Unmanned aerial vehicle cluster preset performance fault-tolerant formation control method based on constraint grading

Abstract

The invention provides an unmanned aerial vehicle cluster preset performance fault-tolerant formation control method based on constraint grading, and relates to the technical field of unmanned aerial vehicle cooperative control. The method comprises the following steps: constructing a kinetic model of a disturbed unmanned aerial vehicle in an unmanned aerial vehicle cluster; according to the relative distance between the position of the disturbed unmanned aerial vehicle and the adjacent unmanned aerial vehicle and the expected safety distance, determining the tracking error of the adjacent unmanned aerial vehicle; according to an error conversion function designed according to a preset performance function, the adjacent machine tracking error is converted into an unconstrained variable; and according to the lumped uncertainty error set obtained by the preset time observer, the unconstrained variable and the dynamical model, determining a tracking control scheme enabling the unmanned aerial vehicle cluster to maintain an expected formation.

Description

Technical Field

[0001] This disclosure relates to the field of unmanned aerial vehicle (UAV) cooperative control technology, and more specifically, to a constrained hierarchical UAV swarm preset performance fault-tolerant formation control method. Background Technology

[0002] With the widespread application of drone swarms in areas such as regional monitoring, collaborative transportation, and emergency rescue, formation control technology has become a core research issue in the field of multi-agent collaboration. Compared with single drones, drone swarms, through distributed collaboration, can significantly improve the robustness, scalability, and overall efficiency of mission execution, enabling multiple small drones to cooperate in completing tasks that are complex or inefficient for a single high-performance drone. The foundation for effective collaboration lies in formation control, which requires each drone to maintain a specific spatial geometric configuration based on local interactive information.

[0003] To ensure the safety and reliability of formation flight, a series of stringent safety constraints must be met. The primary constraint is the inter-drone safety distance: drones must maintain a minimum safety distance to avoid collisions, while simultaneously maintaining communication links and collaborative sensing, they must not exceed the maximum connectivity distance. Furthermore, in actual missions, drones may encounter actuator (such as servos or motors) or sensor malfunctions, leading to a decrease in their maneuverability. This makes achieving formation tracking while meeting precise distance constraints particularly difficult. Moreover, when drones experience a decrease in maneuverability due to actuator malfunctions or external disturbances, strict speed constraints may conflict with collision avoidance and connectivity safety distance constraints. Therefore, it is urgent to address the rigid constraint handling and conflict-prone nature of existing drone formation control systems. Summary of the Invention

[0004] In view of this, this disclosure provides a constrained hierarchical method for pre-defined performance-tolerant formation control of UAV swarms.

[0005] One aspect of this disclosure provides a constrained hierarchical UAV swarm preset performance fault-tolerant formation control method, comprising: constructing a dynamic model of a disturbed UAV in the UAV swarm; determining the neighbor tracking error based on the relative distance between the position of the disturbed UAV and its neighboring UAVs and the desired safe distance; converting the neighbor tracking error into an unconstrained variable using an error transformation function designed according to a preset performance function; and determining a tracking control scheme that enables the UAV swarm to maintain a desired formation based on the lumped uncertainty error set obtained from a preset time observer, the unconstrained variable, and the dynamic model; wherein the neighbor tracking error is within a preset safety boundary; and the maximum speed of each UAV in the UAV swarm is determined by a speed upper limit function constructed from the unconstrained variable.

[0006] According to embodiments of this disclosure, the fault type of the aforementioned disturbed UAV is a multiplicative fault. In this case, the dynamic model of the disturbed UAV is expressed as follows:

[0007] ;

[0008] ;

[0009] in, It is the position of the i-th drone; It is the heading vector of the i-th UAV; It is the speed of the i-th drone; It is the linear velocity of the i-th drone; It is the linear velocity error of the i-th drone; It is the angular velocity of the i-th drone; It is the angular velocity error of the i-th UAV; ω is the angular velocity of the i-th UAV; [·] is the matrix operator; It is a multiplicative actuator malfunction; It is an additive actuator malfunction. It is an unknown time-varying external disturbance; It is the lower limit of multiplicative actuator failure; This is the upper limit of multiplicative actuator failure.

[0010] According to embodiments of this disclosure, the above-mentioned error conversion function is expressed as:

[0011] ;

[0012] ;

[0013]

[0014] ;

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] in, These are unconstrained variables; Let be the time-varying coefficient that represents the upper bound of the modulation error between UAVs i and j; This is the modulation error; The squared distance error between drones i and j; Let be the lower bound time-varying coefficient of the modulation error between UAVs i and j; An exponential performance function for controlling the evolution of error; The value of the exponential performance function at the initial moment; The value of the exponential performance function at the steady-state moment; This refers to the tracking error of the adjacent aircraft. Let i be the distance between drones i and j; Let i be the expected distance between drones i and j; Let i be the relative position vector between drones i and j; The location of drone i; Let j be the position of the drone. This represents the minimum squared distance error between drones i and j. This is the lower bound of the squared distance error between UAVs i and j; This represents the upper limit of the squared distance error between drones i and j; This represents the maximum value of the squared distance error between drones i and j.

[0020] According to embodiments of this disclosure, the above-mentioned speed upper limit function is expressed as:

[0021] ;

[0022] ;

[0023] in, This represents the upper limit of the effective speed of drone i; For the introduction of dynamic relaxation terms; This is the preset speed limit for drone i; Let be the time derivative of the adaptive relaxation term for the velocity constraint of UAV i; The decay coefficient of the adaptive update law; For the adaptive relaxation term of the velocity constraint of UAV i; The trigger threshold for the adaptive update law; These are unconstrained variables.

[0024] According to embodiments of this disclosure, the speed of each drone in the aforementioned drone swarm is expressed as follows:

[0025] ;

[0026] in, The speed of drone i; This represents the upper limit of the effective speed of drone i; It is a sufficiently small constant.

[0027] According to embodiments of this disclosure, the distributed controller for each drone in the aforementioned drone swarm is represented as follows:

[0028] ;

[0029] ;

[0030] in, It is the linear velocity of the i-th drone; The speed of drone i; It is the angular velocity of the i-th drone; This is the soft-constraint gain; Let be the control gain between the i-th and j-th UAVs; These are auxiliary parameters for unconstrained error dynamics; These are unconstrained variables; Let be the relative position vector between the i-th and j-th UAVs; This is an estimate of the lumped uncertainty of linear motion; This is an estimate of the multiplicative fault of angular velocity; Let be the adjacency set of the i-th UAV; It is the heading vector of the i-th UAV; This represents the upper limit of the effective speed of drone i; It is a sufficiently small constant.

