Low-energy low-altitude unmanned aerial vehicle formation safe anti-disturbance control method

Abstract

The application provides a kind of low-energy consumption low-altitude unmanned aerial vehicle formation safety anti-disturbance control method, comprising: constructing multiple fixed-wing unmanned aerial vehicle system model, constructing cluster comprehensive error system, defining safety set and constructing control barrier function, constructing value function under the framework of double-person zero-sum game, solving game optimal strategy based on Bellman principle, constructing critic neural network, constructing neural network weight updating law of fixed time convergence, constructing learning-driven event trigger mechanism, finally realizing and applying approximate optimal safety cooperative control;The application designs cluster-level safety-optimal formation flight control strategy, realizes the dynamic balance of optimality and safety inside unmanned aerial vehicle cluster;Solve the problem of easy divergence and collision of formation under strong interference condition, while eliminating the uncertainty of convergence time;Realize the significant reduction of communication frequency and the maintenance of formation stability, solve the efficient communication problem of unmanned aerial vehicle cluster under the condition of limited communication resources.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) swarm control technology, specifically relating to a low-energy-consumption, low-altitude UAV formation safety anti-interference control method. Background Technology

[0002] Formation tracking and control of unmanned aerial vehicles (UAVs) is a key technology for achieving accurate trajectory tracking and stable formation maintenance in dynamic environments, and is crucial for intelligent UAV systems in highly dynamic and autonomous scenarios (such as logistics, reconnaissance, and collaborative operations). However, with the increase in formation size, mission complexity, and the unpredictability of low-altitude environments, system energy consumption has become a core bottleneck restricting its long endurance and high-efficiency operation (L. Xue, B. Ma, Y. Wu, and et al. “Anti-JammingAttack Mixed Strategy for Formation Tracking Control via Game-TheoreticalReinforcement Learning,” IEEE Transactions on Intelligent Vehicles, pp. 1–16, 2024.).

[0003] Reinforcement learning, with its model-free interactive learning characteristics, has demonstrated significant advantages in drone swarm control in complex and dynamic scenarios. However, the asymptotic convergence of traditional reinforcement learning struggles to meet the stringent stability requirements of dynamic tasks. While fixed-time reinforcement learning addresses this issue by improving the convergence mechanism, its periodic control update mechanism triggers high-frequency communication interactions in large-scale drone swarms. This interaction leads to an exponential increase in communication energy consumption within the swarm with the number of drones, significantly shortening system endurance and becoming a key obstacle to large-scale deployment. To alleviate this communication burden, an event-triggered mechanism is introduced into the learning process, aiming to reduce energy consumption by communicating only when necessary. For example, while patents CN202311765377 "A Multi-UAV Formation Control Method and Device Based on Event-Triggered Communication" and CN202211446866 "A Distributed UAV Formation Control Method Based on Event-Driven Strategy" propose UAV swarm formation control methods based on event-driven strategies, most existing event-triggered mechanisms based on time-varying thresholds fail to fully consider the strong dependence of the learning process on high-quality, timely data samples. Excessively reducing the trigger frequency (although saving communication energy) can lead to the accumulation of value function estimation bias, significantly reducing tracking accuracy and formation maintenance performance, forming a "resource-accuracy trade-off dilemma," which is particularly prominent in high-precision tasks such as reconnaissance (L. Wei, M. Chen, and S. Shi, "Dynamic Event-Triggered Consensus Cost-Based Switching Control for UAV Formation with Disturbances," IEEE Transactions on Intelligent Vehicles, vol. 9, no. 2, pp. 3531–3543, 2024.).

[0004] Besides communication energy consumption, the control energy consumption that drives the UAV's actuators is equally crucial. Existing formation control strategies mostly focus on single-objective optimization, such as minimizing tracking error or suppressing specific disturbances. They lack a globally optimal framework for coordinating and optimizing control resource consumption, tracking error accuracy, and disturbance suppression effectiveness in complex low-altitude environments with strong aerodynamic coupling, multi-source environmental disturbances, and sensor noise. This lack of optimization directly leads to inappropriate control frequency or amplitude, resulting in unnecessary control energy consumption.

[0005] Furthermore, event-driven fixed-time reinforcement learning requires exploring sufficient states to gain comprehensive experience. Blind exploration may lead to UAV formations deviating from their planned routes, colliding, or entering dangerous states. Emergency avoidance maneuvers triggered by such unsafe events consume significant additional energy, substantially increasing the overall energy burden of the system. While safety reinforcement learning based on obstacle control functions provides a solution for single-UAV safety, its effective extension into multi-UAV formation cooperative systems remains a gap, particularly lacking an efficient mechanism to resolve dynamic safety conflicts between agents. When existing single-UAV safety reinforcement learning algorithms are directly applied to formations, they easily trigger conservative or conflicting obstacle avoidance behaviors, threatening safety and increasing control and communication energy consumption due to uncoordinated actions. For example, patent CN202510054331, "Multi-UAV Formation and Obstacle Avoidance Control Method Based on Safety Reinforcement Learning in Low-Altitude Environments," while improving the autonomous formation and obstacle avoidance capabilities of multi-UAV systems in unknown environments and enabling autonomous cooperative formation and obstacle avoidance flight, does not consider energy consumption issues. In addition, existing methods often ignore actual disturbances such as strong aerodynamic coupling effects and sensor noise. These factors not only interfere with control accuracy and energy consumption, but also undermine the accurate assessment of safety constraints. They may lead to false triggering of ineffective control energy consumption or the risk of missing judgments in high-energy-consumption emergency avoidance, further deteriorating the system's energy consumption and safety status. Summary of the Invention

