A CFO-based anti-disturbance control method and system for UAV formation and product thereof

Abstract

The present application relates to the technical field of unmanned aerial vehicle formation, and provides an unmanned aerial vehicle formation anti-interference control method, system and product based on CFO, which comprises the following steps: constructing an unmanned aerial vehicle model containing unmodeled dynamics and external environmental disturbance; designing a compensation function observer; constructing an auxiliary controller by using a backstepping method based on the disturbance estimation value of the compensation function observer; constructing a distributed Lyapunov model predictive control method which fuses the auxiliary control law with disturbance compensation and the dynamic virtual pipe space constraint; solving the optimization problem of the distributed Lyapunov model predictive control method, and driving the unmanned aerial vehicle formation to safely and quickly reach the target area in the dynamic virtual pipe according to the optimal control input of each unmanned aerial vehicle. The present application provides a cooperative control method with anti-interference ability, obstacle avoidance flexibility and formation stability for unmanned aerial vehicle formation in a complex low-altitude environment, and realizes autonomous and safe arrival of the formation in the low-altitude environment.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) formation technology, and in particular to a UAV formation anti-interference control method, system, and product based on CFO (Control-Oriented Function). Background Technology

[0002] When unmanned aerial vehicle (UAV) swarms perform collaborative missions in complex low-altitude airspace, their operational integrity and mission effectiveness are constrained by a combination of factors. On the one hand, strong random environmental disturbances continuously affect the swarm, disrupting formation stability and trajectory tracking accuracy. On the other hand, sudden obstacles compress the safe flight corridor, placing extremely high demands on real-time perception and obstacle avoidance capabilities. Furthermore, frequent interruptions in inter-UAV communication due to signal obstruction, interference, or topology changes may lead to swarm collaborative control failures and even trigger chain collision risks.

[0003] In complex low-altitude environments, UAV swarms are not only affected by external environmental disturbances such as time-varying wind, but also face internal uncertainties such as system modeling errors and parameter perturbations. These factors can significantly reduce trajectory tracking accuracy and formation keeping performance, and even lead to system instability. Although Active Disturbance Rejection Control (ADRC) estimates and compensates for total disturbances through ESO (Extended State Observer), its observation accuracy is often insufficient when facing high-frequency nonlinear disturbances, resulting in lag in disturbance compensation. While Standard Model Predictive Control (SMMC) has the ability to handle constraints and optimization, its robustness is limited, making it difficult to guarantee closed-loop stability under large disturbances. Existing research often separates the design of disturbance rejection control and formation optimization, failing to fully utilize disturbance observation information to guide the stability constraints of predictive control, thus limiting the overall performance of the system under strong disturbance environments. Summary of the Invention

[0004] This invention aims to at least solve one of the technical problems existing in related technologies. To this end, this invention provides a UAV formation anti-disturbance control method, system, and product based on CFO (Compensation Function Observer), providing a collaborative control method for UAV formations in complex low-altitude environments that combines anti-disturbance capability, obstacle avoidance flexibility, and formation stability, enabling formations to reach their destination autonomously and safely in low-altitude environments.

[0005] This invention provides a CFO-based method for anti-interference control of UAV formations, comprising: S1: Construct a drone model that includes lumped perturbations; S2: Design a compensation function observer for each UAV based on the UAV model, and use the compensation function observer to estimate the lumped disturbances experienced by the UAV online, thereby obtaining the disturbance estimate value of the compensation function observer; S3: The disturbance estimate based on the compensation function observer is used to construct an auxiliary controller using the backstepping method to obtain an auxiliary control law with disturbance compensation; S4: Generate dynamic virtual pipelines for UAV formations based on collaborative guidance points with internal geometric relationships; S5: Construct a distributed Lyapunov model predictive control method that integrates auxiliary control law with disturbance compensation and dynamic virtual pipeline space constraints; S6: Construct the optimization problem of the distributed Lyapunov model predictive control method, solve the optimization problem of the distributed Lyapunov model predictive control method, obtain the optimal control input of each UAV, and drive the UAV formation to reach the target area in a dynamic virtual pipeline under the condition of satisfying collision avoidance and obstacle avoidance constraints according to the optimal control input of each UAV.

[0006] Furthermore, the cost function of the distributed Lyapunov model predictive control method includes the guide point attraction cost, formation holding cost, dynamic virtual pipeline constraint cost, collision avoidance cost between UAVs, obstacle avoidance constraint cost, control energy consumption cost, velocity alignment cost, and velocity maximization cost. The constraints of the distributed Lyapunov model predictive control method include flight dynamics equality constraints, initial condition constraints, physical input constraints, and Lyapunov stability constraints.

[0007] Furthermore, the attraction cost of the guide point is the deviation between the actual position of the guide point and the center position of the target area. The actual position of the guide point is calculated from the midpoint of the line connecting the positions of the two designated UAVs. The formation maintenance cost is based on the desired formation geometry and calculates the relative position error between each UAV in real time to minimize the formation error. The dynamic virtual pipeline constraint cost dynamically adjusts the boundary constraint weights based on the ratio of obstacle width to pipeline width. The collision avoidance cost between drones is determined by penalizing the deviation between the relative distance between drones and the buffer distance. The obstacle avoidance constraint cost is based on the safe distance between the UAV and the obstacle. It uses a soft obstacle avoidance penalty term constructed with a logarithmic function of the distance between the UAV and the obstacle as the independent variable, as well as obstacle avoidance weights, to respond in a timely manner to local dynamic threats that cannot be covered by pipeline constraints. The control energy consumption cost is used to minimize the energy consumption required for the UAV to execute control commands; The velocity alignment cost ensures that the velocity direction of each drone is aligned with the tangent direction of the virtual pipeline centerline; The speed maximization cost is used to maximize the flight speed of the drone.

[0008] Furthermore, the flight dynamics equation constraint is to embed the UAV dynamics model into the optimization framework in the form of equation constraints to ensure that the control sequence satisfies the dynamic evolution relationship of the system; The initial condition constraint is to force the first step state in the optimization time domain to be equal to the actual flight state measured by the sensor at the current moment; The physical input constraint is that the control quantity is limited to the amplitude range allowed by the UAV actuator; The Lyapunov stability constraint requires that the derivative of the Lyapunov function corresponding to the control sequence obtained through optimization should not exceed the reference decay value calculated by the auxiliary control law.