[0031] Another aspect of this disclosure provides a constrained hierarchical UAV swarm preset performance fault-tolerant formation control device, comprising: a model building module for building a dynamic model of a disturbed UAV in the UAV swarm; an error determination module for determining the neighbor tracking error based on the relative distance between the position of the disturbed UAV and its neighboring UAVs and a desired safe distance; a variable transformation module for converting the neighbor tracking error into an unconstrained variable based on an error transformation function designed according to a preset performance function; and a scheme determination module for determining a tracking control scheme that maintains the desired formation of the UAV swarm based on the lumped uncertainty error set obtained from a preset time observer, the unconstrained variable, and the dynamic model; wherein the neighbor tracking error is within a preset safety boundary; and the maximum speed of each UAV in the UAV swarm is determined by a speed upper limit function constructed from the unconstrained variable.

[0032] Another aspect of this disclosure provides an electronic device comprising: one or more processors; and a memory for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to perform the methods described above.

[0033] Another aspect of this disclosure provides a computer-readable storage medium storing computer-executable instructions, which, when executed, are used to implement the methods described above.

[0034] Another aspect of this disclosure provides a computer program product including computer-executable instructions that, when executed, implement the methods described above.

[0035] According to embodiments of this disclosure, by constructing a dynamic model of the disturbed UAVs and introducing neighboring UAV tracking errors, the formation deviation characteristics of the UAV swarm under disturbed environments are accurately characterized, ensuring that the neighboring UAV tracking errors are always within a preset safety boundary. Based on error transformation using a preset performance function, the constrained tracking control problem is transformed into an unconstrained variable optimization problem, effectively reducing the solution complexity of the control algorithm. Combined with lumped uncertainty error compensation using a preset time observer, the robustness of the control system to external disturbances and internal uncertainties is improved, ensuring that the UAV swarm can maintain a stable desired formation even in complex environments. By constructing a velocity upper limit function using unconstrained variables, the maximum flight speed of each UAV is reasonably limited, avoiding the risk of swarm collisions caused by speed exceeding limits, further enhancing the safety and reliability of UAV swarm cooperative control. Attached Figure Description

[0036] The above and other objects, features and advantages of this disclosure will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0037] Figure 1 A flowchart illustrating a constrained hierarchical unmanned aerial vehicle (UAV) swarm preset performance fault-tolerant formation control method according to an embodiment of the present disclosure is shown in the schematic diagram.

[0038] Figure 2 This illustration schematically depicts a secure formation control framework with constraint conflict resolution according to an embodiment of the present disclosure.

[0039] Figure 3 The diagram illustrates the formation configuration of eight drones in different simulation test scenarios according to embodiments of the present disclosure: Figure (a) shows the formation configuration of eight drones in scenario a; Figure (b) shows the formation configuration of eight drones in scenario b.

[0040] Figure 4 The diagram illustrates the trajectories of a formation of eight drones at different times and the position tracking error of the following drones according to an embodiment of the present disclosure: Figure (a) shows the trajectory of the formation of eight drones at different times; Figure (b) shows the position tracking error of the following drones.

[0041] Figure 5 The following diagrams illustrate lumped uncertainty estimation errors according to embodiments of the present disclosure: Figure (a) shows a schematic diagram of linear lumped uncertainty estimation errors; Figure (b) shows a schematic diagram of angular lumped uncertainty estimation errors.

[0042] Figure 6 The following schematic diagrams illustrate the squared distance error and preset performance constraints of a follower drone according to embodiments of the present disclosure: Figure (a) shows the squared distance error and preset performance constraints of drone 4; Figure (b) shows the squared distance error and preset performance constraints of drone 5; Figure (c) shows the squared distance error and preset performance constraints of drone 6; Figure (d) shows the squared distance error and preset performance constraints of drone 7; Figure (e) shows the squared distance error and preset performance constraints of drone 8.

[0043] Figure 7 A schematic diagram illustrating the speed of a follower drone according to an embodiment of the present disclosure is shown.

[0044] Figure 8 The diagram illustrates the formation trajectories of UAVs under soft velocity constraints and hard velocity constraints, and their positions at different times, according to embodiments of the present disclosure: Figure (a) shows the formation trajectory of UAVs under soft velocity constraints and their positions at different times; Figure (b) shows the formation trajectory of UAVs under hard velocity constraints and their positions at different times.

[0045] Figure 9 The diagram illustrates the velocity curves of a follower drone under soft and hard velocity constraints according to embodiments of the present disclosure.

[0046] Figure 10 The schematic diagram illustrates the position tracking errors of a follower drone under soft velocity constraints and hard velocity constraints according to embodiments of the present disclosure;

[0047] Figure 11 The diagram illustrates the squared distance error of a follower drone under soft velocity constraints and hard velocity constraints according to embodiments of the present disclosure: wherein, Figure (a) shows the squared distance error of the follower drone under soft velocity constraints; and Figure (b) shows the squared distance error of the follower drone under hard velocity constraints.

[0048] Figure 12 A block diagram of a constrained hierarchical unmanned aerial vehicle (UAV) swarm preset performance fault-tolerant formation control device according to an embodiment of the present disclosure is shown schematically.

[0049] Figure 13A block diagram of an electronic device suitable for implementing a constraint-based hierarchical unmanned aerial vehicle (UAV) swarm preset performance fault-tolerant formation control method is illustrated according to an embodiment of the present disclosure. Detailed Implementation

[0050] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0051] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0052] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0053] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0054] In the embodiments disclosed herein, the collection, updating, analysis, processing, use, transmission, provision, disclosure, and storage of data (e.g., including but not limited to user personal information) comply with relevant laws and regulations, are used for legitimate purposes, and do not violate public order and good morals. In particular, necessary measures have been taken to prevent unauthorized access to user personal information data and to safeguard user personal information security, network security, and national security.

[0055] In the embodiments disclosed herein, user authorization or consent is obtained before acquiring or collecting user personal information.

[0056] To ensure the safety and reliability of formation flying, a series of stringent safety constraints must be met. Existing research mainly focuses on two directions. On the one hand, for the distance constraint problem, various control strategies have been proposed, such as combining artificial potential fields and spatial partitioning to construct a repulsive field to prevent collisions; using model predictive control (MPC) for online rolling optimization combined with collision-free constraint functions; and using data-driven methods such as deep reinforcement learning (DRL) to directly generate control strategies that meet the constraints. On the other hand, to improve the system's survivability under faults, fault-tolerant control has been introduced into the formation framework. Existing methods achieve safe inter-aircraft distances even under actuator gain faults and bias faults by incorporating the gradient of the repulsive potential function into a fixed-time sliding mode controller, or by combining a barrier function with an adaptive compensation mechanism.