[0006] To address the problems existing in current technologies, this invention discloses a low-energy-consumption, safe anti-disturbance control method for low-altitude UAV swarms. The design concept of this method is as follows: First, through precise modeling, a dynamic model of the fixed-wing UAV swarm and its leader is constructed, and the tracking error is transformed into a comprehensive error system, providing a foundation for subsequent control strategies. Second, the concept of a safety set is introduced and expressed using a control obstacle function to set a safety boundary for the UAV swarm flight, ensuring flight safety. Third, based on a zero-sum game framework, a safe optimal control strategy and a disturbance strategy are designed. The core of this strategy is to balance the competition and cooperation relationships within the UAV swarm, achieving fixed-time convergence of the swarm tracking error without exceeding the safety boundary. Finally, a learning-driven event triggering mechanism is designed. By dynamically adjusting the trigger threshold to reduce the communication frequency, the UAV swarm intelligently determines the timing of communication, optimizes the utilization of communication resources, and improves system efficiency.

[0007] The method of this invention is applied to a drone swarm system consisting of N drones, each drone being equipped with an autopilot, specifically including:

[0008] Step 1: Construct a multi-fixed-wing UAV system model, namely, establish the dynamic model of the UAV and the dynamic model of the virtual leader;

[0009] Step 2: Construct a cluster comprehensive error system, that is, based on the dynamic model in Step 1, calculate the tracking error of each UAV relative to the virtual leader, and construct a comprehensive error that reflects the overall collaborative performance of the cluster.

[0010] Step 3: Define a safe set and construct a control barrier function, that is, construct a control barrier function based on the set of cluster safe operation characterized by the comprehensive error, so that the comprehensive error is always within the safe set;

[0011] Step 4: Construct the value function under the two-player zero-sum game framework. That is, based on the two-player zero-sum game theory, model the control design problem as a two-player zero-sum differential game and design a value function that includes a tracking error penalty term, a control input penalty term, and a control obstacle function term.

[0012] Step 5: Solve for the optimal strategy in the game based on Bellman's principle. That is, apply Bellman's optimality principle to find the expressions for the optimal control strategy and the optimal disturbance strategy that minimize the control law player and maximize the disturbance player under a given value function.

[0013] Step 6: Construct a commentator neural network, that is, use the approximation ability of the neural network to learn online and approximate the gradient of the value function on which the optimal policy in Step 5 depends;

[0014] Step 7: Construct a fixed-time convergent neural network weight update law, that is, estimate and train the weights of the neural network based on the gradient descent method to obtain approximate weights and their gradients.

[0015] Step 8: Construct a learning-driven event triggering mechanism, that is, design event triggering conditions based on the evolution process of neural network weights and the change of comprehensive error;

[0016] Step 9: Implement and apply near-optimal safety cooperative control, that is, substitute the approximate weights and their gradients in Step 7 and the event triggering conditions in Step 8 into the optimal control strategy and optimal disturbance strategy in Step 5, and apply them to the UAV dynamics model in Step 1.

[0017] Compared with the prior art, the advantages of the present invention are as follows:

[0018] (1) This invention proposes a unified representation method for the safety of the formation based on the control obstacle function, designs a cluster-level safety-optimal formation flight control strategy, realizes the dynamic balance between the optimality and safety of the UAV cluster, and solves the contradiction between individual obstacle avoidance and formation geometry maintenance of the UAV cluster.

[0019] (2) In order to combat disturbances such as aerodynamic coupling and noise and model uncertainty, this invention reconstructs the safety tracking control problem into a zero-sum game problem with safety constraints. It learns a safety Nash equilibrium strategy through a fixed-time reinforcement learning strategy with only commentators, which solves the problem of formation divergence and collision under strong interference conditions and eliminates the uncertainty of convergence time.

[0020] (3) This invention proposes a learning-driven event triggering mechanism, which dynamically adjusts the triggering rules based on the learning state and state changes, thereby achieving a significant reduction in communication frequency and maintaining formation stability, and solving the problem of efficient communication of UAV clusters under conditions of limited communication resources. Attached Figure Description

[0021] Figure 1 This is a flowchart of the process of the present invention;

[0022] Figure 2 This is a graph showing the actual positions and flight status of five drones in an embodiment of the present invention.

[0023] Figure 3 This is a graph showing the tracking error curves of the position and flight status of five UAVs in an embodiment of the present invention;

[0024] Figure 4 This is a diagram showing the weight update rate of the UAV and the triggering time based on the update rate in an embodiment of the present invention;

[0025] Figure 5 This is a safety performance diagram of five drones in an embodiment of the present invention;

[0026] Figure 6 This is a three-dimensional diagram of the drone swarm flight in an embodiment of the present invention; Detailed Implementation

[0027] This invention relates to a drone swarm system consisting of N drones, each equipped with an autopilot responsible for adjusting the drone's speed, heading angle, and pitch angle, and interacting with the control method program. The expected trajectory of each drone is generated based on a virtual leader, and multiple agents form a designated formation around the virtual leader. The specific steps of this invention are as follows:

[0028] Step 1: Construct a multi-fixed-wing UAV system model, namely, establish the dynamic model of the UAV and the dynamic model of the virtual leader.

