Unmanned aerial vehicle cluster cooperative formation control method based on hawks process

Abstract

This invention belongs to the technical field of UAV cooperative control, and more specifically, relates to a UAV swarm cooperative formation control method based on Hawkes processes. The method includes: system initialization and problem definition; defining scenario-based cooperative events and trigger thresholds; establishing a multivariate Hawkes process event interaction model with selectable multi-core functions; designing a constrained event intensity-formation deviation mapping relationship; lightweight online parameter estimation; predicting future event intensity; constructing a distributed optimization problem with consistency constraints; stochastic gradient online optimization solution; execution control and event detection; event recording and sliding window updating; rolling optimization and repeated execution. This invention solves the problems of existing methods being unable to quantify the dynamic interaction impact of decision events between UAVs, and the current high computational cost. The limited computing power resources of UAV onboard processors make it difficult to support complex iterative calculations, easily leading to control command lag and thus causing safety hazards.

Description

Technical Field

[0001] This invention belongs to the technical field of UAV cooperative control, and more specifically, relates to a UAV swarm cooperative formation control method based on Hawkes processes. Background Technology

[0002] As the low-altitude economy is incorporated into modern emerging industries, the UAV industry is undergoing a major transformation from single-aircraft operation to swarm collaborative operation. UAV swarm collaborative formation control is a core technology in the UAV field. Through information interaction and behavior coordination among multiple UAVs, specific spatial configurations and mission objectives can be achieved, and it is widely used in reconnaissance, disaster relief, environmental monitoring and other fields.

[0003] Chinese invention patent CN120428742A discloses a method for efficient collaborative control of multiple UAV formations. Through the collaboration of a generator and discriminator, a training strategy utilizing diverse scenarios and fault models is employed in a digital twin model. A multi-level reward function is designed and dynamically adjusted to better handle complex tasks and scenarios, comprehensively improving collaborative efficiency. The method uses digital twin dynamics simulation to predict UAV states and correct errors. A real-time closed-loop optimization mechanism can quickly replan the path when flight anomalies occur. Furthermore, a domain adaptive module reduces the difference between virtual and real data. When encountering new obstacles, the technical solution of this invention can replan a safe path, while simultaneously achieving collaborative planning and obstacle avoidance through the integration of multiple technologies.

[0004] The existing core technologies can be divided into three categories, each with its own advantages and disadvantages and obvious limitations: First, the leader-follower method, which is simple in principle and easy to implement, and is suitable for static, low-interference scenarios (such as farmland spraying). However, the state of the leader directly determines the stability of the formation. Once the leader fails or loses its signal, the formation is prone to collapse. Moreover, it does not consider the mutual influence between followers, and there is a risk of local collisions when the formation is dense. Second, the virtual structure method, which treats the cluster as a rigid virtual body, is suitable for high-precision formation transformation scenarios (such as aerial performances). The formation has strong integrity and high configuration accuracy, but it has extremely high requirements for the synchronization of UAV states, large global information interaction volume, and high communication overhead. The rigid assumption makes it difficult to adapt to dynamic obstacle avoidance requirements. Third, the behavior-based method, which adopts a distributed architecture, is suitable for exploring unknown environments (such as disaster area search and rescue). It has strong flexibility and a certain degree of autonomous adaptability, but the behavior weights lack a unified quantitative standard and rely more on experience settings. In complex scenarios, behavior conflicts are prone to occur, leading to decision confusion.

[0005] Furthermore, existing control schemes that incorporate Hawkes processes are only theoretically modeled and are not adapted to the actual scenario where UAVs have limited onboard resources. The use of traditional MLE and EM algorithms results in excessive computing power and has specific problems such as unconstrained mapping between event intensity and formation deviation and lack of consistency mechanism in distributed optimization, making it difficult to implement in engineering. Summary of the Invention

[0006] The present invention aims to overcome at least one of the defects of the prior art and provide a method for cooperative formation control of UAV swarms based on Hawkes processes.

[0007] First, existing methods cannot quantify the dynamic interaction effects of decision-making events among UAVs. UAV decision-making behaviors exhibit obvious mutual triggering characteristics. For example, if one UAV triggers obstacle avoidance behavior, it will significantly increase the obstacle avoidance probability of surrounding UAVs. However, existing technologies are mostly based on deterministic models or simple random disturbance models to design control strategies, which cannot quantitatively model this dynamic interaction process. They can only rely on empirical rules for rough control, resulting in control strategies that are either too conservative and limit maneuverability or too aggressive and increase formation instability.

[0008] Secondly, existing solutions incorporating the Hawkes process commonly employ MLE or EM algorithms for parameter estimation. These algorithms require global iterative calculations on a large amount of historical data, resulting in significant computational overhead. However, UAV onboard processors are limited by size, weight, and power consumption, making it difficult to support complex iterative calculations. This can easily lead to control command lag, thereby causing safety hazards. Furthermore, the mapping relationship between event intensity and formation deviation lacks constraints, often employing a simple linear mapping. When formation deviation becomes excessive, event intensity can increase indefinitely, causing control inputs to exceed the actuator's capacity, leading to actuator overload, accelerated equipment wear, and even UAV loss of control.

[0009] Furthermore, the distributed optimization process lacks neighbor consistency constraints. Each drone makes decisions based solely on local information, without considering the optimization goals of neighboring drones. This can easily lead to disagreements in the cluster's collaborative goals, resulting in "internal friction" between drones and affecting the overall formation. Historical event data is stored without restrictions and lacks a reasonable management strategy. As runtime increases, redundant data accumulates, not only consuming significant onboard storage resources but also increasing computational complexity and reducing control efficiency. In existing Hawkes process modeling, the decay kernel function type is singular, often employing exponential decay, which cannot adapt to the complex impact patterns of different types of events. This results in insufficient accuracy in characterizing event interaction models, affecting subsequent prediction and optimization performance.

[0010] The detailed technical solution of this invention is as follows: A method for cooperative formation control of UAV swarms based on Hawkes processes, the method comprising: S1. Initialize the state vector, control input, control constraints, and sliding window historical event set of the drone cluster; at the same time, define the scenario-based collaborative event types and set the event trigger thresholds; Based on control constraints, the current state vector of the UAV is changed by adjusting the control input to achieve the desired formation state for the UAV to trigger events; S2. If a drone triggers an event, an event intensity function is constructed for the event type of the drones involved through a multivariate Hawkes process, defining the impact pattern of that type of event. S3. Set the expected event intensity of the drone-triggered event according to the trigger event type; S4. The recursive moment matching method is used for online parameter estimation. Based on historical event data within the sliding window, the parameters of the Hawkes process are iteratively updated. S5. Based on the Hawkes process parameters estimated by the UAV at the current moment and the historical event data within the sliding window, the intensity of various types of UAV events in the future time domain is predicted based on the constructed event intensity function to obtain the predicted event intensity. S6. Construct and minimize the cost function of the UAV, including minimizing the deviation between the predicted event intensity and the expected event intensity, as well as the regularization term of the control input; At the same time, constraints are set, including: ensuring that the deviation of the cost function value between the current drone and the neighboring drone does not exceed the preset consistency error limit, and ensuring that the state and control input of the drone are within the set safety range; After solving, the optimal future control input sequence within the preset time range that satisfies the constraints is obtained; S7. Each UAV executes the first element of the optimal future control input sequence to achieve the desired formation state after the UAV triggers an event. Then, it detects whether various events are triggered, and the frequency of event detection is synchronized with the control cycle. If an event is triggered, the event is recorded; then a new round of drone cooperative formation control continues.

[0011] Furthermore, the state vector includes key parameters such as the number, position, speed, heading, and attitude angle of the UAVs, which can be set according to the control settings of the UAV model; The control inputs are the control quantities of the UAV actuators, including but not limited to motor speed and servo angle.