[0057] When a UAV's maneuverability decreases due to actuator failure or external disturbances, strict speed constraints may conflict with safety distance constraints such as collision avoidance and connectivity. Traditional methods often sacrifice maneuverability due to excessive conservatism or introduce safety risks due to constraint conflicts. To address this, this disclosure proposes a constraint conflict resolution framework: defining safety distance requirements as hard constraints that must be absolutely satisfied, and employing a pre-set performance control law to strictly ensure their non-violation; defining the maximum speed limit as a dynamically adjustable soft constraint, and designing an adaptive update mechanism that allows temporary and controlled relaxation of the speed limit when a conflict between hard and soft constraints is detected. This method achieves an effective balance between formation safety and maneuverability under fault and disturbance environments by intelligently adjusting performance boundaries while ensuring safety.

[0058] This disclosure presents a novel safety formation control framework based on constraint conflict resolution. Its core innovation lies in the hierarchical and dynamic coordination of constraints: First, safety-critical distance constraints (collision avoidance, connectivity maintenance) are defined as hard constraints that must be strictly adhered to, while maximum speed constraints are defined as soft constraints that can be temporarily adjusted. Second, a robust preset performance controller is designed to strictly ensure that hard constraints are always satisfied. Finally, an adaptive relaxation mechanism is introduced to intelligently and appropriately relax the speed limit when a potential conflict is detected, restoring it after the risk is eliminated. This framework significantly improves the system's flexibility and feasibility under faults and disturbances while ensuring absolute safety.

[0059] The advantages and features of this disclosure are mainly reflected in the following aspects:

[0060] First, a safety formation conflict coordination framework based on constraint priority is constructed. Compared with existing methods that treat both safety distance and speed limits as inviolable hard constraints, this disclosure innovatively establishes a constraint hierarchy strategy, defining collision avoidance and connectivity maintenance as hard constraints that must be absolutely satisfied, and defining maximum speed as a smartly adjustable soft constraint. This framework provides, for the first time, a built-in priority resolution mechanism for constraint conflicts, fundamentally ensuring the feasibility of controlling the problem under faults or disturbances, and overcoming the limitation of traditional methods that easily fall into unsolvable deadlocks when constraint conflicts occur.

[0061] Second, a pre-defined performance-soft constraint coordination mechanism integrating hard constraint guarantees and adaptive relaxation is designed. Compared with existing fault-tolerant control methods that can only guarantee that the error is eventually bounded but cannot precisely constrain its transient behavior, the pre-defined performance control law introduced in this disclosure can ensure that the tracking error related to hard constraints is strictly limited within the preset safety boundary; at the same time, the matching adaptive soft constraint update law can dynamically adjust the speed limit according to real-time risk. This coordination mechanism realizes the full-process customizability of safety performance and the dynamic maximization of system maneuverability, solving the problems of existing methods being either too conservative or lacking safety controllability.

[0062] Third, an integrated controller architecture combining error transformation, state observation, and distributed control is proposed. Unlike existing methods that often handle uncertainty estimation, performance constraints, and control law design in isolation, this disclosure systematically integrates a time-determined uncertainty observer, a hierarchical pre-defined performance error transformation, and a distributed fault-tolerant control law based on azimuth projection. This architecture ensures that, even with only local azimuth information, it can simultaneously and accurately compensate for multiple uncertainties, strictly constrain error trajectories, and generate feasible control commands, achieving a balance between theoretical rigor and engineering feasibility.

[0063] Through the aforementioned technical means, this disclosure achieves the following technical effects: First, the proposed constraint conflict resolution framework enables the system to maintain safety and feasibility through intelligent coordination when encountering actuator failures or sudden disturbances, significantly enhancing its survivability in complex environments; Second, the combination of predetermined performance control and adaptive relaxation mechanism achieves, for the first time, precise planning of transient and steady-state error behavior and dynamic optimization of speed constraints in fault-tolerant formation control, greatly improving the reliability and efficiency of task execution; Third, the integrated controller design takes into account the implementation requirements of distributed and low communication dependency, with clear parameter conditions and low computational complexity, providing a reliable technical solution for the engineering application of large-scale UAV swarms.

[0064] This disclosure constructs a hierarchical framework of hard constraints (collision avoidance, communication maintenance) and soft constraints (speed limits), ensures strict satisfaction of hard constraints through robust preset performance control laws, and designs an adaptive mechanism to dynamically relax speed constraints in the event of conflict. Under actuator failure and external disturbances, it can ensure that formation tracking errors always conform to preset transient and steady-state performance boundaries, achieving safe and reliable cooperative flight control.

[0065] Based on this Figure 1 A flowchart illustrating a constrained hierarchical unmanned aerial vehicle (UAV) swarm preset performance fault-tolerant formation control method according to an embodiment of the present disclosure is shown.

[0066] like Figure 1 As shown, the method includes operations S101 to S104.

[0067] Using S101, a dynamic model of the disturbed drones in the drone swarm is constructed.

[0068] In operation S102, the tracking error of the neighboring drone is determined based on the position of the disturbed drone, the relative distance between it and the neighboring drone, and the expected safe distance.

[0069] In operation S103, the neighbor tracking error is converted into an unconstrained variable by an error transformation function designed according to the preset performance function.

[0070] In operation S104, based on the lumped uncertainty error set obtained from the preset time observer, unconstrained variables, and dynamic model, a tracking control scheme is determined to maintain the desired formation of the UAV swarm; wherein, the tracking error of neighboring UAVs is within a preset safety boundary; the maximum speed of each UAV in the UAV swarm is determined by a speed upper limit function constructed from unconstrained variables.

[0071] Taking fixed-wing UAVs as an example, a mathematical model of a fixed-wing UAV swarm is established to lay the foundation for subsequent observer and control law design. Specifically, a UAV swarm consisting of n fixed-wing UAVs is considered, with each UAV treated as a rigid body, its motion described by both the ground inertial coordinate system and the body coordinate system. This embodiment establishes a dynamic model encompassing nonholonomic constraints and comprehensively considers multiple uncertainties present in actual flight, including thrust saturation, multiplicative efficiency losses and additive bias faults of actuators, system parameter perturbations, and external environmental disturbances. For ease of analysis and compensation, all the above uncertainties are uniformly modeled as a comprehensive "cluster uncertainty." The model constructed from all the above uncertainties accurately characterizes the dynamic behavior of the UAV swarm system under faults and disturbances, and is the core theoretical basis for the subsequent design of a time-defined observer, hierarchical error transformation, and fault-tolerant control law.

[0072] The following section provides a detailed explanation of the overall architecture and mathematical model of this embodiment, using a fixed-wing UAV swarm system as an example. This section provides the foundation for performing all the above steps.

[0073] Consider a group of n fixed-wing drones, where the index i denotes the i-th drone. Assume the drones... Leaders, drones It is a follower, the leader drone index is Follower drone index is The dynamic model of each UAV is described in two reference frames: (1) Earth-fixed coordinate system (2) Body coordinate system . The origin is located at the center of mass of the drone. The axis is aligned with the drone's heading. Two reference frames are used to decouple the motion description: the global coordinate system represents the absolute position of each drone, and the body coordinate system represents the attitude and forces acting on each drone. The rotation matrix R... i Description from arrive The relative direction.