[0029] The dynamic model of the i-th UAV swarm system consisting of N fixed-wing UAVs is expressed as:

[0030]

[0031] In the formula: x i ,yi ,z i Let v be the position of the i-th UAV along the x, y, z axes. i Let ψ be the velocity of the i-th UAV in the body coordinate system. i Let θ be the heading angle of the i-th UAV. i Let d be the pitch angle of the i-th UAV; xi ,d yi ,d zi This represents the disturbance caused by strong winds along the x, y, and z axes.

[0032] Standard autopilots precisely control the speed v of drones i , heading angle ψ i and the rate of change of pitch angle θ i There are limitations, primarily stemming from the speed dynamic internal parameter α measured by the autopilot. v The dynamic internal parameter α of the heading angle ψ The internal dynamic parameter α of the yaw angle θ Difficulty in accurately identifying or calibrating leads to a decrease in control precision for critical states. The deterministic nature of the internal speed dynamic parameters of the autopilot is defined as Δα. v The dynamic internal parameter of the heading angle is deterministically Δα ψ The dynamic internal parameter of the yaw angle is deterministically Δα θ The flight state system of a fixed-wing UAV is modeled as follows:

[0033]

[0034] In the formula: The speed command for the i-th drone is... Let be the heading angle command for the i-th UAV. v is the pitch angle command for the i-th UAV; i Let ψ be the actual speed of the i-th drone. i Let θ be the actual heading angle of the i-th UAV. i Let be the actual pitch angle of the i-th drone; define For the lumped interference of the velocity channel of the i-th UAV, For the lumped interference of the heading angle channel of the i-th UAV, This is the lumped interference in the yaw angle channel of the i-th UAV.

[0035] To generate reference commands for the formation, the dynamic model of the virtual leader is constructed as follows:

[0036]

[0037] In the formula: x r ,y r ,zr v represents the virtual leader's position along the x, y, z axes. r For the pre-generated virtual leader velocity, ψ r θ is the heading angle of the pre-generated virtual leader. r The pitch angle for a pre-generated virtual leader.

[0038] Step 2: Construct a cluster comprehensive error system, that is, based on the dynamic model in Step 1, calculate the tracking error of each UAV relative to the virtual leader, and construct a comprehensive error that reflects the overall collaborative performance of the cluster.

[0039] First, the location information x of the i-th drone. i ,y i ,z i Integrate into a three-dimensional position vector P i =[x i ,y i ,z i ] T The leader's location information x r ,y r ,z r Integrate into a three-dimensional position vector P r =[x r ,y r ,z r ] T The flight status v of the i-th drone i ,ψ i ,θ i Integrate into a three-dimensional flight state vector The leader's flight status information v r ,ψ r ,θ r Integrate into a three-dimensional flight state vector The tracking error of the i-th UAV is:

[0040]

[0041] In the formula: This represents the position tracking error of the i-th UAV. This represents the tracking error of the i-th UAV in terms of speed, heading angle, and pitch angle. Let be the expected relative distance between the i-th drone and the leader.

[0042] Combining the dynamic models (1)-(3), the tracking error of the i-th UAV is converted into a comprehensive error:

[0043]

[0044] In the formula: Let u be the comprehensive error vector. i To control the input, d i =[d xi ,d yi ,d zi ,d vi ,d ψi ,d θi ] T To centralize interference,

[0045] Step 3: Define a safe set and construct a control barrier function. This involves defining a set based on the comprehensive error characterizing the safe operation of the cluster and constructing a control barrier function to ensure that the comprehensive error always remains within the safe set. This is specifically divided into the following sub-steps:

[0046] Step 3.1: Construction of a safety set based on error constraints: To ensure that the UAVs in the formation maintain a minimum safe distance, the safety set is defined as the set that satisfies that the distance between each pair of UAVs is not less than a preset minimum safe distance. Specifically, for the i-th UAV, its distance from its nearest neighbor UAV (located denoted as x) is... j ,y j ,z j The minimum safe distance requirement between them is Its size can be determined by The calculation yielded the result.

[0047] Therefore, the following security set is designed for the i-th drone. Ensure that its positional error meets the following requirements:

[0048]

[0049] In the formula: It is a compact set containing the origin, with the nonlinear term F. i On It satisfies Lipschitz continuity.

[0050] Step 3.2: Construction of the control barrier function based on the safety set: To quantize and ensure the forward invariance of the safety set (6), the control barrier function ρ is constructed. i for:

[0051]

[0052] By designing a control obstacle function to constrain the tracking error of each UAV to always be less than half of its actual distance from neighboring UAVs, collisions between UAVs are prevented, while maintaining the stable configuration of the formation and overall operational safety.