[0012] The control constraints, or problem definition, include: formation expectation, prediction time domain, control time domain, and control period. They determine the basic parameters, boundary conditions, and core constraints of the control problem, and clarify the "basic rules and parameters of control". The desired geometry of the formation is determined by a set of relative displacement vectors. Define, where ,and , Indicates the first The drone relative to the first The desired location of the drones, and the number of drones in the swarm. Formation expectation refers to the formation state that the UAV wants to achieve after triggering an event (including key parameters such as position, speed, heading, and attitude angle). Set the prediction time domain as Control time domain is and the control cycle is ,satisfy The prediction time domain is used to predict the intensity of events over a future period; the control time domain is used to limit the time range for generating the optimal control input vector, i.e., from the current time t. k to t k +T c The time period; the control cycle is That is, every A control update is performed once a time interval.

[0013] Initialize the sliding window history event set Empty, set the length of the sliding window to , It is a positive integer, storing only the most recent occurrence. Event data; historical events exceeding the window length will be automatically deleted.

[0014] Furthermore, defining scenario-based collaborative event types and setting trigger thresholds means defining [something] for each drone. Types of collaborative events , Each event is associated with a clearly defined quantified trigger threshold, enabling accurate event detection while adapting to different task scenarios, specifically including: Obstacle avoidance events When drones The distance to obstacles or teammates is less than the safe threshold. When the obstacle avoidance maneuver is triggered; safety threshold The speed is determined by the drone's fuselage size and flight speed; the faster the flight speed, the better. The larger the value, the more time is reserved for obstacle avoidance reaction.

[0015] Formation Position Achievement Event When drones Relative positional deviation from neighboring drones Less than the tolerance threshold When the desired formation position is achieved, the tolerance threshold is considered to be met. Set according to the formation accuracy requirements of the mission.

[0016] Communication quality degradation events When drones The signal-to-noise ratio (SNR) of the communication link with neighboring drones is below a threshold. When this occurs, it is determined to be a communication quality degradation; threshold Based on the performance of the communication module and the data transmission requirements, ensure that the UAV can adjust the communication strategy or control parameters in a timely manner when the communication quality deteriorates.

[0017] Formation change event When a drone receives a formation change command, and the deviation between its current position and the target position is greater than the change threshold... At this time, the formation change behavior is triggered. Change threshold. The settings are based on the amplitude and speed requirements of formation changes.

[0018] event The time of occurrence is recorded as ,in The event ordinal number represents the drone. No. The first type of event The timing of the event is determined by a clearly defined quantitative threshold, enabling precise and controllable event triggering and avoiding the ambiguity of event triggering in traditional behavior-based methods.

[0019] Furthermore, the construction of the event intensity function specifically includes: For the The first drone Class events, at time Event intensity Based on a multivariate Hawkes process, this system supports the adaptive selection of various decay kernel functions to accurately characterize the impact patterns of different types of events. The expression for the intensity function is as follows: (1) The meanings and optimization designs of each parameter in formula (1) are as follows: Drones No. The base strength of a type of event represents the probability of that type of event occurring spontaneously when there are no historical events affecting it. The base strength can be preset according to the task scenario. Event interaction excitation coefficient, representing the drone The occurrence of the first Similar events, for drones The occurrence of the first The intensity of the impact of such events; The set of historical events within the sliding window, including only the most recent ones. Individual event data, For drones The first occurrence The first type of event The next occurrence time; : Decay kernel function, where This is an index for kernel function types, used to describe the decay pattern of the impact intensity of historical events over time. Three kernel function types are supported, and the drone adaptively selects the appropriate type based on the event type. Exponential decay kernel, : Obstacle avoidance events are defined. Events related to formation positioning , Indicates the time difference, i.e., the current moment. With the moment of historical events The difference is , is the decay coefficient of the exponential decay kernel.

[0020] Power-law decay kernel, : Used to define formation change events In the formula, is the decay coefficient of the power-law decay kernel.

[0021] Segmented decay kernel, : 2) Communication quality degradation events used for definition ;In formula (2), The first half of the segmented decay kernel The exponential decay coefficient; The latter half of the segmented decay kernel The power-law decay coefficient; This is the time boundary point of the segmented attenuation kernel, used to divide the applicable intervals of the two attenuation laws.

[0022] By adaptively selecting multiple kernel functions, this model can accurately match the impact patterns of different types of events, significantly improving the characterization accuracy compared to traditional single kernel function models. It abandons the limitations of traditional single decay kernel functions, supporting the adaptive selection of multiple decay kernel functions adapted to the impact patterns of different events. Simultaneously, combined with a defined sliding window historical event management strategy, it stores only the most recently occurring event data, achieving a balance between the accuracy of the event interaction model and the utilization of onboard resources, accurately depicting the dynamic interaction relationships of different types of decision-making events among UAVs.

[0023] Furthermore, S3 specifically includes: S31. Define formation position error for: (3) In formula (3), Indicates the first The drone relative to the first The desired location of the drone; For the first A drone at all times The position vector; For the first A drone at all times The position vector; S32. Design the expected event intensity function with upper limit constraint. ,as follows: (4) The parameters in formula (4) are described as follows: : No. The intensity limit of such events is determined by the response capability of the drone's actuators; : No. Event weight coefficients are used to adjust the priority of different types of events; The deviation mapping function selects different function forms based on the event type, including: (1) Obstacle avoidance events, Choose a monotonically increasing function. , This indicates the formation position error. The greater the formation deviation, the higher the expected intensity of the obstacle avoidance event, prompting the UAV to quickly adjust its attitude to avoid obstacles. (2) Formation positioning achievement event, Choose Gaussian function When the formation deviation is small, the expected intensity is high, prompting the UAVs to maintain their formation position; when the formation deviation is too large, the expected intensity tends to stabilize, avoiding control input saturation. (3) Communication quality degradation events, Choose a monotonically decreasing function. , The deviation between SNR and the threshold. To adjust parameters, the greater the communication deviation, the higher the expected intensity, prompting the UAV to adjust its communication strategy; (4) Formation change event, : Choosing a piecewise function , This ensures that the intensity is controllable during the transformation process and avoids over-adjustment.

[0024] Furthermore, the iterative update of the Hawkes process parameters specifically includes: Online parameter estimation is performed using a recursive moment matching method based on historical event data within a sliding window. Iteratively update the parameters of the Hawkes process. , is the The core parameter set for the Hawkes process of launching a drone. For drones No. The base strength of a class of events, representing the situation when there are no historical events affecting it; The event interaction excitation coefficient represents the drone. The occurrence of the first Similar events, for drones The occurrence of the first The intensity of the impact of such events; This is the attenuation coefficient.

[0025] The recursive form of the parameter update rule is as follows: (5) In formula (5): For the first The parameter values ​​for the next iteration. For the first The parameter values ​​for the next iteration; The step size is determined by the control cycle. The shorter the adjustment and control cycle, the smaller the step size. It is a set of Hawkes process parameters The gradient operator is used to measure the rate and direction of change of the objective function as a function of parameters. The objective function for moment matching is to match the theoretical moments and actual moments of event intensity.

[0026] Furthermore, S5 specifically includes: At the present moment drones Based on the estimated Hawkes process parameters and the collection of historical events within the sliding window Predicting future time domain The intensity of various events within itself ,as follows: (6) In formula (6), It is the integration variable, representing the integration interval. The traversal time within the interval is used to traverse all time points within that interval; It is a drone The Class events at time Based on historical event sets The intensity of the event.