[0074] In order to describe from arrive Perform the following rotation operation in the relative directions: Around Axis rotation angle Then Around Axis rotation angle Therefore, the resulting rotation matrix can be expressed as:

[0075] ;

[0076] Assuming the thrust is along the velocity vector direction and the UAV always performs coordinated maneuvers, the dynamics of UAV i can be expressed as:

[0077] ;

[0078] in, Is the i-th drone in Position within. Heading vector. yes The first column. It is a linear velocity that takes into account faults and uncertainties. It is the angular velocity that takes into account faults and uncertainties, where and They are along and The angular velocity of the axis. In this embodiment, only the failure or interference of the follower is considered.

[0079] In real-world drone swarm flight scenarios, drones are susceptible to various actuator failures and external uncertainties during formation maneuvers. The input to a faulty actuator can be modeled as: ;in, It is the nominal linear velocity input. It's a multiplicative actuator malfunction. The multiplicative actuator fault corresponds to the linear velocity of the i-th UAV. Let be the lower limit coefficient for the failure of the multi-tasking actuator of the i-th UAV; This is the upper limit coefficient for the failure of the multi-tasking actuator of the i-th UAV; It is an additive actuator malfunction. It is an unknown time-varying external disturbance.

[0080] This embodiment considers the following two typical fault types:

[0081] when and At this time, the actuator may experience partial efficiency loss due to faults such as control surface jamming, actuator degradation, or insufficient power supply voltage.

[0082] when and When the actuator is subjected to a bias fault, such as potentiometer drift, mechanical misalignment, or constant control signal bias, the actuator may be affected.

[0083] For angular velocity dynamics, considering that bias faults in angular velocity sensors can usually be eliminated through calibration or filtering techniques, multiplicative faults caused by sensor scaling errors, gain variations, or actuator efficiency degradation, where the actuator experiences partial efficiency loss, have a more direct and lasting impact on system stability and control performance. Therefore, this embodiment considers multiplicative faults as... ,in, It is the nominal angular velocity input. It is a multiplicative fault, indicating the impact on the angular motion of the UAV.

[0084] make The dynamics of the faulty drone are derived as follows:

[0085] ;

[0086] Let the desired position vector of the stack be The desired formation configuration can be represented as ,in, , This is the desired communication topology diagram for the drone swarm; Desired communication topology diagram The vertex set (each vertex corresponds to 1 drone). Desired communication topology diagram The edge set (each edge corresponds to a communication connection between 2 drones); m is the expected total number of communication connections in the drone swarm; n is the total number of drones in the swarm; the relative positions of agents i and j are defined as: .in, Is it the j-th drone in The position in the middle.

[0087] Let the distance between drones i and j be... ,side The distance error is This shows ,in, This represents the edge set of the wireless communication topology graph. Represents the connection between vertices v in an undirected communication topology graph. i and v j An undirected edge.

[0088] Figure 2 The illustration shows a schematic diagram of a secure formation control framework with constraint conflict resolution according to an embodiment of the present disclosure.

[0089] like Figure 2 As shown, the framework proposed in this disclosure systematically solves the formation control problem through three parts: First, a robust preset performance control law enforces hard position constraints (collision avoidance and connectivity maintenance) by ensuring that the distance tracking error evolves strictly within user-defined boundaries; second, an adaptive soft constraint update law establishes a priority-based relationship between hard and soft constraints, allowing for appropriate relaxation of velocity constraints while maintaining system safety; third, a distributed safe formation controller achieves the formation control objective while compensating for faults and disturbances through preset time uncertainty observations. These components together constitute a constraint conflict resolution framework, achieving an effective trade-off between tracking performance and safety requirements.

[0090] The three parts of the framework proposed in the embodiments of this disclosure will be described below.

[0091] To ensure a safe distance between UAVs, a pre-defined performance control method is adopted, based on a robust pre-defined performance control law. This is achieved by designing a time-varying performance boundary function. constrained distance tracking error Mapping to unconstrained variables The controller stabilizes This ensures the actual error. Always compressed within the preset safety boundary This ensures that collision avoidance and communication connectivity are not violated.

[0092] To ensure that drones never collide and always remain within communication range, a method called preset performance control is employed. This is a hard constraint guarantee mechanism based on pre-defined performance. The core of this method is to pre-set a dynamically shrinking safe allowable range for distance tracking errors over time. Specifically, through a mathematical transformation, the error signal, originally limited by this strict range, is converted into a new, unrestricted variable. The controller's task is to stabilize this new variable. As long as this new variable remains stable, it ensures that the actual distance error always remains within the preset safe corridor, thus fundamentally eliminating the risk of collisions and communication interruptions.

[0093] Continuing with the example of a drone swarm consisting of n fixed-wing drones, the hard constraints are preset performance error transformations used for collision avoidance and connectivity maintenance. To ensure strict collision avoidance and connectivity maintenance between adjacent drones, a preset performance control framework is employed. This method transforms the inherently constrained formation control problem into an unconstrained stabilization task through error transformation, ensuring that the distance error between agents remains within a predefined performance bound.

[0094] The squared distance error between agents i and j is defined as: .

[0095] Define an exponential performance function that controls the evolution of error: .in, and If satisfied Then the security and connectivity constraints are satisfied, where and Time-varying boundaries were defined.

[0096] The modulation error introduced is: A smooth, strictly increasing transformation function Mapping the constrained modulation error to an unconstrained variable: .

[0097] For unconstrained variables Differentiation yields the unconstrained error dynamics: .in, .

[0098] The compact form of error dynamics is expressed as: ;in, and .

[0099] The dynamics of the squared distance error are derived from the rigidity formula: The compact form is: .in, and , This transformation constitutes a hard constraint component, ensuring that violations of performance bounds (and thus collision avoidance or connectivity) are equivalent to... It becomes unbounded, which will be prevented through controller stability analysis.

[0100] in, Let be the time-varying coefficient that represents the upper bound of the modulation error between UAVs i and j; This is the modulation error; The squared distance error between drones i and j; Let be the lower bound time-varying coefficient of the modulation error between UAVs i and j; An exponential performance function for controlling the evolution of error; The value of the exponential performance function at the initial moment; The value of the exponential performance function at the steady-state moment; This refers to the tracking error of the adjacent aircraft. Let i be the distance between drones i and j; Let i be the expected distance between drones i and j; This represents the minimum squared distance error between drones i and j. This is the lower bound of the squared distance error between UAVs i and j; This represents the upper limit of the squared distance error between drones i and j; This represents the maximum value of the squared distance error between drones i and j.