[0009] Furthermore, the compensation function observer is designed for the total transformation disturbance of the UAV, satisfying the assumptions of high-order differentiability and boundedness. It achieves high-precision disturbance estimation through feedback of state error and disturbance error. The total transformation disturbance is determined based on the lumped disturbance of the UAV and the rotation matrix from the UAV coordinate system to the world coordinate system.

[0010] Furthermore, step S3 includes: S31: Defines the positional error between the current position of the UAV and the desired target position; S32: Construct the first Lyapunov function based on the position error between the current position of the UAV and the desired target position; S33: Design a virtual control quantity such that the derivative of the first Lyapunov function is negative definite; S34: Define the speed error based on the virtual control quantity, and construct the second Lyapunov function based on the speed error; S35: Based on the derivative of the second Lyapunov function and the Lyapunov stability theorem, the auxiliary controller is derived. The disturbance value estimated by the compensation function observer is substituted into the auxiliary controller to obtain the auxiliary control law with disturbance compensation.

[0011] Furthermore, in step S4, the actual position of the guide point is calculated from the midpoint of the line connecting the positions of the two designated drones. The position and speed information of the two drones are shared by all drones and used to coordinately guide the entire drone formation to move toward the target area, thus constraining the drone formation within a dynamically generated virtual pipe space.

[0012] Furthermore, each drone in the drone formation is equipped with the same controller structure. Each drone relies only on the state information of its local neighbors to make control decisions and achieves collaborative formation by sharing the state of the formation guidance point.

[0013] This invention also provides a CFO-based UAV formation anti-interference control system for executing the aforementioned CFO-based UAV formation anti-interference control method, comprising: A drone model building module, which builds a drone model containing lumped perturbations; The disturbance construction module designs a compensation function observer for each UAV based on the UAV model, and performs online estimation of the lumped disturbances experienced by the UAV through the compensation function observer to obtain the disturbance estimate value of the compensation function observer. An auxiliary control law construction module is used to construct an auxiliary controller based on the disturbance estimate of the compensation function observer using the backstepping method, thereby obtaining an auxiliary control law with disturbance compensation. A dynamic virtual pipeline construction module generates dynamic virtual pipelines for UAV formations based on collaborative guidance points of internal geometric relationships. A predictive control method construction module is provided, which constructs a distributed Lyapunov model predictive control method that integrates an auxiliary control law with disturbance compensation and dynamic virtual pipeline space constraints. An optimization solution module is used to construct an optimization problem of the distributed Lyapunov model predictive control method, solve the optimization problem of the distributed Lyapunov model predictive control method, obtain the optimal control input of each UAV, and drive the UAV formation to reach the target area within a dynamic virtual pipeline under the condition of satisfying collision avoidance and obstacle avoidance constraints.

[0014] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described CFO-based unmanned aerial vehicle (UAV) formation anti-interference control method.

[0015] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects: This invention effectively improves the accuracy of state prediction under time-varying disturbances. It utilizes an auxiliary control law based on CFO estimation information to design a stable contraction constraint for the MPC (Model Predictive Control) optimization problem, theoretically guaranteeing the stability of the closed-loop system and significantly enhancing the algorithm's robustness. By introducing collision avoidance and obstacle avoidance cost functions into the optimization objective, this invention can meet the safety requirements of swarm flight. This invention not only enables the rapid formation of UAV formations but also guides UAVs to reach the target area more efficiently.

[0016] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating a CFO-based anti-disturbance control method for UAV formations provided by the present invention.

[0019] Figure 2 This is a three-dimensional flight control effect diagram of a drone formation provided in an embodiment of the present invention.

[0020] Figure 3 This is a schematic diagram of the position change of the drone formation provided in an embodiment of the present invention, wherein... Figure 3 Figure (a) shows the change in the x-axis position of the UAV formation. Figure 3 Figure (b) shows the change in the y-axis position of the UAV formation. Figure 3 Figure (c) in the diagram is a schematic diagram of the z-axis position change of the UAV formation.

[0021] Figure 4 This is a schematic diagram of drone formation maintenance error provided in an embodiment of the present invention, wherein... Figure 4 Figure (a) in the figure is a schematic diagram of the error maintenance of UAV formation along the x-axis. Figure 4 Figure (b) in the diagram is a schematic diagram of the y-axis UAV formation maintaining error. Figure 4 Figure (c) in the diagram is a schematic diagram of the error maintenance of UAV formation along the z-axis.

[0022] Figure 5 This is a schematic diagram illustrating the observation effects of a CFO-based perturbation observer and an ESO-based perturbation observer applying perturbations to different channels. Figure 5 Figure (a) in the figure is a schematic diagram of the observed changes in the x-axis perturbation. Figure 5 Figure (b) in the diagram is a schematic diagram of the observed changes in the y-axis perturbation. Figure 5 Figure (c) in the diagram is a schematic diagram of the observed changes in the z-axis perturbation. Figure 5 Figure (d) in the diagram is a schematic diagram of the observed changes in yaw disturbance.

[0023] Figure 6 This is a three-dimensional flight control effect diagram of a traditional MPC provided in an embodiment of the present invention.

[0024] Figure 7 This is a schematic diagram of drone formation holding error in a conventional MPC provided by an embodiment of the invention, wherein... Figure 7 Figure (a) shows a schematic diagram of the drone formation maintenance error in traditional MPC along the x-axis. Figure 7Figure (b) in the figure is a schematic diagram of the drone formation maintaining error in traditional MPC along the y-axis. Figure 7 Figure (c) in the diagram is a schematic diagram of the drone formation maintaining error in the traditional MPC along the z-axis.

[0025] Figure 8 This is a schematic diagram illustrating the formation flight effect of drones in an environment with obstacles, according to an embodiment of the present invention.

[0026] Figure 9 This is a schematic diagram illustrating the positional changes of a drone formation with obstacles in an environment according to an embodiment of the present invention. Figure 9 Figure (a) shows the x-axis position change of a drone formation with obstacles in the environment. Figure 9 Figure (b) shows the y-axis position change of a drone formation with obstacles in the environment. Figure 9 Figure (c) shows the z-axis position change of a drone formation with obstacles in the environment.