[0027] Furthermore, S6 specifically includes: In the local optimization problem of each drone, a neighbor cost function consistency constraint is introduced to construct a constrained optimization objective function. For each drone... The optimization objective is to minimize its own cost function. At the same time, it ensures that the deviation of the cost function from that of neighboring drones does not exceed the preset consistency error limit. And to keep the drone's status and control inputs within a set safety range; Cost function It consists of two parts. The first part is the integral term of the event intensity bias, which is used to minimize the predicted event intensity. With expected event intensity The first part is to control the deviation, thus achieving the core objective of formation control; the second part is the regularization term of the control input, used to balance control accuracy and energy consumption, and to avoid excessive control input. The objective function is optimized as follows: (7) In formula (7), , indicating drone The future control input sequence within the control time domain. Indicates future time The corresponding number The first drone The expected event intensity of the event type; The weight for the event intensity deviation; To control the weights of the inputs; The scene is identified autonomously by the drone through environmental perception. For consistency constraints, drones are required The cost function and neighboring drones The deviation of the cost function value does not exceed upper limit of consistency error Based on the task scenario; For dynamic constraints, represent the dynamic model of the UAV, describing how the UAV's state changes with control input; and These are state constraints and input constraints, respectively, to ensure that the state and control inputs of the UAV are within a safe range.

[0028] By solving the objective function, the cost function is minimized. Satisfying consistency constraints and dynamic constraints, the final result is obtained. The optimal future control input sequence for a drone in the control time domain ; The optimal control input sequence Substitute into the cost function , can obtain the first The optimal cost function value of a drone .

[0029] Furthermore, S7 specifically includes: S71, Execution Control and Event Detection; Each drone The control sequence obtained by performing optimization The first element This drives the drone to adjust its own state vector, gradually reaching the desired formation state after the drone triggers an event, that is, only executing the optimal control input at the current moment; the control input at subsequent moments will be updated through rolling optimization in the next control cycle; Meanwhile, the drone monitors its own status, environmental information, and communication information in real time, compares them with set trigger thresholds, and detects various events. Whether it is triggered, and the frequency of event detection is synchronized with the control cycle; S72, Event logging and sliding window updates; If drone At any moment The first was detected When a class event is triggered, immediately send the event information. Write the event list to the local machine; The drone broadcasts an event summary via neighbor communication only when a new event is detected. The summary includes information such as the event type, the time of occurrence, and the drone number. After receiving the event summary broadcast by a neighboring drone, the drone verifies the reasonableness of the event's time of occurrence, i.e., its difference from the local time, through the communication link. After successful verification, update the local sliding window history event set. Otherwise, discard the event summary; Furthermore, the update rule is: if the number of events in the event set does not exceed the window length... If the number of events exceeds the window length, then add a new event directly; If the earliest event occurs, the new event is deleted, and then a new event is added. This sliding window update strategy keeps the historical event set lightweight, reducing storage and computational overhead.

[0030] S73, Rolling Optimization and Repeated Execution; Reaching the next control cycle The drone will update the current time to The historical event collection has been updated to ; Then, S5 to S7 are executed repeatedly to enter a new round of drone collaborative formation control and event updates, forming a closed-loop rolling optimization control.

[0031] Through this closed-loop rolling optimization approach, drone swarms can continuously adapt to changes in the dynamic environment, achieving adaptive collaborative formation control. Regardless of the type of interference encountered, the drones can adjust their control strategies through real-time prediction and optimization, ensuring formation stability and mission safety.

[0032] In another aspect of the invention, an electronic device is also provided, comprising: At least one processor; and The memory stores instructions that, when executed by the at least one processor, cause the at least one processor to perform the Hawkes process-based UAV swarm cooperative formation control method as described above.

[0033] In another aspect of the invention, a computer-readable storage medium is also provided, which stores executable instructions that, when executed, cause the machine to perform the Hawkes process-based UAV swarm cooperative formation control method as described above.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention discloses a UAV swarm collaborative formation control method based on Hawkes process. It uses a recursive moment matching method for lightweight online parameter estimation, combines stochastic gradient descent and early stopping strategies for optimization, and uses a sliding window to manage historical event data. This greatly enhances the adaptability of computing power, effectively reduces the computational overhead of parameter estimation and optimization, and can be well adapted to the actual scenario where UAV onboard resources are limited. It ensures the real-time response of control commands, meets the real-time requirements of UAV swarm collaborative control, and avoids the control lag problem caused by insufficient computing power.

[0035] (2) This invention discloses a method for collaborative formation control of UAV swarms based on Hawkes process. By designing an event intensity-formation deviation mapping relationship with upper limit constraint and setting an upper limit for event intensity, the control stability is significantly improved, effectively avoiding overload of the actuator, ensuring the safe and stable operation of the actuator, improving formation control accuracy and mission execution reliability, and reducing equipment wear and loss of control risk.

[0036] (3) This invention discloses a method for collaborative formation control of UAV swarm based on Hawkes process. By introducing the consistency constraint of neighbor cost function and using sliding window to manage historical event data, it improves the collaborative consistency of the swarm, eliminates the "internal friction" between UAVs, enhances the overall integrity and stability of the formation, reduces storage redundancy, reduces energy consumption, extends system endurance, and improves long-term operational stability.

[0037] (4) This invention discloses a method for collaborative formation control of UAV swarms based on Hawkes processes. By establishing a multivariate Hawkes process event interaction model with selectable multi-core functions and combining iterative numerical approximation method to predict the intensity of future events, it enhances the forward-looking collaborative capability, realizes the proactive prediction of event interaction between UAVs, adjusts the control strategy in advance, and enhances the robustness of the swarm in complex dynamic environments, providing support for the implementation and large-scale application of the technology. Attached Figure Description

[0038] Figure 1 This is a flowchart of the UAV swarm cooperative formation control method based on Hawkes processes described in this invention.

[0039] Figure 2 This is a schematic diagram of the distributed control architecture of the UAV cluster in Embodiment 1 of the present invention.

[0040] Figure 3 This is a schematic diagram comparing the formation control effects in Embodiment 1 of the present invention.

[0041] Figure 4 This is a schematic diagram comparing the decay patterns of the multi-core function in Embodiment 1 of the present invention. Detailed Implementation

[0042] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0043] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0044] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0045] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0046] Example 1 Reference Figure 1 In this example, a cooperative formation control method for UAV swarms based on Hawkes process is provided. The method includes: S1. Initialize parameters and define scenario-based cooperative events and triggering thresholds; Initialize the state vector, control input, control constraints, and sliding window historical event set of the UAV swarm; meanwhile, define the types of scenario-based cooperative events and set the triggering thresholds of the events; According to the control constraints, change the current state vector of the UAV by adjusting the control input to achieve the desired formation state for the UAV to trigger an event.

[0047] Set the number of the UAV swarm to where is a positive integer and can be flexibly adjusted according to mission requirements. Define the state of the -th UAV ( ) at time as , is the dimension of the state vector, and the state vector includes key information such as the position, speed, heading, and attitude angle of the UAV; define the control input vector as , is the dimension of the control input vector, and the control input vector includes control quantities of actuators such as motor speed and servo angle.

[0048] The desired geometric configuration of the formation is defined by a set of relative displacement vectors where , and , represents the desired position of the -th UAV relative to the -th UAV.

[0049] Set the prediction horizon to , the control horizon to and the control period to , satisfying . The prediction horizon is used to predict the event intensity in the future for a period of time, and the control horizon is used to generate the optimal control input vector. The control period is , that is, the control update is executed every time.

[0050] Control period: time interval, defined as "execute the control update every Δt time", which is the update frequency of the control instruction. For example, the control is updated every 0.5 s. It is a single "time difference" and does not involve a "time range", only specifying "how often to update".