[0101] This embodiment utilizes hard constraints to transform the strict safety distance requirements (collision avoidance and connectivity) between UAVs into a stable problem that can be handled by standard control methods. Overall, this constraint is the cornerstone of the entire safety control framework. Through ingenious mathematical transformation, it provides a way to achieve rigorous, verifiable, and integrable implementation of hard safety constraints.

[0102] For the adaptive soft constraint update law, this embodiment treats the maximum speed as a dynamically adjustable soft constraint and designs a corresponding adaptive relaxation strategy. Specifically:

[0103] The upper limit of linear velocity for each drone is , forming a soft constraint set To avoid conflicts with hard constraints that could render the system infeasible, the speed limit can be temporarily relaxed.

[0104] Adaptive relaxation law design: Introducing dynamic relaxation terms The effective speed limit is defined as Design Adaptive Update Law: .in, The attenuation coefficient is... As the trigger threshold, Transformation error from the hard constraint layer.

[0105] The soft constraint management mechanism, also known as adaptive speed limit adjustment, limits the maximum flight speed of a UAV, i.e., restricts the UAV's linear velocity. This embodiment treats the maximum flight speed limit as a smartly adjustable soft requirement and designs an adaptive regulator that dynamically adjusts the actual value of the speed limit based on the current system safety status. When the system determines that the safe distance is well maintained and there is no risk of conflict, the regulator will ensure that the UAV strictly adheres to the nominal speed limit. Once the system predicts that higher maneuverability may be needed to meet safety requirements such as emergency collision avoidance, the regulator will automatically and temporarily relax the speed limit, reserving additional maneuverability to ensure safety. This achieves flexible management of performance limits while prioritizing safety, ensuring smooth control actions and preventing aggressive maneuvers that may jeopardize system stability.

[0106] The velocity saturation function is defined as: ;in, x represents the maximum speed under soft constraints. i It is the linear velocity control quantity generated during the controller design phase; It is a sufficiently small constant.

[0107] Adaptive mechanism dynamically adjusts saturation threshold: ,in, Controlled by the law of adaptation: ,in, initial conditions .in, This represents the upper limit of the effective speed of drone i; For the introduction of dynamic relaxation terms; This is the preset speed limit for drone i; Let be the time derivative of the adaptive relaxation term for the velocity constraint of UAV i; The decay coefficient for the adaptive update rate; For the adaptive relaxation term of the velocity constraint of UAV i; The trigger threshold for adaptive update rate; These are unconstrained variables. Because... It is always positive, therefore This ensures the forward invariance of the constraint set: .

[0108] The saturation function has an equivalent representation: Among them, state-dependent gain for: .

[0109] Through the aforementioned adaptive speed saturation mechanism, the embodiments of this disclosure extend from rigid speed limits to elastic performance boundaries, ensuring that the UAV can obtain the necessary maneuverability when dealing with sudden safety needs, while maintaining the continuity and smoothness of system control commands, avoiding the sudden changes in control commands or system infeasibility caused by rigid limitations in traditional methods.

[0110] The advantage of this embodiment lies in its adaptability throughout the entire process, meaning that the speed constraint can be dynamically adjusted according to the real-time safety status, achieving an optimal balance between safety and performance throughout the mission; it also features coordinated priority management, clarifying the dominance of safety constraints over performance constraints through an adaptive mechanism, thereby intelligently reconfiguring system resources when conflicts occur; furthermore, the robustness of this embodiment is significantly enhanced, ensuring the feasibility and overall stability of the control system through the synergy of soft and hard constraints even under actuator failures, external disturbances, and complex maneuvering tasks.

[0111] For a distributed secure formation controller, to achieve formation convergence and incorporate fault compensation, the final distributed controller is designed. First, uncertainty estimation integration is performed: a pre-set time lumped uncertainty observer is designed. This observer can perform uncertainty estimation within a user-preset time. Within, it accurately estimates the combined uncertainties caused by actuator failures, disturbances, etc. To obtain the estimated value .

[0112] Distributed fault-tolerant control law design: The control commands for each UAV i are designed as follows: ;in, It is the linear velocity of the i-th drone; The speed of drone i; It is the angular velocity of the i-th drone; This is the soft-constraint gain; Let be the control gain between the i-th and j-th UAVs; These are auxiliary parameters for unconstrained error dynamics; These are unconstrained variables; Let be the relative position vector between the i-th and j-th UAVs; This is an estimate of the lumped uncertainty of linear motion; This is an estimate of the multiplicative fault of angular velocity; Let i be the adjacency set of the i-th UAV (the set of neighboring UAVs within the communication range). It is the heading vector of the i-th UAV.

[0113] The performance feedback term incorporates hard-constraint errors (i.e., unconstrained variables). With soft constraint gain Driven formation tracking. Fault tolerance compensation item. Utilizing observer estimates feedforward to compensate for uncertainties improves robustness. Soft constraint gain. It achieves smooth saturation of control commands and satisfies soft constraints.

[0114] Using this distributed control law, the closed-loop system is proven stable under Assumption 1 (rigid topology) and Assumption 2 (leader reference). Ultimately, as time approaches infinity, the relative configurations of all UAVs converge to the isometric transformation set of the desired formation. In this context, Iso is an abbreviation for Isometry, meaning a transformation that preserves distance. F* refers to the desired communication topology of the formation. The set of isometry transformations includes the desired total number of communication connections m of the UAV swarm, the total number of UAVs n, and the desired stacking position vectors. The vertex set of the desired communication topology graph and the edge set of the desired communication topology graph Meanwhile, the position and velocity tracking errors asymptotically approach zero, fully achieving the three core objectives of satisfying hard constraints, satisfying soft constraints, and formation convergence.

[0115] To achieve integrated fault-tolerant control and formation convergence, the aforementioned safety mechanisms are combined with a fault handling system to form a complete distributed controller. This distributed controller includes an observer capable of rapidly and accurately estimating the combined effects of faults and disturbances within a predetermined timeframe. Control commands are generated collaboratively from three parts: first, based on the processed safety error signal, the UAVs are driven to the correct position; second, the aforementioned adaptive speed adjustment is incorporated to ensure smooth and feasible commands; and third, proactive compensation is performed using fault estimation information provided by the observer to offset its adverse effects on the system. This integrated control law ultimately ensures that the UAV formation can safely and stably converge and maintain the desired formation while coping with various uncertainties.