[0027] Figure 10 This is a schematic diagram illustrating the formation maintenance error of drones in an environment with obstacles, according to an embodiment of the present invention. Figure 10 Figure (a) shows a schematic diagram of the x-axis retention error of a UAV formation with obstacles in the environment. Figure 10 Figure (b) shows a schematic diagram of the y-axis retention error of a drone formation with obstacles in the environment. Figure 10 Figure (c) shows a schematic diagram of the z-axis error retention of a UAV formation with obstacles in the environment.

[0028] Figure 11 This is a schematic diagram of a CFO-based anti-interference control system for unmanned aerial vehicle (UAV) formations, provided by the present invention.

[0029] Figure label: 101. UAV Model Construction Module; 102. Disturbance Construction Module; 103. Auxiliary Control Law Construction Module; 104. Dynamic Virtual Pipeline Construction Module; 105. Predictive Control Method Construction Module; 106. Optimization Solution Module. Detailed Implementation

[0030] 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. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. 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. The following embodiments are used to illustrate this invention but cannot be used to limit the scope of this invention.

[0031] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0032] The following is combined with Figures 1 to 11 This invention describes a CFO-based anti-disturbance control method for unmanned aerial vehicle (UAV) formations.

[0033] like Figure 1 As shown, a CFO-based method for anti-interference control of UAV formations includes: S1: Construct a drone model that includes lumped perturbations; The lumped disturbances experienced by the drone include unmodeled dynamics and external environmental disturbances. Both unmodeled dynamics and external environmental disturbances are... Differentiable in order, and its All derivatives of order are bounded, that is, they satisfy... , , , ..., ,in, For aggregated disturbances, This is the upper bound of the lumped disturbance amplitude. For the first derivative of the lumped perturbation, The second derivative of the lumped perturbation. For aggregated disturbances First derivative, This is the upper bound of the first derivative of the lumped perturbation. This is the upper bound of the second derivative of the lumped perturbation. For aggregated disturbance Upper bound of the first derivative It is an infinite norm.

[0034] definition The drone model is as follows: in, For the first The position vector of the drone, For the first The rate of change of position of the drone Let the rotation matrix be the one from the UAV coordinate system to the world coordinate system. For the first The yaw angle of the drone, For the first The speed of the drone For the first The first identifiable model parameters of the drone. For the first The second recognizable model parameters of the drone. For antisymmetric matrices, , For the first Control input for the drone , For drones The forward speed, drones Side flight speed input, For drones The input of the rate of ascent, For drones Yaw speed input, For the first Lumped disturbance of drones This is the transpose of the matrix. for The derivative of Forward speed gain, For side-flight speed gain, For the gain of the ascent rate, For yaw speed gain, Forward flight control gain, For side-flight control gain, To increase the control gain, This is the yaw control gain.

[0035] S2: Design a compensation function observer for each UAV based on the UAV model, and use the compensation function observer to estimate the lumped disturbances experienced by the UAV online, thereby obtaining the disturbance estimate value of the compensation function observer; The compensation function observer is designed for the total disturbance of UAV transformation, satisfies the assumptions of high-order differentiability and boundedness, and achieves high-precision disturbance estimation through feedback of state error and disturbance error.

[0036] Total disturbance Determined based on the lumped disturbance of the UAV and the rotation matrix from the UAV coordinate system to the world coordinate system. , for The estimated value, for The estimated value, for The estimated value is used to define the position state estimation error. , Velocity state estimation error , Total perturbation estimation error For drones The specific design of its CFO is as follows: in, for The observation gain matrix, , for The observed gain value, for The observation gain matrix, , for The observed gain value, Here is the filtering matrix. , These are the filter coefficients. It is a nonlinear compensation function. , as well as All are diagonal arrays. It is a positive number. drones The expected position vector along the z-axis, for The estimated value, .

[0037] The lumped disturbances experienced by the UAV are estimated online using a compensation function observer, and the disturbance estimate value of the compensation function observer is obtained.

[0038] S3: The disturbance estimate based on the compensation function observer is used to construct an auxiliary controller using the backstepping method to obtain an auxiliary control law with disturbance compensation; S31: Defines the positional error between the current position of the UAV and the desired target position; Assuming the desired target location , , For drones The expected position vector along the x-axis, For drones The expected position vector along the y-axis. drones The expected position vector along the z-axis, drones Desired yaw angle, desired position error , .

[0039] S32: Based on the position error between the current position of the UAV and the desired target position, construct the first Lyapunov function, and calculate its expression as follows: in, For the first The first Lyapunov function for unmanned aerial vehicles. For the first The position error coefficient matrix of the drone , The x-axis position error coefficient. This is the y-axis position error coefficient. The z-axis position error coefficient. is the yaw angle position error coefficient, and All are positive numbers.

[0040] S33: Design a virtual control quantity such that the derivative of the first Lyapunov function is negative definite; The derivative is: in, For the first The speed of the drone; Design virtual control quantity satisfy: in, It is a positive definite fourth-order diagonal matrix; S34: Define the speed error based on the virtual control quantity, and construct the second Lyapunov function based on the speed error; The expression for calculating the speed error is: in, For speed error; The derivative is: but: The derivative is: Definition of the first The second Lyapunov function of the drone for: in, It is a positive definite fourth-order diagonal matrix.

[0041] S35: Based on the derivative of the second Lyapunov function and the Lyapunov stability theorem, the auxiliary controller is derived. The disturbance value estimated by the compensation function observer is substituted into the auxiliary controller to obtain the auxiliary control law with disturbance compensation. The derivative is: but: According to Lyapunov's stability theorem, to make the system asymptotically stable, it is only necessary to ensure that... Therefore, the auxiliary controller can be derived as follows: because Since the disturbance is unknown, CFO (Disturbance Forecasting) is needed for disturbance estimation in actual controller design. Based on CFO, the auxiliary control law with disturbance compensation can be: in, for The estimated value; S4: Generate dynamic virtual pipelines for UAV formations based on collaborative guidance points with internal geometric relationships; The collaborative guidance point based on the internal geometry of the formation is defined as the center position of the line connecting specific drones. The actual position of the guidance point is calculated from the midpoint of the line connecting the positions of two designated drones (such as drone 2 and drone 3). The position and speed information of the two drones are shared by all drones and used to collaboratively guide the entire formation to move toward the target area without having to pre-set a precise tracking trajectory for the guidance point.