[0051] Control Time Domain: Time range, defined as "from the current time t" k to t k +T c The "time period" is used to generate the optimal control input vector within that time period. It is a "continuous time interval" that specifies "how long the control instructions are generated in one optimization".

[0052] Initialize the sliding window history event set Empty, set the length of the sliding window to , It is a positive integer, storing only the most recent occurrence. Event data is stored in a single window; historical events exceeding the window length will be automatically deleted to reduce storage resource consumption. The length of the sliding window... The onboard storage capacity of the drone can be flexibly adjusted according to the drone's onboard storage capacity and mission requirements. For example, in short-duration, high-intensity missions, a smaller capacity can be set. This value speeds up data updates; in long-running, low-dynamic tasks, a larger value can be set. This improves the accuracy of parameter estimation.

[0053] Preferably, the definition of scenario-based collaborative events and trigger thresholds specifically includes: Define each drone Types of collaborative events ( Each event is associated with a clearly defined quantified trigger threshold, enabling accurate event detection and adapting to different task scenarios. The specific event types and trigger thresholds are defined as follows: Obstacle avoidance events When drones The distance to obstacles or teammates is less than the safe threshold. At this time, obstacle avoidance maneuvers are triggered. Safety threshold. The speed is determined by the drone's fuselage size and flight speed; the faster the flight speed, the better. The larger the value, the more time is reserved for obstacle avoidance reaction.

[0054] Formation Position Achievement Event When drones Relative positional deviation from neighboring drones Less than the tolerance threshold When the desired formation position is achieved, the tolerance threshold is determined. The formation accuracy requirements are set according to the mission's requirements; for example, in an air show mission, The value is relatively small to ensure the accuracy of the formation; in environmental monitoring tasks, The value can be appropriately increased to improve the maneuverability and flexibility of the drone.

[0055] Communication quality degradation events When drones The signal-to-noise ratio (SNR) of the communication link with neighboring drones is below a threshold. When this occurs, it is determined to be a communication quality degradation. Threshold Based on the performance of the communication module and the data transmission requirements, ensure that the UAV can adjust the communication strategy or control parameters in a timely manner when the communication quality deteriorates.

[0056] Formation change event When a drone receives a formation change command, and the deviation between its current position and the target position is greater than the change threshold... At this time, the formation change behavior is triggered. Change threshold. The settings are based on the amplitude and speed requirements of formation changes.

[0057] event The time of occurrence is recorded as ,in The event ordinal number represents the drone. No. The first type of event The timing of the event is determined by a clearly defined quantitative threshold, enabling precise and controllable event triggering and avoiding the ambiguity of event triggering in traditional behavior-based methods.

[0058] S2. Establish a multi-core function-selectable multivariate Hawkes process event interaction model to confirm the event intensity function; If a drone triggers an event, an event intensity function is constructed for the event type of the drones involved through a multivariate Hawkes process, defining the impact pattern of that type of event.

[0059] Preferably, S2 specifically includes: For the The first drone Class of events, which at time Event intensity Based on a multivariate Hawkes process, this system supports the adaptive selection of various decay kernel functions to accurately characterize the impact patterns of different types of events. The expression for the intensity function is as follows: (1) The meanings and optimization designs of each parameter in formula (1) are as follows: Drones No. The base strength of an event class represents the probability of that class of events occurring spontaneously without any historical influence. The base strength of obstacle avoidance events is pre-defined based on the mission scenario, such as in a undisturbed formation-keeping scenario. Smaller; in complex obstacle environments, The value is relatively large.

[0060] Event interaction excitation coefficient, representing the drone The occurrence of the first Similar events, for drones The occurrence of the first The intensity of the impact of a class of events. When When, it indicates a positive incentive, i.e., drones. The Such events will increase drones No. The probability of a class of events occurring; when When the value is zero, it indicates no impact. The magnitude of the excitation coefficient reflects the strength of the event's impact; for example, a drone... Obstacle avoidance events for neighboring drones The incentive coefficient for obstacle avoidance events is relatively large, while the incentive coefficient for long-range drones is relatively small.

[0061] The set of historical events within the sliding window, including only the most recent ones. Individual event data avoids the accumulation of redundant data and reduces computational and storage overhead. For drones The first occurrence The first type of event The next occurrence time : Decay kernel function, This is an index for the kernel function type, used to describe the decay pattern of the impact intensity of historical events over time. This invention supports three kernel function types, and the drone can adaptively select the appropriate type based on the event type: (1) Exponential decay kernel ( ): This formula is applicable to events where the intensity of the impact decays rapidly over time, such as obstacle avoidance events; where, Indicates the time difference, i.e., the current moment. With the moment of historical events The difference (i.e.) (), used to describe the decay of the impact of historical events over time; This is the decay coefficient of the exponentially decaying kernel, used to adjust the rate of exponential decay. The larger the value, the faster the impact of historical events diminishes.

[0062] (2) Power-law decay kernel ( ): This formula is applicable to events whose influence intensity decays slowly over time, such as formation changes; where, This is the decay coefficient of the power-law decay kernel, used to adjust the rate of power-law decay. The larger the value, the slower the impact of historical events diminishes.

[0063] (3) Segmented decay kernel ( ): (2) This is applicable to complex mixed events with influencing patterns, such as communication quality degradation events; in formula (2), The first half of the segmented decay kernel The exponential decay coefficient; The latter half of the segmented decay kernel The power-law decay coefficient; This is the time boundary point of the segmented attenuation kernel, used to divide the applicable intervals of the two attenuation laws.

[0064] This invention, through the adaptive selection of multiple kernel functions, can accurately match the influence patterns of different types of events, significantly improving the characterization accuracy compared to traditional single kernel function models. It abandons the limitations of traditional single decay kernel functions, supporting the adaptive selection of multiple decay kernel functions adapted to the influence patterns of different events. Simultaneously, combined with a set sliding window historical event management strategy, it stores only the most recently occurring event data, achieving a balance between the accuracy of the event interaction model and the utilization of airborne resources, accurately depicting the dynamic interaction relationships of different types of decision-making events among UAVs.

[0065] S3. Set the expected event intensity of the drone-triggered event according to the trigger event type; Define an expected event intensity function with an upper limit constraint, select different preset function forms according to the event type, determine the expected event intensity, predict the intensity of subsequent future events, and set an expected intensity benchmark in advance to provide a basis for comparison for subsequent predictions.

[0066] This embodiment overcomes the shortcomings of traditional simple linear mapping by constructing a nonlinear mapping relationship with upper limit constraints. It selects an appropriate deviation mapping according to different event types and sets an upper limit for event intensity to ensure that the control input is always within the carrying capacity of the UAV actuator, avoiding overload of the actuator and balancing control accuracy and equipment operation safety.

[0067] The core is to design a constrained event intensity-formation deviation mapping relationship. Specifically, this involves defining the formation position error, constructing an expected event intensity function with an upper limit constraint, and using this function to match and adapt the deviation mapping for different types of events (obstacle avoidance, formation maintenance, etc.). An upper limit for event intensity is set, and the priority of various events is adjusted through weight coefficients to avoid unbounded growth of event intensity.

[0068] Relevance to context 1. Related to the previous text: S2 has established a multivariate Hawkes process event interaction model with selectable multi-core functions, and obtained the method for calculating event intensity; S3, based on this model, correlates event intensity with the formation position deviation defined in S1 and the trigger thresholds of various events in S1, solving the problem of "disconnect between event intensity and formation control target". At the same time, for the prediction of future event intensity in S5, the expected intensity benchmark is set in advance to provide a basis for comparison for subsequent predictions.