[0116] After completing system modeling, hard constraint design, and soft constraint design, this embodiment further proposes a safe formation controller that integrates hard constraints, soft constraints, and lumped uncertainty estimation. The distributed controller implementation for each UAV i is as follows: ;in, It comes from Soft velocity constraints, Indicates from The transformation error of enforcing hard constraints, , δ is the estimated ensemble uncertainty value obtained through a pre-defined time observer:

[0117] ; ;

[0118] in, and They are and The estimated value. and It is the estimation error of position and heading. and They are and The estimated value, The positive gain parameter represents the linear velocity observer of the i-th UAV. The positive gain parameter representing the angular velocity observer of the i-th UAV The nominal linear velocity input is the i-th UAV. The positive gain parameter representing the sign function of the UAV linear velocity observer. The positive gain parameter represents the sign function of the integral term of the linear velocity observer for the i-th UAV. The positive gain parameter represents the sign function of the angular velocity observer for the i-th UAV. The positive gain parameter represents the sign function of the integral term of the i-th UAV angular velocity observer.

[0119] and Depend on The following transformation is given: The estimation error is defined as follows: and .

[0120] for These are the parameters of the observer. It is the preset time scaling function, given as: ;in, and These are the start time and the end time, respectively. It is the preset convergence time period. .Notice exist The time decreases monotonically. Defined as: .

[0121] The closed-loop error system mainly includes the following components: position error: Speed ​​error: Composite error: Local projection composite error: .in, This represents the actual velocity vector of the UAV. The derivative of the desired velocity; For design parameters; This is a normalization factor used to balance the impact of differences in the number of neighbors on the control effect; This is the local projection matrix.

[0122] Combining the control law, the actual closed-loop error dynamics can be obtained as follows: Among them, the uncertainty is The accurate estimate has been obtained through the observer within the specified time; For error feedback gain; These are the Jacobian matrices of the error transformation, respectively. The derivative of the desired velocity, For error transformation variables.

[0123] To analyze stability, the Lyapunov function is defined as follows: This function comprehensively considers the changes in velocity error, position error, and combined error, thus fully reflecting the degree of deviation of the system. Differentiating, we have: .

[0124] Combining the control law expression with error dynamics, we can obtain: .

[0125] Further utilize neighbor projection matrix Properties, namely We can obtain: .in: This represents the upper bound of the acceleration of the desired trajectory; This represents the upper bound of the uncertainty; It is the minimum eigenvalue of the neighbor projection matrix.

[0126] If the control gain satisfies the following condition: Then the above disturbance terms can be completely canceled out, and thus we have: .

[0127] According to Lyapunov's stability theorem: 1. All error variables are uniformly bounded; 2. Further combining this with the error transformation relationship, we can obtain the original error... 3. The system remains within the preset performance boundaries throughout the entire process; 4. The system asymptotically stabilizes under specified performance constraints.

[0128] This embodiment organically combines preset performance error transformation (handling hard constraints), adaptive speed saturation (handling soft constraints), and preset time uncertainty observer (handling faults and disturbances) to provide a complete distributed safe formation solution. It not only strictly ensures the physical safety and communication connectivity between UAVs, but also intelligently manages maneuverability and achieves reliable formation and maintenance under various uncertainties.

[0129] This embodiment achieves distributed safe formation control relying only on local orientation information, eliminating the need for global positioning and enhancing the system's applicability in constrained environments. Through time-bound observations and hierarchical error transformation under safety constraints, it ensures that formation errors are controlled throughout the entire process and strictly meets preset safety boundaries, significantly improving the reliability and predictability of the mission. The designed control law has clear parameter conditions and low computational complexity, making it easy to deploy and verify in large-scale UAV swarms, demonstrating good engineering practical value and promising prospects for widespread application.

[0130] The following simulation examples demonstrate the verification and illustration of the constrained hierarchical UAV swarm preset performance fault-tolerant formation control method disclosed in this invention.

[0131] First, a simulation of a pre-defined, safe formation maneuver scenario is performed. In this simulation scenario, a group of 8 drones are considered to form a cube formation, where drones 1-3 are selected as leaders, and drones 4-8 are followers. The communication topology between the drones satisfies the Henneberg-0 extension, such as... Figure 3 As shown in (a), the initial position of the follower drone is set to , , , , The follower's initial heading is set to... The expected speed of the leader drone is given as... The maximum connectivity distance and minimum safe distance are set as follows: and .

[0132] The controller parameters are set to for as well as for . The upper limit of speed in Set as The parameters in the soft constraint update law are set to... and Lumped uncertainty observer and The parameters are respectively , and Preset time scaling function and Set as .

[0133] During formation maneuvers, actuator malfunctions were introduced into UAVs 7 and 8. Detailed fault injection settings are summarized in Table 1.

[0134] Table 1 Summary of Fault Injection Settings

[0135]

[0136] Simulation results are as follows Figures 4 to 7 As shown. Figure 4 (a) The trajectory of the drone was depicted and labeled. The position at that time indicates that all agents are in exist At that time, actuator malfunctions were injected into UAVs 7 and 8. Despite these sudden malfunctions, the proposed controller ensured that the tracking error remained within the preset performance limits, and that both UAVs... During this period, the formation gradually converged back to the desired configuration. Figure 4 (b) illustrates the formation tracking error of the follower drones. As expected, due to the injected fault, the tracking errors of UAV 7 and UAV 8 were... The deviation increases sharply at times, but then converges to zero. Furthermore, because drone 8 has drone 7 as its neighbor, the deviation of drone 8 is more pronounced than that of drone 7. Figure 5 This demonstrates the aggregate uncertainty of followers. and The estimation errors converge to near zero. Figure 6 The squared distance error was shown. And preset performance limits. Although the error is in While transient increases may occur, they remain strictly within predefined bounds, validating the pre-defined performance guarantee. Finally, Figure 7 The speed of the follower drone was displayed. They always satisfy the soft velocity constraint.

[0137] The following is a simulation experiment of a formation tracking scenario with soft velocity constraints. To demonstrate the effectiveness of soft velocity constraints, consider a simple formation consisting of four UAVs translating at a constant speed along the x-axis. Figure 3 As shown in (b), drones 1, 2, and 3 are leaders, and drone 4 is a follower. The initial positions of the drones... , , , The follower's initial heading is set to... The given speed of the drone is .

[0138] The maximum connectivity distance and minimum safe distance are set to and The expected distance between followers and leaders is set to... The default performance constraints are set to... , , as well as Actuator failure in The time is injected into drone 4, with the following parameters: The environmental disturbance is modeled as a second-order Gaussian-Markov process, in which... and The parameters of the controller and observer remain the same as those in the previous simulation.

[0139] In addition to environmental disturbances and In addition, A sudden internal disturbance was introduced to induce the drone to temporarily deviate from its nominal trajectory. This setup allows for the systematic evaluation of convergence behavior under different speed constraints when subjected to sudden environmental disturbances (such as gusts of wind).

[0140] To demonstrate the effectiveness of the proposed soft velocity constraint, consider comparing the following two velocity constraints: 1. Having Soft velocity constraints and 2. Has an upper limit Hard speed constraints.