[0042] The overall movement of the drone formation is constrained within a dynamically generated virtual conduit space. Given the abundance of passable redundancy in low-altitude flight environments, strict conduit boundary constraints are unnecessary and may even limit the formation's maneuverability. Therefore, the virtual conduit is treated as a flexible spatial guidance domain, allowing the formation to maneuver autonomously and flexibly within dynamically adjusted conduit boundaries. This enhances the formation's spatial adaptability to the environment while ensuring overall guidance and obstacle avoidance safety.

[0043] Dynamic virtual pipelines provide a flexible and safe corridor for the formation topology without collisions with large obstacles, thereby transforming complex obstacle avoidance constraints into pipeline boundary constraints that the formation must follow, simplifying the difficulty of handling obstacle avoidance problems.

[0044] S5: Construct a distributed Lyapunov model predictive control method that integrates auxiliary control law with disturbance compensation and dynamic virtual pipeline space constraints; In the distributed formation control architecture of the present invention, each UAV is equipped with the same controller structure. Each UAV in the UAV formation is equipped with the same controller structure. Each UAV only relies on the state information of its local neighbors to make control decisions and achieves cooperative formation by sharing the state of the formation guidance point.

[0045] To enable drone formations to maintain formation flight while navigating towards a designated area within a dynamic virtual conduit, and to achieve collision avoidance between drones and obstacle avoidance between drones; The cost function of the distributed Lyapunov model predictive control method includes the guide point attraction cost, formation holding cost, dynamic virtual pipeline constraint cost, collision avoidance cost between UAVs, obstacle avoidance constraint cost, control energy consumption cost, velocity alignment cost, and velocity maximization cost. The attraction cost of the guide point is the deviation between the actual position of the guide point and the center position of the target area. The actual position of the guide point is calculated from the midpoint of the line connecting the positions of the two specified UAVs. The formation maintenance cost is based on the desired formation geometry and calculates the relative position error between each UAV in real time to minimize the formation error. The dynamic virtual pipeline constraint cost dynamically adjusts the boundary constraint weights based on the ratio of obstacle width to pipeline width. The collision avoidance cost between drones is determined by penalizing the deviation between the relative distance between drones and the buffer distance. The obstacle avoidance constraint cost is based on the safe distance between the UAV and the obstacle. It uses a soft obstacle avoidance penalty term constructed with a logarithmic function of the distance between the UAV and the obstacle as the independent variable, as well as obstacle avoidance weights, to respond in a timely manner to local dynamic threats that cannot be covered by pipeline constraints. The control energy consumption cost is used to minimize the energy consumption required for the UAV to execute control commands; The velocity alignment cost ensures that the velocity direction of each drone is aligned with the tangent direction of the virtual pipeline centerline; The speed maximization cost is used to maximize the flight speed of the drone.

[0046] Specifically, the cost function of the distributed Lyapunov model predictive control method incorporates the following key factors: the guide point attraction cost. Formation maintenance costs Dynamic pipeline boundary constraint cost Cost of collision avoidance between drones The cost of obstacle avoidance between drones and obstacles and the minimum cost of consuming energy At the same time, in order to allow the drone formation to quickly reach the target area along a better route, the drones... The velocity direction moves rapidly along the tangent of the virtual centerline, thus introducing a velocity direction alignment cost. and the cost of maximizing speed .

[0047] Global cost function It can be represented as: in, For the prediction time domain of the Distributed Lyapunov Model Predictive Control (DLMPC) method, The step size for prediction; To achieve rapid convergence of the UAV formation to the target area, a guiding point attraction cost term is introduced into the cost function. . Defined as the deviation between the actual position of the guide point and the center position of the target area, where the actual position of the guide point is calculated from the midpoint of the line connecting the positions of the two specified drones, and its specific mathematical expression is as follows: in, The weighting coefficients for the attraction cost of the guiding point. In order to be in Time prediction The position vector of the guiding point at time t. The center position of the target area of ​​the drone formation.

[0048] To ensure that a drone swarm maintains its formation while flying towards the target area, a formation-keeping cost term is introduced into the optimization objective. This allows each UAV to maintain formation stability during motion planning. The cost term, based on the desired triangular geometry, calculates the relative positional error between UAVs in real time and incorporates it as a penalty function into the overall cost function. By appropriately designing weighting factors, the system can minimize formation error in dynamic environments, thereby ensuring the swarm maintains a stable formation throughout flight.

[0049] in, For drones and drones adjacency matrix The element in the middle, To maintain the weighting coefficients of the cost terms in the formation, For drones exist Time prediction Location at any given moment For drones exist Time prediction Location at any given moment For drones in formation configuration and drones The relative distance between them.

[0050] To simplify the obstacle avoidance constraint model for UAV formations in complex environments and to fully explore the passable space in low-altitude environments, this invention introduces dynamic virtual pipeline boundary constraints. An adaptive weight adjustment strategy was designed. The core idea of ​​this strategy is to dynamically adjust the boundary constraint weights based on the ratio of obstacle width to pipe width. Specifically, when the obstacle occupies a smaller proportion, a larger weight is assigned to the virtual pipe constraint, forcing the formation to stay inside the pipe; as the obstacle occupies a larger proportion, i.e., when the pipe is severely blocked, the constraint weight is appropriately reduced, allowing the UAVs to briefly fly out of the pipe boundary. Through this mechanism, the formation's maneuverability during obstacle avoidance can be improved while ensuring flight safety, thereby enhancing overall obstacle avoidance performance.

[0051] in, This is an adaptive weight adjustment factor for the constraint cost of the dynamic virtual pipeline. These are the weighting coefficients. Location of the obstacle. The centerline of the constructed virtual pipeline, It is half the width of the virtual pipe. This represents the weight decay rate. The width of the obstacle. The function is for finding the maximum value.

