A Random Delay UAV Formation Control Method and System Based on Event Triggering Mechanism

Abstract

This invention provides a method and system for random-delay UAV formation control based on an event-triggered mechanism, belonging to the field of UAV formation control technology. The invention establishes a global inertial coordinate system and normalizes the original motion state to a standard motion state; it defines the true value of lumped disturbance using heterogeneous dynamic constraint equations; it designs a nonlinear disturbance observer with auxiliary variables to calculate the estimated value of lumped disturbance approximating the true value; it constructs a full-state coupled dynamic event-triggered mechanism to calculate a dynamic triggering threshold that includes a minimum interval protection term and is negatively correlated with the disturbance magnitude; it corrects neighbor nodes with random communication delays based on the estimated value of lumped disturbance to obtain the predicted neighbor motion state; it uses a stable manifold neural network to infer the optimal costate vector and combines it with disturbance feedforward compensation to generate physical control commands. This invention improves the formation's anti-interference capability while reducing communication load.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) formation control technology, specifically to a random time-delay UAV formation control method and system based on an event-triggered mechanism. Background Technology

[0002] With the widespread application of drone swarm technology in fields such as power line inspection, emergency rescue, and smart cities, multi-agent formation control has become a core direction for the integration of automation technology and the aviation industry. In actual operations, drone formations not only need to maintain high-precision coordinated formations but also need to cope with stringent constraints on communication bandwidth and computing resources. Therefore, applying advanced control algorithms to flight systems to achieve coordinated optimization of "communication-computation-control" is a key path to improve swarm efficiency.

[0003] In existing technologies, some progress has been made in optimizing control and reducing communication load for UAV formations. A paper published in the journal *Automatika*, titled "Optimal control for quadrotors UAV based on deep neural network approximations of stable manifold of HJB equation," discloses a method that uses a deep neural network to approximate the stable manifold of the HJB equation. This method replaces online partial differential equation solving with offline training of the neural network, achieving millisecond-level optimal control signal generation and significantly improving control real-time performance. On the other hand, publication number CN117991823A discloses a random-delay UAV formation control method based on an event-triggered mechanism. By setting trigger conditions, data is transmitted only when necessary, thereby reducing network load.

[0004] However, the aforementioned technologies still have significant shortcomings when facing the complex and ever-changing nonlinear physical disturbances in real flight environments. First, existing cooperative control schemes are typically based on idealized deterministic dynamic models. These methods often fail to capture constantly changing real-time disturbances, thus simplifying airflow gusts, propeller aerodynamic disturbances, and airframe gyroscopic effects to Gaussian white noise or ignoring them completely, lacking active observation and feedforward compensation mechanisms for lumped disturbances. When encountering sudden wind or load changes that cause model parameter mismatch, this open-loop optimal control law is prone to failure, leading to tracking error divergence. Second, in environments with strong disturbances, traditional event-triggered mechanisms face severe challenges: external disturbances can cause drastic fluctuations in the system state. If the trigger threshold is not dynamically coupled with the disturbance intensity, the triggering conditions can be frequently met, leading to the Zeno phenomenon. This not only causes the control command update frequency to exceed the hardware processing capacity but also generates a large number of redundant data packets, worsening the communication load and making the mechanism originally intended to save bandwidth counterproductive. Therefore, there is an urgent need for a comprehensive control scheme that can both retain adaptability to random time delays and solve the problems of model mismatch and communication-triggered storms under strong interference through active anti-disturbance mechanisms.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a random time-delay UAV formation control method and system based on an event-triggered mechanism to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] The random time-delay UAV formation control method based on event-triggered mechanism includes the following steps:

[0009] A global inertial coordinate system is established to acquire the original motion state of each node in the formation cluster in real time and perform per-unit processing to obtain the standard motion state. The original motion state includes position, velocity, rotation angle and angular velocity.

[0010] Based on the standard motion state, physical constraints are established using the Newton-Euler equations, heterogeneous dynamic constraint equations for translational and rotational channels are constructed, and the true value of lumped disturbance is defined.

[0011] By combining heterogeneous dynamic constraint equations and introducing auxiliary variables, the differential operation on the motion state is transformed into an integral operation. A dual-channel nonlinear disturbance observer is designed, and the lumped disturbance estimate approximates the true value of the lumped disturbance is calculated through nonlinear iteration.