[0141] Simulation results are as follows Figures 8-11 As shown. Figure 8 The formation trajectory was displayed and marked. The position at that time can be observed to show that, after being subjected to actuator failure and sudden disturbances during the [35,40] seconds, both soft and hard velocity constraint strategies allowed the UAV swarm to effectively recover its formation. Position tracking error Sum of squared distance tracking error Each as Figure 10 and Figure 11 As shown, this indicates that soft velocity constraints are more effective in the post-fault stage compared to hard velocity constraints. It exhibits faster recovery and less overshoot. (Speed ​​curve) like Figure 9 As shown, this indicates that the velocity curve under soft constraints remains smooth and stable throughout the maneuver, while the velocity curve under hard constraints suffers abrupt changes and greater overshoot under actuator failure and sudden disturbances. These results demonstrate that the proposed soft velocity constraints improve robustness against actuator failure and disturbances.

[0142] This disclosure proposes a constraint conflict resolution framework for distributed safe formation control of fixed-wing UAV swarms. This framework systematically resolves the conflict between safety-critical distance and velocity constraints by treating distance requirements as hard constraints and velocity limits as soft constraints. By integrating pre-defined performance controls for hard constraint enforcement and adaptive relaxation for soft constraints, this method achieves effective conflict resolution while maintaining system stability. Simulation studies verify that the proposed framework can successfully handle constraint conflicts under actuator failures, providing a smoother drive response compared to traditional hard constraint methods. Future work will focus on extending the conflict resolution framework to large-scale swarms with dynamic topologies and experimental verification. Through rigorous stability analysis and comparative simulation verification, this disclosure outperforms existing methods in both convergence performance and fault tolerance. Its key advantages are: the use of more realistic UAV dynamics modeling; the guarantee of specified performance tracking throughout the process through hierarchical error transformation; and the effective integration of specified performance control into the orientation-based control framework, achieving stable and efficient formation control even with information loss due to projection calculations.

[0143] Figure 12 A block diagram of a constraint-based hierarchical unmanned aerial vehicle (UAV) swarm preset performance fault-tolerant formation control device according to an embodiment of the present disclosure is shown schematically.

[0144] like Figure 12 As shown, the constrained hierarchical UAV swarm preset performance fault-tolerant formation control device 1200 includes a model building module 1210, an error determination module 1220, a variable transformation module 1230, and a scheme determination module 1240.

[0145] Model building module 1210 is used to build dynamic models of disturbed drones in a drone swarm.

[0146] The error determination module 1220 is used to determine the neighbor drone tracking error based on the relative distance between the position of the disturbed drone and the neighboring drones and the expected safe distance.

[0147] The variable transformation module 1230 is used to convert the neighboring machine tracking error into an unconstrained variable based on the error transformation function designed according to the preset performance function.

[0148] The scheme determination module 1240 is used to determine a tracking control scheme that enables the UAV swarm to maintain the desired formation based on the lumped uncertainty error set, unconstrained variables, and dynamic model obtained from the preset time observer; wherein, the tracking error of the neighboring UAV is within the preset safety boundary; the maximum speed of each UAV in the UAV swarm is determined by a speed upper limit function constructed from the unconstrained variables.

[0149] Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure, or at least part of the functions of any one or more of them, can be implemented in one module. Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be implemented by dividing them into multiple modules. Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be at least partially implemented as hardware circuitry, such as a Field-Programmable Gate Array (FPGA), a Programmable Logic Array (PLA), a System-on-Chip, a System-on-a-Substrate, a System-on-Package, an Application-Specific Integrated Circuit (ASIC), or implemented in hardware or firmware by any other reasonable means of integrating or packaging circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be at least partially implemented as computer program modules, which, when run, can perform corresponding functions.

[0150] For example, any plurality of the model building module 1210, error determination module 1220, variable transformation module 1230, and scheme determination module 1240 can be combined into one module / unit / subunit, or any one of these modules / units / subunits can be split into multiple modules / units / subunits. Alternatively, at least part of the functionality of one or more of these modules / units / subunits can be combined with at least part of the functionality of other modules / units / subunits and implemented in one module / unit / subunit. According to embodiments of the present disclosure, at least one of the model building module 1210, error determination module 1220, variable transformation module 1230, and scheme determination module 1240 can be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), a programmable logic array (PLA), a system-on-a-chip, a system-on-a-substrate, a system-on-package, an application-specific integrated circuit (ASIC), or any other reasonable means of integrating or packaging the circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, at least one of the model building module 1210, error determination module 1220, variable transformation module 1230, and scheme determination module 1240 can be at least partially implemented as a computer program module, which can perform corresponding functions when the computer program module is run.

[0151] It should be noted that the data processing system part in the embodiments of this disclosure corresponds to the data processing method part in the embodiments of this disclosure. The specific description of the data processing system part is referred to in the data processing method part, and will not be repeated here.

[0152] Figure 13 A block diagram of an electronic device suitable for implementing a constraint-based hierarchical unmanned aerial vehicle (UAV) swarm preset performance fault-tolerant formation control method is illustrated according to an embodiment of the present disclosure. Figure 13 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0153] like Figure 13 As shown, an electronic device 1300 according to an embodiment of the present disclosure includes a processor 1301, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1302 or a program loaded from a storage portion 1308 into a random access memory (RAM) 1303. The processor 1301 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 1301 may also include onboard memory for caching purposes. The processor 1301 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present disclosure.

[0154] RAM 1303 stores various programs and data required for the operation of electronic device 1300. Processor 1301, ROM 1302, and RAM 1303 are interconnected via bus 1304. Processor 1301 performs various operations of the method flow according to embodiments of the present disclosure by executing programs in ROM 1302 and / or RAM 1303. It should be noted that the programs may also be stored in one or more memories other than ROM 1302 and RAM 1303. Processor 1301 may also perform various operations of the method flow according to embodiments of the present disclosure by executing programs stored in said one or more memories.

[0155] According to embodiments of this disclosure, the electronic device 1300 may further include an input / output (I / O) interface 1305, which is also connected to a bus 1304. The electronic device 1300 may also include one or more of the following components connected to the input / output (I / O) interface 1305: an input section 1306 including a keyboard, mouse, etc.; an output section 1307 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 1308 including a hard disk, etc.; and a communication section 1309 including a network interface card such as a LAN card, modem, etc. The communication section 1309 performs communication processing via a network such as the Internet. A drive 1310 is also connected to the input / output (I / O) interface 1305 as needed. A removable medium 1311, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 1310 as needed so that computer programs read from it can be installed into the storage section 1308 as needed.

[0156] According to embodiments of this disclosure, the method flow according to embodiments of this disclosure can be implemented as a computer software program. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowchart. In such embodiments, the computer program can be downloaded and installed from a network via communication section 1309, and / or installed from removable medium 1311. When the computer program is executed by processor 1301, it performs the functions defined in the system of embodiments of this disclosure. According to embodiments of this disclosure, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0157] This disclosure also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs that, when executed, implement the method according to the embodiments of this disclosure.