[0052] Virtual pipeline boundary constraints achieve flexible constraints through adaptive weight adjustment. In unobstructed or low-threat areas, the formation can make full use of the pipeline's internal space, while in high-threat areas, the boundary constraints are strengthened by increasing the weight, forming a flexible safety corridor that is dynamically adjusted according to the level of threat.

[0053] During UAV formation flight, reliable inter-UAV collision avoidance is a core prerequisite for ensuring flight safety. To further improve collision avoidance performance, this invention constructs a collision avoidance buffer zone, aiming to reserve sufficient safe distance between UAVs, and introduces an inter-UAV collision avoidance cost term based on this buffer zone. This penalty term, by penalizing the deviation between the relative distance and the buffer distance between drones, guides the formation to actively avoid getting close to each other during motion planning, thereby effectively preventing collisions.

[0054] in, To avoid collisions with weighting coefficients, Where is the radius of the buffer zone. For drone swarms.

[0055] While dynamic virtual pipe constraints can effectively simplify obstacle avoidance problems in complex static environments, the small and dynamic obstacles prevalent in low-altitude environments are difficult to completely avoid using fixed pipe boundaries. To ensure absolute safety in formation flying, this invention further introduces obstacle avoidance constraint costs into the objective function. The aim is to respond promptly to local dynamic threats that cannot be covered by pipeline constraints, thereby building a more complete fleet security system.

[0056] in, For obstacle avoidance weighting coefficients, The safe distance between the drone and the obstacle.

[0057] To enhance the sustained operational capability of drone swarms in complex missions, energy consumption will be controlled. The optimization objective is to minimize the energy consumption required for the UAV to execute control commands by optimizing flight trajectory and attitude adjustments, thereby reducing unnecessary power loss. Minimizing energy consumption during formation flight can effectively extend the UAV's endurance, thus supporting long-duration, long-distance collaborative formation missions.

[0058] in, As a weight for energy consumption cost, For drones exist Time prediction Time-based control input.

[0059] To achieve fast and accurate navigation of UAV formations within a dynamic virtual pipeline, a velocity alignment term is introduced into the cost function. With speed maximization term The velocity alignment term aims to force the velocity direction of each UAV to align with the tangent direction of the virtual pipeline's centerline, thereby ensuring the formation travels efficiently along the predetermined path. The velocity maximization term incentivizes the UAVs to fly at the highest possible speed to shorten the time to reach the target area. Through the coordinated optimization of these two terms, the formation can achieve motion planning that combines path guidance and time optimization while adhering to the pipeline's geometric constraints.

[0060] in, For drones exist Time prediction The speed of time, For the virtual center line at The derivative vector at time t, These are the weighting coefficients for the velocity alignment term.

[0061] in, The dynamic weighting coefficient for the maximum speed term. In order to be in The location of the guide point at all times. The weighting coefficient for the maximum speed term. The dynamic weights for the maximum speed term, The desired target location.

[0062] To ensure the physical feasibility and engineering feasibility of the planned trajectory, the following constraints are proposed, taking into account the dynamic characteristics of the UAV, its initial flight state, and the physical limitations of its actuators. These constraints aim to ensure that the control commands obtained through optimization can be executed by the actual flight control system, while satisfying flight safety boundaries.

[0063] The constraints of the distributed Lyapunov model predictive control method include flight dynamics equality constraints, initial condition constraints, physical input constraints, and Lyapunov stability constraints.

[0064] The flight dynamics equality constraint is to embed the UAV dynamics model into the optimization framework in the form of equality constraints to ensure that the control sequence satisfies the dynamic evolution relationship of the system. The initial condition constraint is to force the first step state in the optimization time domain to be equal to the actual flight state measured by the sensor at the current moment; The physical input constraint is that the control quantity is limited to the amplitude range allowed by the UAV actuator; The Lyapunov stability constraint requires that the derivative of the Lyapunov function corresponding to the control sequence obtained through optimization should not exceed the reference decay value calculated by the auxiliary control law.

[0065] Specifically, to ensure that the designed controller output conforms to the physical motion laws of the UAV, the UAV's flight dynamics model is embedded into the DLMPC framework in the form of equality constraints. By introducing these flight dynamics equality constraints, it can be guaranteed that the optimized control sequence strictly satisfies the dynamic evolution relationship of the system at each sampling time, thereby improving the physical executability of the control commands. The calculation expression is as follows: in, For dynamic consistency constraints, For drones exist Time prediction Rate of change of state at time t, For drones The state dynamics function; In the design of UAV formation controllers based on model predictive control, it is essential to ensure that the solution to the optimization problem strictly matches the actual flight conditions. To this end, the following two types of necessary constraints are introduced into the constraint set of DLMPC: initial condition constraints. This means that the initial state variable in the optimization time domain must be forced to equal the actual flight state measured by the sensor at the current moment to ensure the continuity of control commands and the accuracy of real-time feedback; physical input constraints In other words, the control output of the actuator must be strictly limited to a permissible amplitude range to satisfy the physical limits of the actuator. These two types of constraints together constitute the feasible region boundary of the optimization problem, ensuring that the planned control command is not only mathematically optimal but also physically realizable. The calculation expression is: in, This represents the maximum control input that a drone can achieve.

[0066] In the CFO-based DLMPC control framework, Lyapunov stability constraints are introduced to ensure the robust stability of the UAV closed-loop system in disturbed environments. This constraint requires that the derivative of the Lyapunov function corresponding to the control sequence obtained through optimization should not exceed the reference attenuation value calculated by the auxiliary control law. The auxiliary control law is no longer based solely on the nominal model design, but integrates real-time estimation information from the disturbance observer, enabling it to maintain the expected Lyapunov attenuation performance even in the presence of external wind disturbances, model mismatch, or unmodeled dynamics. The calculation expression is as follows: in, In order to be in The optimal control input is obtained by constantly optimizing the solution. This is the control input for the auxiliary control law based on CFO.

[0067] S6: Construct the optimization problem of the distributed Lyapunov model predictive control method, solve the optimization problem of the distributed Lyapunov model predictive control method, obtain the optimal control input of each UAV, and drive the UAV formation to reach the target area in a dynamic virtual pipeline under the condition of satisfying collision avoidance and obstacle avoidance constraints according to the optimal control input of each UAV.