[0012] A full-state coupled dynamic event triggering mechanism is constructed, and a dynamic triggering threshold is calculated. The dynamic triggering threshold is negatively correlated with the magnitude of the lumped interference estimate and includes a minimum interval protection term that decays exponentially with time. When the comprehensive state error exceeds the dynamic triggering threshold, communication is triggered, and the standard motion state is sent to the neighboring nodes and a request to obtain the standard motion state is sent to the neighboring nodes.

[0013] Based on the lumped interference estimate, the motion state of neighboring nodes with random communication delays is corrected for interference to obtain the predicted neighbor motion state.

[0014] A cascaded optimal disturbance rejection controller is constructed. The position and attitude coordination error of the nodes is calculated. The position and attitude coordination error of the nodes is input into an offline trained stable manifold neural network to directly infer the optimal costate vector. The optimal nominal control law is obtained by solving the problem. The lumped disturbance estimate is introduced for feedforward compensation. The final physical control command is generated and executed.

[0015] Furthermore, a three-dimensional rectangular coordinate system is established with the ground control base station as the origin, the horizontal plane as the XY axis plane, and the vertical plane as the XZ axis plane. Each device in the formation cluster is regarded as a different node. The original motion state of each node in the formation cluster is collected in real time through airborne sensors. The original motion state includes the original position vector, the original velocity vector, the original attitude angle vector, and the original angular velocity vector.

[0016] The original motion states of each node are normalized according to the standard unit length, standard unit speed, standard unit attitude angle and standard angular velocity units preset by the relevant staff, so as to obtain the standard motion state of each node.

[0017] Furthermore, physical constraints are established using the Newton-Euler equations based on the standard motion states of each node.

[0018] Based on Newton's second law, and combined with the standard velocity vector in a standard state of motion, we construct the... The equation relating the translational acceleration and force at each node, the first node... The product of the standard mass and standard acceleration vector of each node is equal to the sum of the standard thrust vector, the standard gravity vector, and the true value of the translational lumped disturbance, thus obtaining the dynamic constraint equation of the translational channel.

[0019] Based on Euler's equations for rigid body dynamics, and combined with the standard angular velocity vector in the standard motion state, an equation is constructed between standard angular acceleration and torque. The product of the standard moment of inertia matrix and the standard angular acceleration vector is equal to the sum of the standard control torque vector minus the gyroscopic effect torque term and the true value of the rotational lumped disturbance. The gyroscopic effect torque term is obtained by performing a cross product operation on the standard angular velocity vector and the product of the standard moment of inertia matrix and the standard angular velocity vector. The dynamic constraint equations of the rotation channel are then obtained.

[0020] Furthermore, for translational disturbance observers;

[0021] Based on the auxiliary variable transformation method in the design criteria for nonlinear disturbance observers in control theory, the first... The translational auxiliary variable of the nth node in the translational disturbance estimation calculation is defined as the nth node. The translational auxiliary variable of the nth node and the nth node The estimated translational lumped disturbance of the nth node satisfies a linear transformation relationship, specifically the nth node. The translational auxiliary variable of the nth node is equal to the nth node. The translational lumped disturbance estimate of the nth node minus the translational correction term, where the translational correction term is the preset translational observer gain matrix, the nth node, and the nth node, respectively. The product of the standard mass and standard velocity vector of each node;

[0022] The first The translational auxiliary variable of the nth node and the nth node The linear relationship between the estimated translational lumped disturbance values ​​of the nodes is differentiated with respect to a preset unit time, and the nth node is set according to the negative feedback mechanism. The rate of change of the estimated translational lumped disturbance of the nth node and the 1st node The true value of the translational lumped disturbance of the nth node and the nth node The difference in the estimated translational lumped disturbance of the nth node is proportional to the difference in the estimated values ​​of the nth node. Combined with the dynamic constraint equations of the translational channel, the nth node is calculated. The sum of the standard thrust vector, standard gravity vector, translational auxiliary variable from the previous moment, and translational correction term for each node is then multiplied by the negative value of a preset translational observer gain matrix to obtain the result. The rate of change of the translational auxiliary variable of each node within a preset unit of time;

[0023] Combined with the The rate of change of the translational auxiliary variable at the nth node within a preset unit time is obtained by numerical integration iteration to obtain the nth node at the current time. The translational auxiliary variable of the nth node is substituted into the current time step of the nth node. The translational auxiliary variable of the nth node and the nth node The linear relationship between the estimated translational lumped disturbance values ​​of the n nodes is used to calculate the current time n. Estimates of the translational lumped disturbance of each node;

[0024] The principle for the rotational disturbance observer is the same as that for the translational disturbance observer.

