower at time t k The speed; M is a constant.

[0085] Step 4: Proof of the existence of the minimum trigger interval: Assuming in The trigger condition is met for the first time within the period. ,but: ; Among them, ||v i (τ)|| is the Euclidean norm of the velocity of the i-th follower; ||v i (t k )|| represents the i-th follower at time t k The speed; M is a constant.

[0086] make The above inequality can be rewritten as: ; When τ→0, the left end , right end Therefore, it exists Make: ; Solving for: ; because >0 and Bounded (guaranteed by closed-loop stability), therefore >0 means that the trigger interval has a positive lower bound.

[0087] The above content proposes a fault-tolerant control strategy that integrates a distributed ESO (Electronic State Optimizer) and an adaptive event-triggered mechanism. First, a distributed observer is designed using the relative state information of neighboring nodes to achieve accurate estimation of unmeasurable velocity and lumped disturbances. Second, a dynamic threshold adaptive event-triggered condition is introduced to significantly reduce communication frequency while maintaining control accuracy. Finally, based on Lyapunov stability theory, the asymptotic convergence of the closed-loop system is proved, and the constraints on the observer gain and triggering parameters are rigorously derived. Theoretical analysis shows that the proposed method can maintain system stability under sudden fault changes and external disturbances.

[0088] The fault-tolerant control method for UAV swarms in this embodiment specifically designs a distributed extended state observer to address system uncertainties caused by actuator composite faults and external disturbances. This observer achieves high-precision estimation of unmeasurable states and lumped disturbances by fusing relative state information from neighboring agents. Theoretical analysis shows that the observation error exhibits asymptotic convergence, providing reliable support for fault-tolerant control and serving as a basis for state compensation. A dynamic threshold and adaptive event triggering mechanism is also proposed, which reduces unnecessary communication data by adjusting triggering conditions in real time. Theoretical proof shows that this mechanism effectively avoids Zeno behavior, ensuring the minimum trigger interval exists, thus balancing control accuracy and communication efficiency. Based on Lyapunov stability theory, a fault-tolerant and consistent controller is designed, and the asymptotic stability of the closed-loop system is verified through matrix inequality analysis.

[0089] The steps of the various methods described above are only for clarity. In practice, they can be combined into one step or some steps can be split into multiple steps. As long as they include the same logical relationship, they are all within the protection scope of this invention. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the protection scope of this invention.

[0090] Another embodiment of the present invention relates to a fault-tolerant control system for a drone swarm. The implementation details of the fault-tolerant control system for the drone swarm in this embodiment are described below. The following implementation details are provided for ease of understanding and are not essential for implementing this solution. The fault-tolerant control system for the drone swarm in this embodiment includes: The model building module is used to build a first dynamics model of the leader and a second dynamics model of each follower for a leader and multiple followers in a drone swarm. The state estimation module is used to design a distributed extended observer based on the second dynamic model of multiple followers, and to estimate the state information of each follower and the lumped disturbances consisting of external disturbances and actuator failures of the followers by using the relative state information between each follower and its neighboring followers through the distributed extended observer. The trigger design module is used to determine the leader's state information based on the first dynamic model, and to design an event triggering mechanism based on the first error between the state information of each follower and the leader's state information and the second error between the state information of each follower. The fault-tolerant control module is used to determine the trigger event triggering mechanism when the first error is greater than the first preset threshold or the second error is greater than the second preset threshold, and after the trigger event triggering mechanism is triggered, to control each follower in the drone swarm based on the relative state information between each follower and the estimated lumped interference.

[0091] It is not difficult to see that this embodiment is a system embodiment corresponding to the above method embodiments, and this embodiment can be implemented in conjunction with the above method embodiments. The relevant technical details and technical effects mentioned in the above embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above embodiments.

[0092] It is worth mentioning that all modules involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this invention, this embodiment does not introduce units that are not closely related to solving the technical problem proposed by this invention; however, this does not mean that other units are absent from this embodiment.

[0093] Another embodiment of the present invention relates to a computer device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the fault-tolerant control method for the unmanned aerial vehicle swarm in the above embodiments.