[0053] Step 4: Construct the value function within a two-player zero-sum game framework. Based on two-player zero-sum game theory, the control design problem is modeled as a two-player zero-sum differential game, designing a value function that includes a tracking error penalty term, a control input penalty term, and a control obstacle function term. This two-player zero-sum game framework is the key mechanism for achieving optimal performance. Its core characteristic is that what one player gains is what the other loses. In this game framework: the controller is player one, whose goal is to maximize the performance index of the formation system while satisfying safety constraints. The lumped disturbance is player two, whose goal is to maximize the system loss within the constraints. By solving the Nash equilibrium of this game, an optimal control strategy and an optimal disturbance strategy can be obtained. The key characteristic of this strategy is that even under the most unfavorable disturbance applied by the disturbing party, it can still simultaneously ensure that the formation satisfies the predefined safety constraints and achieves robust optimal performance. Based on this framework and the combined error and control obstacle functions from steps 1-3, the safe-optimal formation control algorithm includes the following key steps:

[0054] Step 4.1: Construct the cost function, which involves designing the cost function based on the optimal control principle and reconstructing the performance indicators by embedding safety constraints to dynamically balance the safety and optimality of the formation. Consider the cost function with safety constraints as follows:

[0055]

[0056] In the formula: The energy of the systematic error, To control the input energy, R i and Q i It is a positive definite matrix. Let J be the energy of the perturbation term, and the negative sign indicates that the perturbation attempts to maximize J. i k iD >0 represents the parameter to be designed, k iB The damping coefficient is used to balance safety and optimality.

[0057] Step 4.2: Based on the cost function in Step 4.1, construct a dynamic characteristic value function to describe the game. Transform the state-constrained zero-sum game into the following unconstrained safe zero-sum game related to the safety set, resulting in the following dynamic characteristic value function:

[0058]

[0059] In the formula: The control objective is to design the optimal control strategy. i and optimal perturbation strategy d i This ensures the optimality of the value function while keeping the error within a safe range.

[0060] Step 5: Solve for the optimal strategy in the game based on Bellman's principle. That is, apply Bellman's optimality principle to find the expressions for the optimal control strategy and the optimal interference strategy that minimize the control law player and maximize the interference player, given the value function.

[0061] By applying the Bellman optimality principle, the value function characterizing the long-term performance of the system and its gradient are obtained, and the explicit optimal control strategy is derived from this. and optimal interference strategy

[0062]

[0063] The Hamilton-Jacobi-Isax (HJI) equations are characterized by transforming a dynamic optimization problem containing both control and disturbance variables into a partial differential equation that depends solely on the gradient of the value function by substituting the optimal policy. Therefore, the optimal control policy is then transformed into a partial differential equation. (10) and optimal interference strategy (11) Substitute into the dynamic characteristic value function (9), and based on the extreme value condition of the Hamiltonian function, eliminate the control variable u. i and interference variable d i And reorganized into a value function gradient ▽V that depends only on the value function gradient. i The nonlinear partial differential equation is in its complete form as follows:

[0064]

[0065] Solving this HJI equation (12) yields the gradient ▽V of the value function. i The optimal strategy is then achieved through equations (10) and (11). This strategy ensures that the system performance reaches its optimal level (minimizes performance indicators) while satisfying safety constraints and effectively copes with worst-case disturbances. Ultimately, this optimal strategy ensures that the UAV swarm can still achieve stable cooperative formation flight within the safety set even under the most unfavorable disturbances.

[0066] Step 6: Construct a critic neural network, which utilizes the approximation capability of neural networks to learn online and approximate the gradient of the value function upon which the optimal policy in Step 5 depends. The neural network structure consists of an input layer with 6 neurons to receive the UAV's state information, a hidden layer with 19 neurons using radial basis functions as activation functions, and an output layer with 6 neurons to output an approximate gradient of the value function, thereby approximating the solution to the HJI equation.

[0067] The approximate value function and gradient based on the critic's neural network are designed as follows:

[0068]

[0069] In the formula: It is the optimal weight vector. For radial basis functions, ∈ i This is an approximation error. Let ▽ be the gradient of the radial basis function with respect to the input vector. i Let ▽ρ′(e be the gradient of the approximation error with respect to the input vector.) i ) represents the gradient of the control barrier function with respect to the input vector. Let ε be a bounded control barrier function, where ε i >0 represents the parameter to be designed to prevent singularities.

[0070] Step 7: Construct a fixed-time convergent neural network weight update law, that is, estimate and train the weights of the neural network based on the gradient descent method to ensure that the optimal weights in formula (13) in step 6 are approximated within a fixed time.

[0071] Due to the optimal weight vector Due to the unknown nature of the weights, the approximate value function and its gradient remain unknown. Therefore, a fixed-time online learning strategy with only commenters is designed to approximate the optimal weight vector and estimate the approximate value function and its gradient:

[0072]

[0073] In the formula: This is an estimate of the expected weights.

[0074] Based on the above derivation, the approximate form of the Hamiltonian function is:

[0075]

[0076] In the formula: For the dynamic term of the safety function, where, and For the approximate optimal strategy to be designed, e i (t) represents the Hamiltonian approximation error.

[0077] The fixed-time convergent weight update rate obtained using gradient descent is:

[0078]

[0079] In the formula: σ iw >0 represents the rate of descent, a i ∈(0,1), b i >1 indicates a power parameter, "·" κ =|·| κ sgn(·) ensures the correctness of the direction.

[0080] Step 8: Construct a learning-driven event triggering mechanism, that is, design event triggering conditions based on the evolution process of neural network weights and the change of comprehensive error.

[0081] Traditional periodic communication requires continuous transmission of status data, resulting in long-term high-power operation of the wireless module. To reduce the communication energy consumption of the cluster system, this invention achieves dynamic optimization of communication resources by designing a learning-driven event-triggered mechanism. First, the historical commentator weight sequence is defined as follows: in, The current weight value, These are the historical weight values ​​before the nth sampling. Based on this, the learning-driving parameters are defined as follows:

[0082]

[0083] In the formula: n is the number of samples, η k The attenuation weighting coefficient satisfies And η1 > η2 > ... > η n , This represents the weight difference between adjacent time points.