[0068] To ensure that drone swarms can safely and quickly reach their target areas, for drones The optimization problem is: st in, for Time of the first Control input for the drone To find the minimum value of the function.

[0069] This invention integrates cost function, dynamic constraints, and Lyapunov stability constraint analysis to construct a DLMPC formation controller that combines disturbance rejection capability with optimal performance. Under the premise of satisfying multiple physical constraints, this controller achieves accurate tracking of the desired formation configuration through online optimization and enhances the system's robustness to uncertain environments by utilizing a disturbance observer. Theoretically, it guarantees the uniform final boundedness of the closed-loop system and the optimality of control performance, thus providing a reliable guarantee for the safe and efficient arrival of UAV formations at the target area.

[0070] like Figure 11As shown, a CFO-based UAV formation anti-interference control system is used to execute the aforementioned CFO-based UAV formation anti-interference control method, comprising: The UAV model building module 101 constructs a UAV model containing lumped perturbations; The disturbance construction module 102 designs a compensation function observer for each UAV based on the UAV model, and performs online estimation of the lumped disturbances experienced by the UAV through the compensation function observer to obtain the disturbance estimate value of the compensation function observer; The auxiliary control law construction module 103 constructs an auxiliary controller based on the disturbance estimate of the compensation function observer using the backstepping method, thereby obtaining an auxiliary control law with disturbance compensation; The dynamic virtual pipeline construction module 104 generates dynamic virtual pipelines for UAV formations based on collaborative guidance points of internal geometric relationships. Predictive control method construction module 105 constructs a distributed Lyapunov model predictive control method that integrates auxiliary control law with disturbance compensation and dynamic virtual pipeline space constraints; The optimization solution module 106 constructs the optimization problem of the distributed Lyapunov model predictive control method, solves the optimization problem of the distributed Lyapunov model predictive control method, obtains the optimal control input of each UAV, and drives the UAV formation to reach the target area in a dynamic virtual pipeline under the condition of satisfying collision avoidance and obstacle avoidance constraints.

[0071] Through the collaborative work of the aforementioned modules, a dynamic virtual pipeline is constructed to provide a flexible and safe corridor for the formation topology, free from major obstacle collisions. This transforms complex obstacle avoidance constraints into pipeline boundary constraints that the formation must adhere to, simplifying the obstacle avoidance problem. Building upon this foundation, to enhance the formation's robustness under complex disturbances, a distributed Lyapunov model predictive control method is introduced. This method not only achieves locally optimal control of each UAV's state through rolling optimization but also ensures the stability of the closed-loop system by embedding Lyapunov constraints. Simultaneously, the controller design explicitly considers collision avoidance between UAVs and obstacle avoidance constraints between UAVs and static or dynamic obstacles, ensuring flight safety.

[0072] To improve estimation accuracy and control robustness under strong disturbances, a compensation function observer is used to estimate and compensate for lumped disturbances in real time. By feeding the disturbance value estimated by the CFO forward to the auxiliary controller of the DLMPC, the impact of external wind disturbances and system uncertainties on formation control performance is effectively suppressed, enhancing the robustness and adaptability of the entire system in complex low-altitude environments.

[0073] This invention solves the problem of achieving cooperative formation flying, collision avoidance between UAVs, and collision avoidance between UAVs and aerial obstacles through local information interaction, thereby improving the system's robustness to unknown environmental disturbances and model uncertainties. The proposed controller integrates the spatial constraint mechanism of a dynamic virtual pipeline, the disturbance estimation and compensation capability of a compensation function observer, and a model predictive control framework with Lyapunov stability guarantees, thus achieving safe, reliable, and disturbance-resistant formation flying in complex low-altitude environments.

[0074] The core idea of ​​DLMPC lies in the organic integration of the predictive optimization capability, the stability guarantee of Lyapunov theory, and the compensation mechanism of disturbance observation: First, model predictive control is responsible for solving the optimal control sequence to improve the efficiency of formation missions under the premise of satisfying system dynamics, physical constraints, and performance indicators; second, the auxiliary control law based on the disturbance observer estimates and counteracts the disturbance effect in real time, providing the system with a "baseline trajectory" and "stability baseline" that can still maintain asymptotic stability in actual disturbance environments; finally, through Lyapunov stability constraints, it is ensured that the entire optimization process will not sacrifice the robust stability of the system in pursuit of performance indicators. This architecture enables UAV formations to fully leverage the advantages of MPC in handling multi-constraint and nonlinear optimization in complex low-altitude environments, while also enhancing the ability to suppress uncertainties with the help of disturbance observers, and theoretically guaranteeing the uniform eventual boundedness of the closed-loop system.

[0075] On the other hand, the present invention also provides a computer program product, the computer program product including a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, and when the program instructions are executed by a computer, the computer is able to execute the above-mentioned CFO-based UAV formation anti-disturbance control method.

[0076] To evaluate the robustness of distributed Lyapunov model predictive control under disturbed environments, this invention designed two sets of simulation scenarios. Both scenarios include external disturbances. The first scenario is obstacle-free to evaluate the algorithm's nominal formation-keeping performance, while the second scenario includes obstacles to test the obstacle avoidance function of this invention. This comparative setting comprehensively examines the effectiveness and reliability of this invention under complex operating conditions, and the effectiveness of this invention is verified through Matlab simulations. The optimized solution of the distributed model predictive control is implemented using the fmincon function in Matlab. Simultaneously, the sampling time of the proposed DLMPC controller is set. The prediction time domain is 0.03 seconds. It is 10.

[0077] During the simulation, the state variables of the UAV are: ,in, The position on the x-axis. The position is on the y-axis. The z-axis position The velocity is in the x-axis direction. The velocity is in the y-axis direction. The velocity is in the z-axis direction. For yaw speed, three drones were considered, with their initial states chosen as [-0.5, 3, 0, 0, 0.3, 0, 0, 0]. T [-0.5, -2, 0, 0, 0.4, 0, 0, 0] T [-0.5, 1, 0, 0, 0.3, 0, 0, 0] T The desired center position of the target area for the UAV formation is [7.4, 0.6, 10]. The perturbation for each UAV during the simulation is as follows: in, For drones The forward speed disturbance, For drones Side flight speed disturbance, For drones The upward velocity disturbance, For drones Yaw speed disturbance, This is the simulation time.