[0069] 2. Practical application: Through this mapping relationship, the expected intensity of various events can be dynamically adjusted according to the size of the formation deviation. This ensures the accuracy of formation control (e.g., increasing the intensity of obstacle avoidance events when the formation deviation is large) while limiting the control input through the intensity upper limit. This prevents the actuator from being overloaded due to excessive event intensity during S5 prediction and S6 optimization, thus ensuring equipment safety.

[0070] 3. Relationship with the following text: The expected event intensity function in S3 is the core input of the "event intensity deviation integral term" when constructing the optimization problem in S6. It provides a clear optimization objective for distributed optimization (minimizing the deviation between the predicted event intensity and the expected intensity) and is a key link connecting event modeling and optimization solution.

[0071] S3 specifically includes: S31. Define formation position error for: (3) In formula (3), Indicates the first The drone relative to the first The desired location of the drone; For the first A drone at all times The position vector; For the first A drone at all times The position vector, Indicates the first The topological neighbor set of a drone.

[0072] Formation position error With the establishment of the first The first drone Class events at time event intensity function There is a close indirect relationship between them; they support each other and work together to serve the formation control objective. The specific relationship is as follows: Established event intensity function Its core function is to characterize the interaction patterns of various collaborative events among drones and quantify the probability intensity of different events, the values ​​of which are derived from a set of historical events. Event interaction incentive coefficient The parameters, such as the decay kernel function, determine the current event interaction state; The formation position error defined at this time It is a quantitative drone The core parameter of the relative positional deviation with neighboring drones is directly related to whether various cooperative events (such as obstacle avoidance events and formation positioning events) are triggered in section 1. The greater the formation positioning deviation, the higher the probability of triggering obstacle avoidance events and formation change events, and the higher the corresponding event intensity in section S2. The intensity of the formation position achievement event will increase accordingly, and conversely, the intensity of the formation position achievement event will increase.

[0073] S32. To avoid overload of the actuator due to the unbounded growth of event intensity, design an expected event intensity function with an upper limit constraint. ,as follows: (4) The parameters in formula (4) are described as follows: : No. The intensity limit of such events is determined by the response capability of the drone's actuators. Intensity Limit Through experimental calibration, it is ensured that the corresponding control input does not exceed the maximum output capacity of the actuator, thereby fundamentally avoiding actuator overload.

[0074] Event type weighting coefficient: Used to adjust the priority of different event types. For example, in obstacle avoidance scenarios, increasing the weighting coefficient of obstacle avoidance events... In formation-keeping scenarios, increase the weighting coefficient of formation position achievement events. .

[0075] Deviation mapping function, different function forms are selected according to the event type: (1) Obstacle avoidance events ( ): Choose a monotonically increasing function , This indicates the formation position error. The greater the formation deviation, the higher the expected intensity of the obstacle avoidance event, prompting the UAV to quickly adjust its attitude to avoid obstacles. (2) Formation position achievement event ( ): Select Gaussian function When the formation deviation is small, the expected intensity is high, prompting the UAVs to maintain their formation position; when the formation deviation is too large, the expected intensity tends to stabilize, avoiding control input saturation. (3) Communication quality degradation events ( ): Choose a monotonically decreasing function , The deviation between SNR and the threshold. To adjust parameters, the greater the communication deviation, the higher the expected intensity, prompting the UAV to adjust its communication strategy; (4) Formation change event ( ): Selecting a piecewise function , This ensures that the intensity is controllable during the transformation process and avoids over-adjustment.

[0076] Among them, the expected event intensity function with upper limit constraint , and the The first drone Class events at time event intensity function Interrelationships: This represents the actual event intensity, constructed based on a multivariate Hawkes process. It is determined by historical events within a sliding window, event interaction excitation coefficients, and a multi-core decay function, reflecting the current actual event state of the UAV; while It is the expected event intensity, based on the actual event intensity of S2 as a reference, combined with the formation position error. Calibration is performed to ensure that the desired intensity matches the actual control requirements and avoids deviating from the actual operating state of the drone.

[0077] This embodiment overcomes the shortcomings of traditional simple linear mapping by constructing a nonlinear mapping relationship with upper limit constraints. It selects an appropriate deviation mapping function according to different event types and sets an upper limit for event intensity to ensure that the control input is always within the carrying capacity of the UAV actuator, avoiding actuator overload and balancing control accuracy and equipment operation safety.

[0078] S4. Lightweight online parameter estimation is performed using the recursive moment matching method. To address the high computational cost of traditional MLE and EM algorithms, this invention employs a recursive moment matching method for online parameter estimation, based on historical event data within a sliding window. Iteratively update the parameters of the Hawkes process. The core advantage of the recursive moment matching method is that it only uses newly added event data to update parameters each time, without needing to perform global iteration on all historical data, thus greatly reducing computational complexity.

[0079] Specifically, It is the first The core parameter set of the Hawkes process for the UAV is used. All three parameters are derived from a multivariate Hawkes process event interaction model. Lightweight online estimation is performed on these parameters to improve model accuracy and support subsequent prediction and optimization. More specifically, if these parameters are set to pre-defined initial values, they cannot adapt to dynamic environmental changes. Therefore, based on historical event data within a sliding window, the parameters are iteratively updated to align with the event interaction patterns in actual UAV operation, thereby improving the accuracy of the event interaction model. The updated parameters are shown below. It will be directly used for future event intensity prediction in S5 (substituting into the prediction formula to calculate the event intensity in the future time domain) and distributed optimization in S6 (constructing a cost function through the predicted intensity), and is a key link connecting event modeling and prediction optimization.

[0080] The recursive form of the parameter update rule is as follows: (5) In formula (5): For the first The parameter values ​​for the next iteration. For the first The parameter values ​​for the next iteration; The step size is determined by the control cycle. Adjustments should be made to control the cycle length and step size to ensure the stability of parameter updates. It is a set of Hawkes process parameters The gradient operator is used to measure the rate and direction of change of the objective function as a function of parameters. To construct the objective function for moment matching, we construct a parameter optimization objective function by matching the theoretical moments and actual moments of event intensity. This enables rapid convergence of parameters.

[0081] Actual moments: These are statistical results from real historical event data and serve as the "benchmark" for parameter optimization. Theoretical moments: These are the statistical results of event intensity output by the model under the current parameters, and are the "objects" that need to be optimized.

[0082] The computation time of the recursive moment matching method is only 1 / 5 to 1 / 3 of that of the traditional EM algorithm, which can meet the computing power requirements of real-time UAV control. At the same time, the historical data management strategy of the sliding window further reduces the amount of data processing for parameter estimation.

[0083] This embodiment replaces the traditional parameter estimation algorithm with high computational overhead. Based on historical event data within a sliding window, it iteratively optimizes the relevant parameters of the Hawkes process using a recursive update method. It eliminates the need for global iterative calculation of all historical data, significantly reducing computational complexity and making it suitable for practical application scenarios where UAV onboard resources are limited.

[0084] S5. Predict the intensity of future events based on the current state and historical data; Based on the Hawkes process parameters estimated by the UAV at the current moment and the historical event data within the sliding window, the intensity of various types of UAV events in the future time domain is predicted using the constructed event intensity function.

[0085] Specifically, S5 is as follows: At the present moment drones Based on the estimated Hawkes process parameters and the collection of historical events within the sliding window Predicting future time domain The intensity of various events within itself The prediction formula is as follows: (6) In formula (6), It is the integration variable, representing the integration interval. The traversal time within the interval is used to traverse all time points within that interval; It is a drone The Class events at time Based on historical event sets The intensity of the event.