[0084] Furthermore, the state sampling error is defined as:

[0085]

[0086] In the formula: e is the sampled value at the k-th trigger time. i This is the current value.

[0087] Therefore, the following event triggering conditions based on changes in learning state and error are proposed:

[0088]

[0089] In the formula: For the (k+1)th sampling time of the i-th drone, For the k-th sampling time of the i-th UAV, σ im (t) is the dynamic sampling threshold, where σ im1 (t) and σ im2 (t) represents the dynamic sampling threshold under different switching logics. The specific switching rules are shown in formulas (20) and (21). For safety and performance comprehensive indicators, For parameters related to the control strategy, b g For matrix-related parameters, For parameters related to external disturbances, e ik For the state sampling error, α i This is a switching parameter; its value can be either 0 or 1. It is a positive number.

[0090] The following is an analysis of the threshold mode switching logic, where a saturation parameter exists. The following conditions must be met:

[0091] like That is, when the weights change drastically, α i =0, event triggering mechanism selected is "busy sampling" mode:

[0092] σ im (t)=σ im1 (t) (20);

[0093] In the formula: σ im1 (t) satisfies These are the parameters to be designed.

[0094] like That is, when the weights are stable, α i =1, the event triggering mechanism is set to "idle sampling" mode:

[0095]

[0096] In the formula: Where t is the time variable, and σ im Based on the basic threshold range.

[0097] Step 9: Implement and apply near-optimal safety cooperative control, that is, substitute the approximate weights and their gradients from Step 7 and the event triggering conditions from Step 8 into the optimal control strategy and optimal disturbance strategy from Step 5, and apply them to the UAV dynamics model from Step 1. Therefore, a fixed-time near-optimal safety control strategy based on learning-triggered communication is obtained:

[0098]

[0099] We obtain a fixed-time approximate optimal perturbation strategy based on learning-triggered communication:

[0100]

[0101] Taking a multi-fixed-wing UAV formation tracking task in a horizontal XYZ three-dimensional plane as an example: the number of UAVs is N=5; the UAV swarm is deployed in an unobstructed area of ​​5000×5000×1000 meters, with the center of the area as the origin, and the east direction defined as the positive X-axis and the north direction as the positive Y-axis. The initial position of the UAV swarm is set as P. r (0) = [40, 0, 600] T P1(0) = [23, 7, 620] TP2(0) = [-27, -95, 613] T P3(0) = [1, 95, 583] T P4(0) = [-77, -66, 595] T P5(0) = [-78, 40, 616] T Initial velocity and angle v i (0) = 10 m / s, ψ i (0) = 0°, θ i (0) = 0°. According to the specific implementation steps of the technical solution of this invention, the method of this invention is simulated and verified using MATLAB / Simulink 2022b software on a laptop computer configured with an Intel(R) Core(TM) i7-14650HX2.20GHz. The specific implementation steps are as follows:

[0102] Step 1: Construct a multi-fixed-wing UAV system model. Establish a fixed-wing UAV swarm system model as shown in equations (1)-(2) and a virtual leader system model as shown in equation (3). The parameters of the fixed-wing UAV model are as follows: the autopilot parameter α... v =1, α ψ =10, α θ =10. The external interference experienced by the drone within [30,70] seconds is set to... Where i = 1, ..., 5, and ξ is arbitrary noise accompanying the disturbance.

[0103] Step 2: Construct the cluster integrated error system. Construct the formation tracking error as shown in Equation (4) and rearrange it into the integrated error system as shown in Equation (5). Where: the expected relative distance between clusters is set as P. 1r =[0,0,0] T P 2r =[-50,-100,0] T P 3r =[-50,100,0] T P 4r =[-100,-50,0] T P 5r =[-100,50,0] T .

[0104] Step 3: Define the safety set and construct the control barrier function. Establish the safety set of the form (6) and design the control barrier function of the form (7) for characterization, where the safety constraint distance satisfies:

[0105] Step 4: Construct the value function under the two-player zero-sum game framework. Based on the control barrier function, construct the value function as shown in Equation (8), and transform the safe formation tracking control problem into a two-player zero-sum game problem with safety constraints as shown in Equation (9).

[0106] Step 5: Solve for the optimal strategy based on Bellman's principle. Using Bellman's minimum principle, solve for the optimal strategy shown in equations (10) and (11) under the two-player zero-sum game in step 4, to achieve stable cooperative formation of the UAV swarm within the safe set. The parameter chosen in the equation is: Q i =20I3, R i =I3,k iB =1.

[0107] Step 6: Construct the critic neural network. Construct a neural network structure of the form (13) to approximate the value function, with an input layer corresponding to 6 dimensions and 19 Gaussian radial basis functions in the hidden layer, with the center c i Uniformly distributed in the state space [-9,9] T In the middle, the width is b i =5, the output layer corresponds to 1 dimension.

[0108] Step 7: Construct a fixed-time convergent neural network weight update law. Gradient descent is used to estimate and train the neural network weights, ensuring convergence to approximately the optimal weights in Step 6 within a fixed time. The approximate weights are shown in equation (16). The parameters are selected as follows: the initial weight values ​​are... Learning rate σ iw =0.01, the power parameter is a i =0.8, b i =1.2, σ i =1. By utilizing the approximation capability of neural networks to approximate the gradient of the value function, the optimal control strategy and optimal disturbance strategy in step 6 can be obtained, thereby improving the adaptability and robustness of the control strategy.