[0025] Construct the first The rotational auxiliary variable of the nth node in the rotational disturbance estimation operation is defined as the nth node. The rotation auxiliary variable of the nth node and the nth node The rotation lumped disturbance estimate of the nth node satisfies a linear transformation relationship, specifically the nth node. The rotation auxiliary variable of the nth node is equal to the nth node. The rotation lumped disturbance estimate of the nth node minus the rotation correction term, where the rotation correction term is the preset rotation observer gain matrix, the th node's rotation lumped disturbance estimate, the lumped disturbance estimate of the nth node, the rotation correction term is the preset rotation observer gain matrix ... The product of the standard moment of inertia matrix and the standard angular velocity vector of each node;

[0026] The first The rotation auxiliary variable of the nth node and the nth node The linear relationship between the estimated lumped disturbance of the rotation at the nth node and the preset unit time is differentiated, and combined with the dynamic constraint equations of the rotation channel, the nth node is calculated. The vector sum of the standard control torque vector of each node, the rotation auxiliary variable of the previous moment, and the rotation correction term, minus the gyroscopic effect torque term, and then multiplying the final difference vector by the negative value of the preset rotation observer gain matrix, yields the result. The rate of change of the rotation auxiliary variable of each node within a preset unit of time;

[0027] Combined with the The rate of change of the rotation auxiliary variable of the nth node within a preset unit time is obtained by numerical integration iteration to obtain the nth node at the current time. The rotation auxiliary variable of the nth node is substituted into the nth node. The rotation auxiliary variable of the nth node and the nth node The linear relationship between the estimated lumped disturbance of the rotation of the nth node is used to calculate the current time. Estimated lumped disturbance of rotation at each node.

[0028] Further, calculate the first The magnitudes of the translational lumped interference estimates and rotational lumped interference estimates of each node are used to quantify the external interference intensity at the current moment, and the difference between the current time and the last triggered communication time is calculated as the elapsed time.

[0029] A fully coupled dynamic event triggering mechanism is constructed, and the dynamic triggering threshold at the current time is calculated. The specific calculation logic for the dynamic triggering threshold is as follows:

[0030] First, the interference adaptation component is calculated. The interference adaptation component is used to adaptively adjust the threshold according to environmental changes. The value is negatively correlated with the intensity of external interference. Specifically, it is obtained by dividing the preset basic error tolerance constant by the weighted sum of interference intensity. The weighted sum of interference intensity is composed of the weighted value of the magnitude of the translational lumped interference estimate, the weighted value of the magnitude of the rotational lumped interference estimate, and the sum of preset constant terms.

[0031] Secondly, the minimum interval protection term is calculated. The minimum interval protection term is used to prevent continuous triggering in a short period of time. Its value decays exponentially with the passage of time. Specifically, it is obtained by multiplying the preset protection term amplitude by the time decay factor. The time decay factor is calculated by performing a negative exponential operation based on the passage of time, so that the component reaches its maximum value at the moment after the communication is triggered and gradually approaches zero over time.

[0032] Finally, a threshold truncation determination is performed. The interference adaptation component is added to the minimum interval protection item to obtain a preliminary calculated threshold. This preliminary calculated threshold is compared with the preset lower limit of the dynamic trigger threshold, and the larger of the two values ​​is selected as the dynamic trigger threshold for the current time.

[0033] Furthermore, the magnitude of the deviation between the standard motion state and the expected motion state at the current moment is calculated using Euclidean distance to obtain the comprehensive state error at the current time. The comprehensive state error at the current time is compared with the dynamic trigger threshold at the current time. If the comprehensive state error at the current time is less than the dynamic trigger threshold at the current time, communication is not triggered. If the comprehensive state error at the current time is greater than or equal to the dynamic trigger threshold at the current time, communication is triggered, and the standard motion state is sent to neighboring nodes, and a request to obtain the standard motion state is sent to neighboring nodes. The expected motion state is the theoretical state at the current time calculated based on a preset spatiotemporal trajectory function, or the theoretical state at the current time derived from the baseline state sent to other nodes by the set leader node.