[0086] In this formula, the last term reflects the contribution of potential future events to the current intensity prediction, which is the core manifestation of the self-excitation characteristic of the Hawkes process. Since this prediction formula involves a system of integral equations, direct solution is difficult. This invention employs an iterative numerical approximation method, limiting the number of iterations to [number missing]. This approach ensures both prediction accuracy and real-time performance. The specific iterative steps are as follows: First, ignore the contribution of future events to obtain initial prediction values; then, substitute these initial prediction values ​​into the integral term to obtain the prediction values ​​after one iteration; finally, determine whether to perform a second iteration based on the convergence of the iterations. Through a finite number of iterations, the prediction results of event intensity are quickly obtained, providing a basis for subsequent optimization solutions.

[0087] S6. Construct a distributed optimization problem with consistency constraints to obtain the control input sequence; To achieve a unified goal of cluster collaboration, this invention introduces a neighbor cost function consistency constraint into the local optimization problem of each UAV, and constructs a constrained optimization objective function, including the cost function and the constraint conditions.

[0088] Build each drone The optimization objective is to minimize its own cost function. And minimize, including: minimizing the intensity of predicted events. With expected event intensity The deviation is used to achieve the core objective of formation control, as well as the regularization term of the control input, which is used to balance control accuracy and energy consumption and avoid excessive control input. At the same time, constraints are set, including: ensuring that the deviation of the cost function value between the current drone and the neighboring drone does not exceed the preset consistency error limit, and ensuring that the state and control input of the drone are within the set safety range; Solving the objective function yields the optimal future control input sequence within a preset time range that satisfies the constraints.

[0089] The objective function is optimized as follows: (7) In formula (7), , indicating drone The future control input sequence within the control time domain. Indicates future time The corresponding number The first drone The expected event intensity of the event type; The weight for the event intensity deviation; To control the weights of the inputs; Scene identification is determined autonomously by the drone through environmental perception; for example, when... In obstacle avoidance scenarios, increase , reduce Prioritize obstacle avoidance performance when To maintain the scene for formation, increase Increase While maintaining formation position, energy consumption is reduced.

[0090] For consistency constraints, drones are required The cost function and neighboring drones The deviation of the cost function value does not exceed Upper limit of consistency error Depending on the mission scenario, the higher the formation accuracy requirement, the better. The smaller the value, the better. This constraint ensures that the optimization goals of the drone swarm remain consistent, avoiding coordination disagreements.

[0091] For dynamic constraints, represent the dynamic model of the UAV, describing how the UAV's state changes with control input; and These are state constraints and input constraints, respectively, to ensure that the state and control inputs of the UAV are within a safe range.

[0092] In summary, by minimizing the cost function By satisfying all constraints, we can finally obtain the first... The optimal future control input sequence for a drone in the control time domain , the optimal control input sequence Substitute into the cost function , can obtain the first The optimal cost function value of a drone .

[0093] Drones only perform The first element (The optimal control input at the current moment) drives the UAV to adjust its state vector, gradually reaching the desired formation state after the UAV triggers the event. The control input for subsequent moments will be used in the next control cycle. By using the rolling optimization of S11, a new solution is obtained. This ensures adaptation to dynamic environmental changes.

[0094] The distributed optimization technique with neighbor consistency constraints disclosed in this embodiment introduces neighbor cost function consistency constraints into the local optimization problem of each UAV, clearly sets an upper limit for consistency error, ensures that the optimization goal of each UAV is consistent with that of neighboring UAVs, eliminates cluster "internal friction" in distributed control, and improves the overall integrity and collaborative stability of UAV swarm formation.

[0095] Preferably, in S6, the objective function is solved using stochastic gradient descent online optimization. Because S6 minimizes the cost function The optimization problem is highly nonlinear and nonconvex, making it difficult to apply traditional analytical solutions. Therefore, stochastic gradient descent (SGD) combined with an early stopping strategy is used for online optimization, which significantly reduces computation time while ensuring optimization performance.

[0096] The gradient update rules are as follows: (8) In formula (8), For the first The control input sequence for each iteration; The scene-adaptive learning rate is based on the scene identifier. Adjustments are made. In complex dynamic scenarios (such as obstacle avoidance and formation changes), the learning rate is reduced to improve the stability of the optimization; in simple static scenarios (such as formation maintenance), the learning rate is increased to accelerate the convergence speed of the optimization. The gradient of the cost function with respect to the control input sequence is used to backpropagate the gradient through the adjoint method or automatic differentiation, and the gradient value is calculated quickly.

[0097] The core of the early stopping strategy is to limit the number of iterations. The iteration can be stopped without waiting for the gradient to fully converge, and the current optimal control sequence can be output. This early stopping strategy effectively reduces computation time, meeting the requirements of real-time UAV control. Experiments show that 3-5 iterations are sufficient to achieve good optimization results for the control input sequence. Further increasing the number of iterations has limited effect on improving the optimization performance but significantly increases computation time.

[0098] The final solution yields the drone Predict the optimal control input sequence in the time domain It also outputs the optimal control command at the current control moment. The optimal control input sequence obtained by solving the problem. The optimal control quantity at the current moment The output is sent to subsequent stages to provide the optimal control input for the next step of executing control commands, rolling time-domain updates, and closed-loop iterations.

[0099] The stochastic gradient descent combined with early stopping online optimization solution technique disclosed in this embodiment is used for nonlinear and nonconvex optimization problems. It adopts a scene-adaptive learning rate adjustment strategy and uses an early stopping mechanism to limit the number of iterations. While ensuring the optimization effect, it significantly reduces the optimization solution time and meets the real-time requirements of UAV swarm collaborative control.

[0100] S7. Execute control and record events, then perform rolling optimization and repeated execution.

[0101] Each drone executes the first element of the optimal future control input sequence to achieve the desired formation state after the drone triggers an event, and then detects whether various events have been triggered, with the frequency of event detection synchronized with the control cycle; If an event is triggered, the event is recorded; then a new round of drone cooperative formation control continues.

[0102] S71, Execution Control and Event Detection; Each drone The control sequence obtained by performing optimization The first element This drives the UAV to adjust its state vector, gradually reaching the desired formation state after the UAV triggers an event. In other words, it only executes the optimal control input for the current moment, and the control input for subsequent moments is updated through rolling optimization in the next control cycle. This rolling optimization execution method can effectively cope with changes in the dynamic environment and improve the adaptability of control.

[0103] Meanwhile, the drone monitors its own status information (position, speed, heading), environmental information (obstacle distance, wind speed and direction), and communication information (signal-to-noise ratio with neighbors) in real time, comparing them with the quantization trigger thresholds set in S1 to detect various events. Whether it is triggered. The frequency of event detection is synchronized with the control cycle to ensure that the event status can be updated in a timely manner within each control cycle.

[0104] S72, Event logging and sliding window updates; If drone At any moment The first was detected When a class event is triggered, immediately send the event information. Write the event list to the local machine. To reduce communication overhead, the drone broadcasts an event summary via neighbor communication only when a new event is detected. The summary information contains only the event type, time of occurrence, and drone number, without redundant data.

[0105] After receiving an event summary broadcast by a neighboring drone, the drone verifies the reasonableness of the event's timing (difference from local time) through the communication link. After successful verification, update the local sliding window history event set. Otherwise, discard the event summary. The update rule is: if the number of events in the event set does not exceed the window length... If the number of events exceeds the window length, then add a new event directly; If the earliest event occurs, the new event is deleted, and then a new event is added. This sliding window update strategy keeps the historical event set lightweight, reducing storage and computational overhead.

[0106] S73, Rolling Optimization and Repeated Execution; Reaching the next control cycle The drone will update the current time to The historical event collection has been updated to Then, S5 to S7 are executed repeatedly, entering a new round of event intensity prediction, distributed optimization, control execution, and event update process, forming a closed-loop rolling optimization control.