[0109] Step 8: Construct a learning-driven event triggering mechanism. Based on the changes in the weight update law, design the triggering conditions for a learning-driven event triggering mechanism of the form (18) to ensure that the communication frequency between UAVs matches the system state evolution during the learning process, reducing unnecessary communication and lowering resource consumption. The parameter η is selected as the triggering condition. k =0.01, b g =1,σ im1 (0)=0.45, σ im2 (0) = 0.5, the basic threshold range is σ im =0.5, The critical value for the rate of change of weight is set to The dynamic attenuation coefficient is The historical weights are n=5, and the weight coefficients are set to ξ=[0.4,0.3,0.2,0.08,0.02].

[0110] Step 9: Implement and apply near-optimal safe cooperative control. Substitute the gradient of the approximate value function output by the neural network and the event triggering conditions into step 5 to calculate the near-optimal control strategy and disturbance strategy as shown in equations (22) and (23), realize safe cooperative flight, and ensure the stable, safe and efficient operation of the UAV swarm in complex environments.

[0111] Figure 1 The flowchart of this invention is as follows: The control process begins with multi-UAV system modeling (step 1), providing basic states by establishing a dynamic model of the UAVs and the virtual leader; then, a cluster comprehensive error system is constructed based on state differences (step 2) to quantify the collaborative deviation; to ensure safety, a safety set is defined and a control obstacle function is constructed to constrain the comprehensive error (step 3); further, the problem is transformed into a two-player zero-sum game, and a value function including tracking error, control energy consumption, and control obstacle function is designed (step 4), and the optimal strategy is solved based on Bellman's principle (step 5); for real-time requirements, a commentator neural network is used to approximate the gradient of the optimal value function online (step 6), supplemented by a fixed-time weight update law to ensure fast convergence (step 7); at the same time, a learning-driven event triggering mechanism is designed based on weight and error changes to reduce communication frequency (step 8); finally, the approximate gradient and triggering conditions are fused to generate the optimal control strategy (step 9), and the closed-loop drive enables the UAVs to achieve safe, optimal, and low-consumption collaborative flight.

[0112] Figure 2 — Figure 6 This diagram illustrates the trajectory tracking performance of five drones on the XYZ axes. The horizontal axis of the simulation graph represents time in seconds, while the vertical axis corresponds to state variables. The legend represents different drones. Figure 2 The figures show the position trajectories of five UAVs on the X, Y, and Z axes, as well as their velocity, heading angle, and yaw angle changes. Figure 2 (a)-(c) show the positional trajectories of the five UAVs along the X, Y, and Z axes; Figure 2 (d)-(f) show the speed, heading angle and yaw angle changes of the five UAVs. Figure 2 It is clearly demonstrated that, under the control strategy described above, all UAVs are able to accurately track their respective designated reference trajectories and precisely form and maintain the desired geometric formation configuration. Figure 3 The figure shows the position tracking errors of five UAVs on the X, Y, and Z axes, as well as the state tracking errors of their speed, heading angle, and yaw angle. Figure 3 (a)-(c) show the position tracking error of the UAV. Figure 3 (d)-(f) show the state tracking errors for speed, heading angle, and yaw angle. Figure 3 It can be seen that the tracking error can converge quickly and stabilize in a small neighborhood near zero. Figure 4 This shows the adaptive update rate of the neural network weights for each drone and the triggering time of the adaptive event triggering conditions designed based on this update rate. Among them, Figure 4 (a) illustrates the dynamic adjustment process of neural network weights in the method of the present invention; Figure 4 (b) shows the actual triggering of the event triggering mechanism designed based on the weight change rate. Figure 4 The study demonstrates that the triggering process is related to weight and state changes. During the learning phase, triggering is more frequent to adapt to dynamic changes in the system. As the system stabilizes, the triggering frequency decreases significantly. Compared to the control strategy described in (Z. Gong, F. Yang, Y. Yuan, Q. Ma, and W. Zheng, “Secure formation control of multi-agent system against FDI attack using fixed-time convergent reinforcement learning,” IEEE Trans. Control Net w. Syst., pp. 1-11, 2025), this strategy saves approximately 61.33% of communication resources. Figure 5 A safety performance diagram of the method of the present invention is shown, wherein... Figure 5 (a) shows that throughout the entire flight mission, the distance between all the drones was always strictly greater than the set minimum safe distance, effectively avoiding collisions. Figure 5 (b) further demonstrates that the critical state tracking error is always constrained within a predefined safety boundary. Figure 6 The image provides a clear, global perspective on the complete process of five drones performing a mission in three-dimensional space. As can be seen, the drone swarm not only precisely maintains the initial desired formation configuration, but also remains stable and coordinated during complex dive maneuvers.