[0078] The dynamic parameters of the UAV dynamics model used are shown in Table 1.

[0079] Table 1 Dynamic parameters

[0080] The parameters for the CFO-based distributed Lyapunov model predictive control are as follows: weight parameters , , Maximum input limit for drones The expected formation vector between drones is , , The parameters selected for the designed CFO are as follows: , , .

[0081] In a low-altitude environment without micro-obstacles, a drone swarm flies towards a designated target area within a dynamic virtual conduit. The 3D flight control effect of the drone swarm is as follows: Figure 2 As shown, the red sphere represents the starting point of the drone, from which... Figure 2As can be seen from the figure, the present invention can form a formation effect faster and allow the entire formation to reach the target area stably, with good anti-interference effect. The gray circular area in the figure represents the target area of ​​the UAV formation. Table 2 shows the comparison results of the formation time and target area arrival time of the present invention and BS (backstep control). As can be seen from Table 2, the formation time and target area arrival time of the controller of the present invention are shorter than those of BS, and it has a better effect. Figure 3 The image shows the changes in the drone formation positions of DLMPC and BS, where... Figure 3 Figure (a) shows the change in the x-axis position of the UAV formation. Figure 3 Figure (b) shows the change in the y-axis position of the UAV formation. Figure 3 Figure (c) in the diagram is a schematic diagram of the z-axis position change of the UAV formation.

[0082] Table 2 Formation time and target area arrival time under different control methods

[0083] Figure 4 This invention demonstrates the error-maintaining mechanism of UAV formations with backstepping control, wherein... Figure 4 Figure (a) in the figure is a schematic diagram of the error maintenance of UAV formation along the x-axis. Figure 4 Figure (b) in the diagram is a schematic diagram of the y-axis UAV formation maintaining error. Figure 4 Figure (c) in the diagram illustrates the z-axis UAV formation maintenance error. Compared to backstepping control, this invention offers faster convergence speed and more stable formation maintenance distance. Figure 5 The observation effects of a CFO-based perturbation observer and an ESO-based perturbation observer on applying the aforementioned perturbations to different channels are demonstrated. Figure 5 Figure (a) in the figure is a schematic diagram of the observed changes in the x-axis perturbation. Figure 5 Figure (b) in the diagram is a schematic diagram of the observed changes in the y-axis perturbation. Figure 5 Figure (c) in the diagram is a schematic diagram of the observed changes in the z-axis perturbation. Figure 5 Figure (d) in the diagram illustrates the observed changes in yaw disturbance. Figure 5 As shown, compared to ESO, the CFO-based disturbance observer can accurately observe time-varying environmental disturbances with smaller observation errors. This improvement is mainly due to its consideration of higher-order derivatives of the disturbance and its ability to predict future behavior. Table 3 further summarizes the quantitative analysis results of the RMSE of the disturbance observer. To compare the impact of different observers on formation control accuracy, Table 4 lists the formation holding errors corresponding to each observer after formation. From Tables 3 and 4, it can be concluded that the CFO-based controller has better formation holding performance.

[0084] Table 3 Root Mean Square Error Analysis of Disturbance Observations

[0085] Table 4 Formation Holding Error Analysis under Different Observers

[0086] To further highlight the advantages of this invention, a comparative analysis is conducted with traditional MPC algorithms that lack disturbance rejection capabilities. The simulated three-dimensional flight control performance of traditional MPC is as follows: Figure 6 As shown. By Figure 6 It can be seen that when there is disturbance in the UAV system, the control effect of traditional MPC is poor, the smoothness of its flight trajectory is insufficient, and it is greatly affected by the disturbance. Figure 7 This demonstrates the drone formation holding error in traditional MPC. Figure 7 Figure (a) shows a schematic diagram of the drone formation maintenance error in traditional MPC along the x-axis. Figure 7 Figure (b) in the figure is a schematic diagram of the drone formation maintaining error in traditional MPC along the y-axis. Figure 7 Figure (c) in the diagram illustrates the drone formation maintenance error in traditional MPC along the z-axis. Figure 7 It can be seen that the formation maintenance error convergence speed of traditional MPC is relatively slow.

[0087] In the second scenario, assuming there are small obstacles in the low-altitude environment, three drones are guided to fly towards the target area in the aforementioned formation while avoiding the obstacles. All parameters involved in formation control are consistent with those in the first scenario. Two obstacles are set with position coordinates [3, 0, 10]. T [6, 2, 10] T .