[0107] Through this closed-loop rolling optimization method, drone swarms can continuously adapt to changes in the dynamic environment, achieving adaptive collaborative formation control. For example... Figure 2As shown, taking three adjacent drones as an example, drone 1, drone 2, and drone 3 respectively perform event detection, Hawkes modeling, parameter estimation, optimization solution, and control execution. Environmental perception provides all drones with unified environmental and self-state inputs. Adjacent drones only exchange core information such as drone number, the time of occurrence of scenario-based collaborative events, and event type through neighbor communication links. A decentralized, fully distributed, event-driven architecture is adopted. Through local rolling optimization and neighbor consistency constraints, adaptive formation control with local autonomous decision-making and global collaborative consistency is formed, effectively reducing communication bandwidth consumption and onboard computing load.

[0108] Regardless of the type of interference encountered (such as strong winds, obstacles, or communication interruptions), the drones can adjust their control strategies through real-time prediction and optimization to ensure the stability of the formation and the safety of the mission.

[0109] The closed-loop rolling optimization adaptive control technology used in this embodiment constructs a closed-loop rolling optimization process of "event prediction - optimization solution - control execution - event update". Combined with the technical design of each preceding step, the relevant process is repeatedly executed in each control cycle to realize the adaptive adjustment of the UAV swarm to complex dynamic environments, continuously optimize the control strategy, enhance the robustness of the swarm in dynamic interference scenarios, and ensure the long-term stability of formation control.

[0110] The method used in this embodiment is compared with the formation control effect of existing technologies, for example... Figure 3 It achieves breakthrough improvements in both dynamic obstacle avoidance trajectory and formation positioning accuracy, as described below: Figure 3 The left image in the figure is a comparison of dynamic obstacle avoidance trajectories. The horizontal axis represents the X position and the vertical axis represents the Y position. The black solid dots in the figure mark the positions of obstacles. The obstacle avoidance trajectory of the traditional method is represented by a red dashed line, which shows obvious oscillations and a broken line shape near the obstacle. The obstacle avoidance trajectory of the method of the present invention is represented by a blue solid line, which forms a smooth path without corners at the obstacle, and achieves smooth dynamic obstacle avoidance. Figure 3 The right-hand figure is a bar chart comparing formation positioning accuracy. The horizontal axis represents three typical task scenarios: formation maintenance, dynamic obstacle avoidance, and formation transformation. The vertical axis represents the average formation deviation. In the figure, red bars represent the formation deviation of the traditional method, and blue bars represent the formation deviation of the present invention. In the formation maintenance scenario, the average deviation of the traditional method is 0.45, while that of the present invention is 0.24, resulting in an accuracy improvement of approximately 46.7%. In the dynamic obstacle avoidance scenario, the average deviation of the traditional method is 0.72, while that of the present invention is 0.41, resulting in an accuracy improvement of approximately 43.1%. In the formation transformation scenario, the average deviation of the traditional method is 0.58, while that of the present invention is 0.38, resulting in an accuracy improvement of approximately 34.5%.

[0111] The comparison curve of the multi-kernel function decay law in the method used in this embodiment is as follows: Figure 4 As shown. Figure 4 This visually illustrates the decay characteristics of the three decay kernel functions, with the horizontal axis representing time. The vertical axis represents the decay kernel function value. The graph contains three comparison curves, and their specific characteristics and parameters are explained below: The solid blue line (exponential decay kernel) contains the decay coefficient. The curve follows The increase shows a smooth exponential decreasing trend, with the initial value close to 1. When the function value decays to approximately 0.09, it demonstrates the rapid decay characteristic of the exponential decay kernel, making it suitable for event scenarios requiring rapid response, such as obstacle avoidance. The orange solid line (power-law decay kernel) represents the decay coefficient. This curve effectively solves the problem of traditional power-law kernels in... The smaller amplitude explosion problem, the overall amplitude matches the exponential decay kernel, and the curve is in It initially takes a value of approximately 1.87, then decreases rapidly. At that time, the decay rate tends to be flat, which is suitable for event scenarios such as formation changes that require long-tail influence; The solid green line (segmented decay kernel) represents the time boundary points. The curve is in The interval completely overlaps with the blue exponential decay kernel curve. The interval switching is to an orange power-law decay kernel curve, which takes into account the fast response advantage of the early exponential decay kernel and the long-tail decay characteristics of the later power-law decay kernel, and is suitable for complex dynamic event scenarios such as communication quality degradation.

[0112] Example 2 This embodiment also provides an electronic device, including: At least one processor; and The memory stores instructions that, when executed by the at least one processor, cause the at least one processor to perform a Hawkes process-based UAV swarm cooperative formation control method as described above.

[0113] In this embodiment, the electronic device may include, but is not limited to: personal computer, server computer, workstation, desktop computer, laptop computer, notebook computer, mobile computing device, smartphone, tablet computer, cellular phone, personal digital assistant (PDA), handheld device, messaging device, wearable computing device, consumer electronic device, etc.

[0114] Example 3 This embodiment also provides a machine-readable storage medium storing executable instructions that, when executed, cause the machine to perform a Hawkes process-based UAV swarm cooperative formation control method as described above.

[0115] Specifically, a system or apparatus equipped with a readable storage medium may be provided, on which software program code implementing the functions of any of the embodiments described above is stored, and the computer or processor of the system or apparatus can read and execute the instructions stored in the readable storage medium.

[0116] In this case, the program code read from the readable medium itself can perform the functions of any of the above embodiments, and therefore the machine-readable code and the readable storage medium storing the machine-readable code constitute a part of this specification.

[0117] Examples of readable storage media include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD-RW), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, program code can be downloaded from a server computer or the cloud via a communication network.

[0118] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0119] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0120] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0121] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0122] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the technical solutions of the present invention, and are not intended to limit the specific implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the claims of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A method for cooperative formation control of UAV swarms based on Hawkes processes, characterized in that, The method includes: S1. Initialize the state vector, control input, control constraints, and sliding window historical event set of the drone cluster; at the same time, define the scenario-based collaborative event types and set the event trigger thresholds; S2. Based on the type of events triggered by the drone, construct an event intensity function for the event type of the drone involved through a multivariate Hawkes process, and define the influence pattern of the event type. S3. Set the expected event intensity of the drone-triggered event according to the trigger event type; S4. The recursive moment matching method is used for online parameter estimation. Based on historical event data within the sliding window, the parameters of the Hawkes process are iteratively updated. S5. Based on the Hawkes process parameters estimated by the UAV at the current moment and the historical event data within the sliding window, the intensity of various types of UAV events in the future time domain is predicted based on the constructed event intensity function to obtain the predicted event intensity. S6. Construct and minimize the cost function of the UAV, including minimizing the deviation between the predicted event intensity and the expected event intensity, as well as the regularization term of the control input; At the same time, constraints are set, including: ensuring that the deviation of the cost function value between the current drone and the neighboring drone does not exceed the preset consistency error limit, and ensuring that the state and control input of the drone are within the set safety range; After solving, the optimal future control input sequence within the preset time range that satisfies the constraints is obtained; S7. Each UAV executes the first element of the optimal future control input sequence to achieve the desired formation state after the UAV triggers an event. Then, it detects whether various events are triggered, and the frequency of event detection is synchronized with the control cycle. If an event is triggered, record the event and continue with a new round of drone collaborative formation control.