[0094] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0095] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0096] Another embodiment of the present invention relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the method embodiments described above.

[0097] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0098] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing the present invention, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of the present invention.

Claims

1. A fault-tolerant control method for unmanned aerial vehicle (UAV) swarms, characterized in that, The method includes: For a drone swarm with one leader and multiple followers, establish a first dynamics model for the leader and a second dynamics model for each follower; Based on the second dynamics model of multiple followers, a distributed extended observer is designed. By using the distributed extended observer, the relative state information between each follower and its neighboring followers is used to estimate the state information of each follower and the lumped disturbances consisting of external disturbances and actuator failures of the followers. Based on the first dynamic model, the leader's state information is determined, and an event triggering mechanism is designed based on the first error between the state information of each follower and the leader's state information, as well as the second error between the state information of each follower. When the first error is greater than the first preset threshold or the second error is greater than the second preset threshold, the trigger event mechanism is determined, and after the trigger event mechanism is determined, each follower in the drone swarm is controlled according to the relative state information between each follower and the estimated lumped interference.

2. The fault-tolerant control method for unmanned aerial vehicle (UAV) swarms according to claim 1, characterized in that, The distributed extended observer is: ； In the formula, , , All values ​​greater than 0 indicate the observer gain. The elements of the adjacency matrix represent the communication weights from j to i. This represents the connection weight between the follower and the leader, where i is the follower index and t is the time. The estimated position of follower i; The estimated velocity of follower i; For the lumped disturbance estimate of follower i; The actual location of neighbor follower j; The actual position of the leader; This is the control input for follower i; Let i be the set of neighbors of follower i.

3. The fault-tolerant control method for unmanned aerial vehicle (UAV) swarms according to claim 2, characterized in that, The following formula is used to determine whether the event triggering mechanism is activated: ； In the formula, It is a drone Measurement error, and They represent followers respectively. The position and velocity at the moment of triggering, and These are the estimated position and estimated velocity of the follower at the current moment, respectively.

4. The fault-tolerant control method for unmanned aerial vehicle (UAV) swarms according to claim 3, characterized in that, Both the first preset threshold and the second preset threshold are updated in real time using the following formula: ； In the formula, >0 represents the dynamic threshold for event triggering of follower i; For η i (t) is the first derivative with respect to time t; α>0 is the threshold attenuation coefficient; β>0 is the threshold amplification coefficient; x̃ j (t)=x j (t)−x̂ j (t) represents the position estimation error of neighbor j; Error in estimating the leader's position; x̂ i (t) represents the estimated position of follower i; ||·|| represents the Euclidean norm.

5. The fault-tolerant control method for unmanned aerial vehicle (UAV) swarms according to claim 4, characterized in that, Each follower in a drone swarm can be controlled using the following formula: ； In the formula, It is the control gain matrix. The lumped disturbance x is estimated using a distributed extended observer. j (t) and x i (t) represents the actual positions of neighbor j and follower i, respectively.

6. A fault-tolerant control system for unmanned aerial vehicle (UAV) swarms, characterized in that, The system includes: The model building module is used to build a first dynamics model of the leader and a second dynamics model of each follower for a leader and multiple followers in a drone swarm. The state estimation module is used to design a distributed extended observer based on the second dynamic model of multiple followers, and to estimate the state information of each follower and the lumped disturbances consisting of external disturbances and actuator failures of the followers by using the relative state information between each follower and its neighboring followers through the distributed extended observer. The trigger design module is used to determine the leader's state information based on the first dynamic model, and to design an event triggering mechanism based on the first error between the state information of each follower and the leader's state information and the second error between the state information of each follower. The fault-tolerant control module is used to determine the trigger event triggering mechanism when the first error is greater than the first preset threshold or the second error is greater than the second preset threshold, and after the trigger event triggering mechanism is triggered, to control each follower in the drone swarm based on the relative state information between each follower and the estimated lumped interference.

7. A computer device, characterized in that, include: At least one processor; And a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the fault-tolerant control method for a drone swarm as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the fault-tolerant control method for the drone swarm as described in any one of claims 1 to 5.

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