Claims

1. A low-energy-consumption, low-altitude unmanned aerial vehicle (UAV) swarm safety and anti-interference control method, wherein the UAV swarm system consists of N UAVs, each UAV is equipped with an autopilot, specifically including: Step 1: Construct a multi-fixed-wing UAV system model, namely, establish the dynamic model of the UAV and the dynamic model of the virtual leader; Step 2: Construct a cluster comprehensive error system, that is, based on the dynamic model in Step 1, calculate the tracking error of each UAV relative to the virtual leader, and construct a comprehensive error that reflects the overall collaborative performance of the cluster. Step 3: Define a safe set and construct a control barrier function, that is, construct a control barrier function based on the set of cluster safe operation characterized by the comprehensive error, so that the comprehensive error is always within the safe set; Step 4: Construct the value function under the two-player zero-sum game framework. That is, based on the two-player zero-sum game theory, model the control design problem as a two-player zero-sum differential game and design a value function that includes a tracking error penalty term, a control input penalty term, and a control obstacle function term. Step 5: Solve for the optimal strategy in the game based on Bellman's principle. That is, apply Bellman's optimality principle to find the expressions for the optimal control strategy and the optimal disturbance strategy that minimize the control law player and maximize the disturbance player under a given value function. Step 6: Construct a commentator neural network, that is, use the approximation ability of the neural network to learn online and approximate the gradient of the value function on which the optimal policy in Step 5 depends; Step 7: Construct a fixed-time convergent neural network weight update law, that is, estimate and train the weights of the neural network based on the gradient descent method to obtain approximate weights and their gradients. Step 8: Construct a learning-driven event triggering mechanism, that is, design event triggering conditions based on the evolution process of neural network weights and the change of comprehensive error; Step 9: Implement and apply near-optimal safety cooperative control, that is, substitute the approximate weights and their gradients in Step 7 and the event triggering conditions in Step 8 into the optimal control strategy and optimal disturbance strategy in Step 5, and apply them to the UAV dynamics model in Step 1.

2. The low-energy consumption, low-altitude UAV formation safety anti-interference control method as described in claim 1, characterized in that: In step 1, the dynamic model of the i-th UAV swarm system consisting of N fixed-wing UAVs is expressed as follows: In the formula: x i ,y i ,z i Let v be the position of the i-th UAV along the x, y, z axes. i Let ψ be the velocity of the i-th UAV in the body coordinate system. i Let θ be the heading angle of the i-th UAV. i Let d be the pitch angle of the i-th UAV; xi ,d yi ,d zi The disturbance is caused by strong winds along the x, y, and z axes; the internal velocity dynamic parameters of the autopilot are deterministically defined as Δα. v The dynamic internal parameter of the heading angle is deterministically Δα ψ The dynamic internal parameter of the yaw angle is deterministically Δα θ The flight state system of a fixed-wing UAV is modeled as follows: In the formula: The speed command for the i-th drone is... Let be the heading angle command for the i-th UAV. v is the pitch angle command for the i-th UAV; i Let ψ be the actual speed of the i-th drone. i Let θ be the actual heading angle of the i-th UAV. i Let be the actual pitch angle of the i-th UAV; define For the lumped interference of the velocity channel of the i-th UAV, For the lumped interference of the heading angle channel of the i-th UAV, The lumped disturbance in the yaw angle channel of the i-th UAV; the dynamic model of the virtual leader is: In the formula: x r ,y r ,z r v represents the virtual leader's position along the x, y, z axes. r For the pre-generated virtual leader velocity, ψ r θ is the heading angle of the pre-generated virtual leader. r The pitch angle for a pre-generated virtual leader.

3. The low-energy consumption, low-altitude UAV formation safety anti-interference control method as described in claim 1, characterized in that: The location information x of the i-th UAV in step 2 i ,y i ,z i Integrate into a three-dimensional position vector P i =[x i ,y i ,z i ] T The leader's location information x r ,y r ,z r Integrate into a three-dimensional position vector P r =[x r ,y r ,z r ] T The flight status v of the i-th drone i ,ψ i ,θ i Integrate into a three-dimensional flight state vector The leader's flight status information v r ,ψ r ,θ r Integrate into a three-dimensional flight state vector The tracking error of the i-th UAV is: In the formula: This represents the position tracking error of the i-th UAV. This represents the tracking error of the i-th UAV in terms of speed, heading angle, and pitch angle. Let be the expected relative distance between the i-th drone and the leader; convert the tracking error of the i-th drone into a comprehensive error: In the formula: Let u be the comprehensive error vector. i To control the input, d i =[d xi ,d yi ,d zi ,d vi ,d ψi ,d θi ] T To centralize interference, 4. The low-energy consumption, low-altitude UAV formation safety anti-interference control method as described in claim 1, characterized in that: Step 3 includes: Step 3.1: Constructing a safety set based on error constraints; Step 3.2: Construct a control barrier function based on a safety set; In step 3.1, for the i-th drone, the minimum safe distance requirement between it and its nearest neighbor drone is: Its size is determined by Calculation yielded; Design the following security set for the i-th drone. In the formula: It is a compact set containing the origin, with the nonlinear term F. i On Satisfies Lipschitz continuity; In step 3.2, the control barrier function ρ is constructed. i for: By designing a control obstacle function, the tracking error of each UAV is constrained to always be less than half of its actual distance from neighboring UAVs.