[0158] According to embodiments of this disclosure, the computer-readable storage medium can be a non-volatile computer-readable storage medium. Examples include, but are not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, the computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0159] For example, according to embodiments of this disclosure, a computer-readable storage medium may include ROM 1302 and / or RAM 1303 and / or one or more memories other than ROM 1302 and RAM 1303 described above.

[0160] Embodiments of this disclosure also include a computer program product comprising a computer program containing program code for performing the methods provided in the embodiments of this disclosure. When the computer program product is run on an electronic device, the program code is used to enable the electronic device to implement the constraint-level-based UAV swarm preset performance fault-tolerant formation control method provided in the embodiments of this disclosure.

[0161] When the computer program is executed by the processor 1301, it performs the functions defined in the system / apparatus of this disclosure embodiments. According to embodiments of this disclosure, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0162] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and may be downloaded and installed via the communication section 1309, and / or installed from the removable medium 1311. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0163] According to embodiments of this disclosure, program code for executing the computer programs provided in embodiments of this disclosure can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, languages ​​such as Java, C++, Python, "C", or similar programming languages. The program code can execute entirely on a user's computing device, partially on a user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0164] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions. Those skilled in the art will understand that the features described in the various embodiments of the present disclosure can be combined and / or combined in various ways, even if such combinations are not explicitly described in the present disclosure. In particular, the features described in the various embodiments of this disclosure can be combined and / or combined in various ways without departing from the spirit and teachings of this disclosure. All such combinations and / or combinations fall within the scope of this disclosure.

[0165] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. A constrained hierarchical UAV swarm pre-set performance fault-tolerant formation control method, characterized in that, The method includes: Construct a dynamic model of disturbed drones in a drone swarm; The neighbor drone tracking error is determined based on the relative distance between the disturbed drone and the adjacent drone and the expected safe distance. The neighbor tracking error is converted into an unconstrained variable by an error transformation function designed according to a preset performance function; Based on the lumped uncertainty error set obtained from the preset time observer, the unconstrained variables, and the dynamic model, a tracking control scheme is determined to maintain the desired formation of the UAV swarm; wherein, the neighbor tracking error is within a preset safety boundary; the maximum speed of each UAV in the UAV swarm is determined by a speed upper limit function constructed from the unconstrained variables.

2. The constrained hierarchical UAV swarm preset performance fault-tolerant formation control method according to claim 1, characterized in that, The fault type of the disturbed UAV is a multiplicative fault. In this case, the dynamic model of the disturbed UAV is expressed as: ； ； in, It is the position of the i-th drone; It is the heading vector of the i-th UAV; It is the speed of the i-th drone; It is the linear velocity of the i-th drone; It is the linear velocity error of the i-th drone; It is the angular velocity of the i-th drone; It is the angular velocity error of the i-th UAV; ω is the angular velocity of the i-th UAV; [·] is the matrix operator; It is a multiplicative actuator malfunction; It is an additive actuator malfunction. It is an unknown time-varying external disturbance; It is the lower limit of multiplicative actuator failure; This is the upper limit of multiplicative actuator failure.

3. The constrained hierarchical UAV swarm preset performance fault-tolerant formation control method according to claim 1, characterized in that, The error transformation function is expressed as follows: ； ； ； ； ； ； ； in, These are unconstrained variables; Let be the time-varying coefficient that represents the upper bound of the modulation error between UAVs i and j; This is the modulation error; The squared distance error between drones i and j; Let be the lower bound time-varying coefficient of the modulation error between UAVs i and j; An exponential performance function for controlling the evolution of error; The value of the exponential performance function at the initial moment; The value of the exponential performance function at the steady-state moment; This refers to the tracking error of the adjacent aircraft. Let i be the distance between drones i and j; Let i be the expected distance between drones i and j; Let i be the relative position vector between drones i and j; The location of drone i; Let j be the position of the drone. This represents the minimum squared distance error between drones i and j. This is the lower bound of the squared distance error between UAVs i and j; This represents the upper limit of the squared distance error between drones i and j; This represents the maximum value of the squared distance error between drones i and j.

4. The constrained hierarchical UAV swarm preset performance fault-tolerant formation control method according to claim 1, characterized in that, The upper limit function for speed is expressed as: ； ； in, This represents the upper limit of the effective speed of drone i; For the introduction of dynamic relaxation terms; This is the preset speed limit for drone i; Let be the time derivative of the adaptive relaxation term for the velocity constraint of UAV i; The decay coefficient of the adaptive update law; For the adaptive relaxation term of the velocity constraint of UAV i; The trigger threshold for the adaptive update law; These are unconstrained variables.

5. The constrained hierarchical UAV swarm preset performance fault-tolerant formation control method according to claim 1, characterized in that, The speed of each drone in the drone swarm is expressed as follows: ； in, The speed of drone i; This represents the upper limit of the effective speed of drone i; It is a sufficiently small constant.

6. The constrained hierarchical UAV swarm preset performance fault-tolerant formation control method according to claim 1, characterized in that, The method includes: the distributed controller of each drone in the drone cluster is represented as follows: ； ； in, It is the linear velocity of the i-th drone; The speed of drone i; It is the angular velocity of the i-th drone; This is the soft-constraint gain; Let be the control gain between the i-th and j-th UAVs; These are auxiliary parameters for unconstrained error dynamics; These are unconstrained variables; Let be the relative position vector between the i-th and j-th UAVs; This is an estimate of the lumped uncertainty of linear motion; This is an estimate of the multiplicative fault of angular velocity; Let be the adjacency set of the i-th UAV; It is the heading vector of the i-th UAV; This represents the upper limit of the effective speed of drone i; It is a sufficiently small constant.

7. A constrained hierarchical UAV swarm preset performance fault-tolerant formation control device, characterized in that, The device includes: The model building module is used to build dynamic models of disturbed drones in a drone swarm; The error determination module is used to determine the neighbor drone tracking error based on the relative distance between the position of the disturbed drone and the adjacent drone and the expected safe distance. The variable transformation module is used to convert the neighbor tracking error into an unconstrained variable based on an error transformation function designed according to a preset performance function. The scheme determination module is used to determine a tracking control scheme that enables the UAV swarm to maintain a desired formation based on the lumped uncertainty error set obtained from a preset time observer, the unconstrained variables, and the dynamic model; wherein the neighbor tracking error is within a preset safety boundary; and the maximum speed of each UAV in the UAV swarm is determined by a speed upper limit function constructed from the unconstrained variables.

8. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs. Wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the method of any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to implement the method of any one of claims 1 to 6.

10. A computer program product, characterized in that, Includes a computer program that, when executed by a processor, implements the method according to any one of claims 1-6.

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