2. The method for cooperative formation control of UAV swarms based on Hawkes processes according to claim 1, characterized in that, The definition of scenario-based collaborative event types and the setting of event trigger thresholds include: Obstacle avoidance events When drones The distance to obstacles or teammates is less than the safe threshold. At that time, obstacle avoidance maneuvers are triggered, and the safety threshold is reached. Determined based on the drone's fuselage size and flight speed; Formation Position Achievement Event When drones Relative positional deviation from neighboring drones Less than the tolerance threshold When the formation is deemed to have reached the desired state that triggered the event, the tolerance threshold is determined. Set according to the formation accuracy requirements of the mission; Communication quality degradation events When drones The signal-to-noise ratio (SNR) of the communication link with neighboring drones is below a threshold. When this occurs, it is determined to be a communication quality degradation; threshold Configured according to the performance of the communication module and data transmission requirements; Formation change event When a drone receives a formation change command, and the deviation between its current position and the target position is greater than the change threshold... When this occurs, a formation change behavior is triggered; the change threshold... Set according to the amplitude and speed requirements of formation changes; event The time of occurrence is recorded as ,in The event ordinal number represents the drone. No. The first type of event The next time it occurs.

3. The method for cooperative formation control of UAV swarms based on Hawkes processes according to claim 2, characterized in that, The function for constructing event intensity specifically includes: For the The first drone Class events, at time Event intensity The intensity function is constructed based on a multivariate Hawkes process and is as follows: （1） In formula (1), For drones No. The base intensity of the event type is preset according to the task scenario; The event interaction excitation coefficient represents the drone. The occurrence of the first Similar events, for drones The occurrence of the first The intensity of the impact of such events; A collection of historical events within a sliding window, including the most recent Individual event data, For drones The first occurrence The first type of event The next occurrence time; For decay kernel function, For kernel function type indexes, the drone adaptively selects based on the event type: Exponential decay kernel, : , used to define obstacle avoidance events Events related to formation positioning , Indicates the time difference, i.e., the current moment. With the moment of historical events The difference is , The decay coefficient of the exponentially decaying kernel; Power-law decay kernel, : Used to define formation change events In the formula, The decay coefficient of the power-law decay kernel; Segmented decay kernel, : （2） Communication quality degradation events used for definition In the formula, The first half of the segmented decay kernel The exponential decay coefficient; The latter half of the segmented decay kernel The power-law decay coefficient; This is the time boundary point for the segmented decay kernel.

4. The method for cooperative formation control of UAV swarms based on Hawkes processes according to claim 3, characterized in that, S3 specifically includes: S31. Define formation position error for: （3） In formula (3), Indicates the first The drone relative to the first The desired location of the drone; For the first A drone at all times The position vector; For the first A drone at all times The position vector; S32. Design the expected event intensity function with upper limit constraint. ,as follows: （4） In formula (4), For the first The intensity limit of such events is determined by the response capability of the drone's actuators; For the first Event weight coefficients are used to adjust the priority of different types of events; For the deviation mapping function, different function forms are selected according to the event type: (1) Obstacle avoidance events, Choose a monotonically increasing function. , Indicates the formation position error; (2) Formation positioning achievement event, Choose Gaussian function ; (3) Communication quality degradation events, Choose a monotonically decreasing function. , The deviation between SNR and the threshold. To adjust the parameters; (4) Formation change event, : Choosing a piecewise function , .

5. The method for cooperative formation control of UAV swarms based on Hawkes processes according to claim 4, characterized in that, The parameters of the iterative update of the Hawkes process specifically include: Online parameter estimation is performed using a recursive moment matching method based on historical event data within a sliding window. Iteratively update the parameters of the Hawkes process. , is the The core parameter set for the Hawkes process of launching a drone. For drones No. The basic strength of the event type; The event interaction excitation coefficient represents the drone. The occurrence of the first Similar events, for drones The occurrence of the first The intensity of the impact of such events; The attenuation coefficient; The recursive form of the parameter update rule is as follows: （5） In formula (5), For the first The parameter values ​​for the next iteration. For the first The parameter values ​​for the next iteration; The step size is determined by the control cycle. Adjustment; It is a set of Hawkes process parameters Operators for finding the gradient; Let be the objective function for moment matching.

6. The method for cooperative formation control of UAV swarms based on Hawkes processes according to claim 5, characterized in that, S5 specifically includes: At the present moment drones Based on the estimated Hawkes process parameters and the collection of historical events within the sliding window , For drones No. The basic strength of the event type; The event interaction excitation coefficient represents the drone. The occurrence of the first Similar events, for drones The occurrence of the first The intensity of the impact of such events; The attenuation coefficient is used to predict future time domain conditions. The intensity of various events within itself ,as follows: （6） In formula (6), It is the integration variable, representing the integration interval. The traversal time within the interval is used to traverse all time points within that interval; It is a drone The Class events at time Based on historical event sets The intensity of the event.

7. The method for cooperative formation control of UAV swarms based on Hawkes processes according to claim 6, characterized in that, S6 specifically includes: In the local optimization problem of each drone, a neighbor cost function consistency constraint is introduced to construct a constrained optimization objective function. For each drone... The optimization objective is to minimize its own cost function. At the same time, it ensures that the deviation of the cost function from that of neighboring drones does not exceed the preset consistency error limit. And to keep the drone's status and control inputs within a set safety range; Cost function It consists of two parts. The first part is the integral term of the event intensity bias, which is used to minimize the predicted event intensity. With expected event intensity The first part is the deviation; the second part is the regularization term of the control input, used to balance control accuracy and energy consumption: The objective function is optimized as follows: （7） In formula (7), , indicating drone The sequence of future control inputs in the control time domain; Indicates future time The corresponding number The first drone The expected event intensity of the event type; The weight for the event intensity deviation; To control the weights of the inputs; The scene is identified autonomously by the drone through environmental perception. For consistency constraints, drones are required The cost function and neighboring drones The deviation of the cost function value does not exceed upper limit of consistency error Based on the task scenario; For dynamic constraints, represent the dynamic model of the UAV, describing how the UAV's state changes with control input; and These are state constraints and input constraints, respectively. The objective function is solved using stochastic gradient descent online optimization to minimize the cost function. Satisfying consistency constraints and dynamic constraints, the final result is obtained. The optimal future control input sequence for a drone in the control time domain ; The optimal control input sequence Substitute into the cost function , can obtain the first The optimal cost function value of a drone .

8. The method for cooperative formation control of UAV swarms based on Hawkes processes according to claim 7, characterized in that, Specifically, S7 includes: S71, Execution Control and Event Detection; Each drone The control sequence obtained by performing optimization The first element This drives the drone to adjust its own state vector to achieve the desired formation state after the drone triggers an event; the control input in subsequent moments will be updated through rolling optimization in the next control cycle. Meanwhile, the drone monitors its own state vector, environmental information, and communication information in real time, compares them with set trigger thresholds, and detects various events. Whether it is triggered, and the frequency of event detection is synchronized with the control cycle; S72, Event logging and sliding window updates; If drone At any moment The first was detected When a class event is triggered, immediately send the event information. Write the event list to the local machine; The drone broadcasts an event summary via neighbor communication only when a new event is detected. The summary includes information such as the event type, the time of occurrence, and the drone number. After receiving the event summary broadcast by a neighboring drone, the drone verifies the reasonableness of the event's time of occurrence, i.e., its difference from the local time, through the communication link. After successful verification, update the local sliding window history event set. Otherwise, discard the event summary; The update rule is: if the number of events in the event set does not exceed the window length. If the number of events exceeds the window length, then add a new event directly; If so, delete the earliest occurring event and then add the new event; S73, Rolling Optimization and Repeated Execution; Reaching the next control cycle The drone will update the current time to The historical event collection has been updated to ; Then, S5 to S7 are executed repeatedly to enter a new round of drone collaborative formation control and event updates, forming a closed-loop rolling optimization control.

9. An electronic device, characterized in that, The electronic device includes: processor; A memory on which computer programs that can run on the processor are stored; When the computer program is executed by the processor, it implements the steps of the Hawkes process-based UAV swarm cooperative formation control method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 8.

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