[0088] Based on the controller of this invention, the formation flight effect of drones in an environment with obstacles is as follows: Figure 8 As shown, from Figure 8 The results show that the drone formation can effectively avoid obstacles and ensure that the drones reach the target area. It also demonstrates that the virtual pipe's boundary constraints can be overcome when obstacles are present in the environment, enhancing the drone formation's obstacle avoidance flexibility. The solid black circles represent two obstacles. Figure 9 The diagram illustrates the position changes of a drone formation in an environment with obstacles, as shown by the controller of this invention. Figure 9 Figure (a) shows the x-axis position change of a drone formation with obstacles in the environment. Figure 9 Figure (b) shows the y-axis position change of a drone formation with obstacles in the environment. Figure 9 Figure (c) shows a schematic diagram of the z-axis position change of a drone formation with obstacles in the environment. Figure 10 This diagram illustrates the formation-keeping error of the controller of the present invention in the presence of obstacles in the environment. Figure 10 Figure (a) shows a schematic diagram of the x-axis retention error of a UAV formation with obstacles in the environment. Figure 10 Figure (b) shows a schematic diagram of the y-axis retention error of a drone formation with obstacles in the environment. Figure 10 Figure (c) shows a schematic diagram of the z-axis retention error of a UAV formation with obstacles in the environment. Figure 10 As can be seen, the formation error of the controller of the present invention fluctuates when there are obstacles, but remains relatively stable overall.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for anti-interference control of UAV formation based on CFO, characterized in that, include: S1: Construct a drone model that includes lumped perturbations; S2: Design a compensation function observer for each UAV based on the UAV model, and use the compensation function observer to estimate the lumped disturbances experienced by the UAV online, thereby obtaining the disturbance estimate value of the compensation function observer; S3: The disturbance estimate based on the compensation function observer is used to construct an auxiliary controller using the backstepping method to obtain an auxiliary control law with disturbance compensation; S4: Generate dynamic virtual pipelines for UAV formations based on collaborative guidance points with internal geometric relationships; S5: Construct a distributed Lyapunov model predictive control method that integrates auxiliary control law with disturbance compensation and dynamic virtual pipeline space constraints; The cost function of the distributed Lyapunov model predictive control method includes the guide point attraction cost, formation maintenance cost, dynamic virtual pipeline constraint cost, collision avoidance cost between UAVs, obstacle avoidance constraint cost, control energy consumption cost, velocity alignment cost, and velocity maximization cost. The attraction cost of the guide point is the deviation between the actual position of the guide point and the center position of the target area. The actual position of the guide point is calculated from the midpoint of the line connecting the positions of the two specified UAVs. The formation maintenance cost is based on the desired formation geometry and calculates the relative position error between each UAV in real time to minimize the formation error. The dynamic virtual pipeline constraint cost dynamically adjusts the boundary constraint weights based on the ratio of obstacle width to pipeline width. The collision avoidance cost between drones is determined by penalizing the deviation between the relative distance between drones and the buffer distance. The obstacle avoidance constraint cost is based on the safe distance between the UAV and the obstacle. It uses a soft obstacle avoidance penalty term constructed with a logarithmic function of the distance between the UAV and the obstacle as the independent variable, as well as obstacle avoidance weights, to respond in a timely manner to local dynamic threats that cannot be covered by pipeline constraints. The control energy consumption cost is used to minimize the energy consumption required for the UAV to execute control commands; The velocity alignment cost ensures that the velocity direction of each drone is aligned with the tangent direction of the virtual pipeline centerline; The speed maximization cost is used to maximize the flight speed of the drone; S6: Construct the optimization problem of the distributed Lyapunov model predictive control method, solve the optimization problem of the distributed Lyapunov model predictive control method, obtain the optimal control input of each UAV, and drive the UAV formation to reach the target area in a dynamic virtual pipeline under the condition of satisfying collision avoidance and obstacle avoidance constraints according to the optimal control input of each UAV.

2. The method for anti-interference control of UAV formation based on CFO according to claim 1, characterized in that, The constraints of the distributed Lyapunov model predictive control method include flight dynamics equality constraints, initial condition constraints, physical input constraints, and Lyapunov stability constraints.

3. The method for anti-interference control of UAV formation based on CFO according to claim 2, characterized in that, The flight dynamics equality constraint is to embed the UAV dynamics model into the optimization framework in the form of equality constraints to ensure that the control sequence satisfies the dynamic evolution relationship of the system. The initial condition constraint is to force the first step state in the optimization time domain to be equal to the actual flight state measured by the sensor at the current moment; The physical input constraint is that the control quantity is limited to the amplitude range allowed by the UAV actuator; The Lyapunov stability constraint requires that the derivative of the Lyapunov function corresponding to the control sequence obtained through optimization should not exceed the reference decay value calculated by the auxiliary control law.

4. The method for anti-interference control of UAV formation based on CFO according to claim 1, characterized in that, The compensation function observer is designed for the total transformation disturbance of the UAV, and satisfies the assumptions of high-order differentiability and boundedness. It achieves high-precision disturbance estimation through feedback of state error and disturbance error. The total transformation disturbance is determined based on the lumped disturbance of the UAV and the rotation matrix from the UAV coordinate system to the world coordinate system.

5. The method for anti-interference control of UAV formation based on CFO according to claim 1, characterized in that, Step S3 includes: S31: Defines the positional error between the current position of the UAV and the desired target position; S32: Construct the first Lyapunov function based on the position error between the current position of the UAV and the desired target position; S33: Design a virtual control quantity such that the derivative of the first Lyapunov function is negative definite; S34: Define the speed error based on the virtual control quantity, and construct the second Lyapunov function based on the speed error; S35: Based on the derivative of the second Lyapunov function and the Lyapunov stability theorem, the auxiliary controller is derived. The disturbance value estimated by the compensation function observer is substituted into the auxiliary controller to obtain the auxiliary control law with disturbance compensation.

6. The method for anti-interference control of UAV formation based on CFO according to claim 1, characterized in that, In step S4, the actual position of the guide point is calculated from the midpoint of the line connecting the positions of the two designated drones. The position and speed information of the two drones are shared by all drones and used to coordinate the movement of the entire drone formation toward the target area, thus constraining the drone formation within a dynamically generated virtual pipe space.

7. The method for anti-interference control of UAV formation based on CFO according to claim 1, characterized in that, In a drone swarm, each drone is equipped with the same controller structure. Each drone relies on the state information of its local neighbors to make control decisions and achieves collaborative formation by sharing the state of the formation guidance point.

8. A CFO-based unmanned aerial vehicle (UAV) formation anti-interference control system, characterized in that, To implement a CFO-based unmanned aerial vehicle (UAV) formation anti-interference control method as described in any one of claims 1 to 7, comprising: A drone model building module, which builds a drone model containing lumped perturbations; The disturbance construction module designs a compensation function observer for each UAV based on the UAV model, and performs online estimation of the lumped disturbances experienced by the UAV through the compensation function observer to obtain the disturbance estimate value of the compensation function observer; An auxiliary control law construction module is used to construct an auxiliary controller based on the disturbance estimate of the compensation function observer using the backstepping method, thereby obtaining an auxiliary control law with disturbance compensation. A dynamic virtual pipeline construction module generates dynamic virtual pipelines for UAV formations based on collaborative guidance points of internal geometric relationships. A predictive control method construction module is provided, which constructs a distributed Lyapunov model predictive control method that integrates an auxiliary control law with disturbance compensation and dynamic virtual pipeline space constraints. An optimization solution module is used to construct an optimization problem of the distributed Lyapunov model predictive control method, solve the optimization problem of the distributed Lyapunov model predictive control method, obtain the optimal control input of each UAV, and drive the UAV formation to reach the target area within a dynamic virtual pipeline under the condition of satisfying collision avoidance and obstacle avoidance constraints.

9. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements a CFO-based unmanned aerial vehicle (UAV) formation anti-disturbance control method as described in any one of claims 1 to 7.

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