5. A low-energy-consumption, low-altitude UAV formation safety anti-interference control method as described in claim 1, characterized in that: In step 4, the controller is player one, and the lumped disturbance is player two. The Nash equilibrium of the two-player zero-sum game is solved to obtain an optimal control strategy and an optimal disturbance strategy. Step 4 includes: Step 4.1: Construct the cost function, that is, design the cost function based on the optimal control principle and reconstruct the performance index by embedding the safety constraints; Step 4.2: Based on the cost function in Step 4.1, construct a value function to describe the dynamic characteristics of the game; The cost function with safety constraints in step 4.1 is: In the formula: The energy of the systematic error, To control the input energy, R i and Q i It is a positive definite matrix. Let J be the energy of the perturbation term, and the negative sign indicates that the perturbation attempts to maximize J. i k iD >0 represents the parameter to be designed, k iB The damping coefficient is used to balance safety and optimality; The dynamic characteristic value function in step 4.2: In the formula: The control objective is to design the optimal control strategy. i and optimal perturbation strategy d i .

6. The low-energy consumption, low-altitude UAV formation safety anti-interference control method as described in claim 1, characterized in that: The optimal control strategy in step 5 is for: Optimal interference strategy for: The HJI equation is: The gradient of the value function obtained by solving this HJI equation 7. A low-energy-consumption, low-altitude UAV formation safety anti-interference control method as described in claim 1, characterized in that: In step 6, the neural network has the following structure: the input layer contains 6 neurons to receive the state information of the UAV, the hidden layer contains 19 neurons and uses radial basis functions as activation functions, and the output layer contains 6 neurons to output an approximate value function gradient. The approximate value function and gradient based on the critic's neural network are designed as follows: In the formula: It is the optimal weight vector. For radial basis functions, ∈ i This is an approximation error. The gradient of the radial basis function with respect to the input vector. The gradient of the approximation error with respect to the input vector. To control the gradient of the barrier function with respect to the input vector, Let ε be a bounded control barrier function, where ε i >0 represents the parameter to be designed.

8. A low-energy-consumption, low-altitude UAV formation safety anti-interference control method as described in claim 1, characterized in that: Step 7 involves designing a fixed-time online learning strategy with only commenters to approximate the optimal weight vector and estimate the approximate value function and its gradient. In the formula: This is an estimate of the expected weights; The approximate form of the Hamiltonian function is: In the formula: For the dynamic term of the safety function, where, and For the approximate optimal strategy to be designed, e i (t) represents the Hamiltonian approximation error; The fixed-time convergent weight update rate obtained using gradient descent is: Where: σ iw >0 represents the rate of descent, a i ∈(0,1), b i >1 indicates a power parameter.

9. A low-energy-consumption, low-altitude UAV formation safety anti-interference control method as described in claim 1, characterized in that: In step 8, the historical commentator weight sequence is defined as follows: in, The current weight value, The learning-driving parameters are defined as follows, representing the historical weight values ​​before the nth sampling: In the formula: n is the number of samples, η k The attenuation weighting coefficient satisfies And η1 > η2 > ... > η n , This represents the weight difference between adjacent time points; The state sampling error is defined as: In the formula: e is the sampled value at the k-th trigger time. i The current value; The event triggering conditions based on changes in learning state and error are as follows: In the formula: For the (k+1)th sampling time of the i-th drone, For the k-th sampling time of the i-th UAV, σ im (t) is the dynamic sampling threshold, where σ im1 (t) and σ im2 (t) represents the dynamic sampling threshold under different switching logics; For safety and performance comprehensive indicators, For parameters related to the control strategy, b g For matrix-related parameters, For parameters related to external disturbances, e ik For the state sampling error, α i This is a switching parameter; its value can be either 0 or 1. It is a positive number; l i For saturation parameters, if That is, when the weights change drastically, α i =0, event triggering mechanism selected is "busy sampling" mode: s im (t)=σ im1 (t); Where: σ im1 (t) satisfies These are the parameters to be designed; like That is, when the weights are stable, α i =1, event triggering mechanism selected is "idle sampling" mode: s im (t)=σ im2 (t); In the formula: Where t is the time variable, and σ im Based on the basic threshold range.

10. A low-energy-consumption, low-altitude UAV formation safety anti-interference control method as described in claim 9, characterized in that: The number of drones N = 5, and the autopilot parameter α in step 1. v =1, α ψ =10, α θ =10; The external interference experienced by the drone within [30,70] seconds is set to Where i = 1, ..., 5, and ξ is arbitrary noise accompanying the disturbance; In step 2, the expected relative distance between clusters is set to P. 1r =[0,0,0] T P 2r =[-50,-100,0] T P 3r =[-50,100,0] T P 4r =[-100,-50,0] T P 5r =[-100,50,0] T ; The safety constraint distance in step 3 is satisfied as follows: In step 5, Q i =20I3, R i =I3,k iB =1; In step 6, the neural network structure approximates the value function. Its input layer corresponds to 6 dimensions, and the hidden layer has 19 Gaussian radial basis functions, with the center c. i Uniformly distributed in the state space [-9,9] T In the middle, the width is b i =5, the output layer corresponds to 1 dimension; The initial weight value in step 7 is Learning rate σ iw =0.01, the power parameter is a i =0.8, b i =1.2, σ i =1; In step 8, η k =0.01, b g =1,σ im1 (0)=0.45, σ im2 (0) = 0.5, the basic threshold range is σ im =0.5, The critical value for the rate of change of weight is set to l i =25; Dynamic attenuation coefficient is The historical weights are n=5, and the weight coefficients are set to ξ=[0.4,0.3,0.2,0.08,0.02]; The fixed-time approximate optimal-security control strategy based on learning-triggered communication in step 9 is as follows: The fixed-time approximate optimal perturbation strategy based on learning-triggered communication is obtained as follows:

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