[0034] Furthermore, the first When a node receives a status data packet sent by a neighboring node, it calculates the difference between the timestamp in the data packet and the current time to obtain the random communication delay, and then normalizes it to obtain the standard random communication delay.

[0035] For the The translational state delay compensation prediction of each node's neighbor nodes is combined with the translational lumped interference estimate sent by the neighbor nodes and the dynamic constraint equations of the translational channel. Based on the kinematic Taylor expansion principle, the predicted neighbor standard position vector after interference compensation is calculated. The specific calculation logic is as follows: taking the standard position vector in the state data packet sent by the neighbor nodes as the reference, firstly, the linear displacement generated by the standard velocity vector of the neighbor nodes within the standard random communication delay is superimposed, and then the second-order dynamic correction displacement generated by the resultant external force is superimposed. The calculation method of the second-order dynamic correction displacement is as follows: calculate the vector sum of the standard thrust vector of the neighbor nodes and the translational lumped interference estimate, divide it by the standard mass of the neighbor nodes to obtain the equivalent acceleration, and then multiply the equivalent acceleration by half of the square of the standard random communication delay to obtain the predicted neighbor standard position vector.

[0036] For the The rotation state delay compensation prediction of each node's neighbor nodes is combined with the rotation lumped interference estimate sent by the neighbor nodes and the dynamic constraint equation of the rotation channel. Based on the Taylor expansion principle of rotational dynamics, the predicted standard attitude angle vector of the neighbor nodes after interference compensation is calculated. The specific calculation logic is as follows: taking the standard attitude angle vector in the state data packet sent by the neighbor nodes as the reference, firstly, the angular displacement generated by the standard angular velocity vector of the neighbor nodes within the standard random communication delay is superimposed, and then the second-order angular dynamic correction displacement generated by the resultant torque is superimposed. The calculation method of the second-order angular dynamic correction displacement is as follows: calculate the vector sum of the standard control torque vector of the neighbor nodes and the rotation lumped interference estimate, use the inverse matrix of the standard rotational inertia matrix of the neighbor nodes to transform the vector sum to obtain the equivalent angular acceleration, and then multiply the equivalent angular acceleration by half of the square of the standard random communication delay to obtain the predicted standard attitude angle vector of the neighbor nodes.

[0037] Furthermore, the comprehensive position error of the current node is calculated in a three-dimensional Cartesian coordinate system. The comprehensive position error of the current node is composed of a weighted sum of the cooperative error with neighboring nodes and the tracking error of the expected motion state at the current moment. Among them, the cooperative error is calculated by... The tracking error is obtained by calculating the difference between the standard position vector of the nth node, the predicted standard position vector of the neighboring nodes, and the expected distance vector, and then weighting the calculated differences. The difference between the standard position vector of the nth node and the expected motion state at the current moment is used to calculate the weighted sum. The combined position error of the nth node is input into a pre-trained position loop-stabilized manifold neural network to obtain the nth node's position error. The optimal co-state vector of the position loop in the HJB equation is the standard motion state of each node. Based on the optimal co-state vector of the position loop, combined with the optimal feedback control law formula and the difference between the estimated value of the translational set disturbance, the three-dimensional disturbance-resistant virtual resultant force vector is obtained.

[0038] The magnitude of the three-dimensional anti-disturbance virtual resultant force vector is calculated to obtain the final total thrust command of the UAV rotor. Based on the three-dimensional anti-disturbance virtual resultant force vector and the preset reference yaw angle, the first thrust is obtained by combining backstepping control. The desired attitude angle vector of the nth node is calculated. The difference between the standard attitude vector and the desired attitude angle vector in the standard motion state of the nth node is used to obtain the attitude tracking deviation vector. The combined position error of the nth node is input into the pre-trained attitude loop stable manifold neural network to obtain the nth node. The optimal co-state vector of the attitude loop in the HJB equation is the standard motion state of each node. Based on the optimal co-state vector of the attitude loop, combined with the optimal feedback control law formula and the difference between the estimated value of the rotation set disturbance, the final disturbance rejection torque command is obtained.

[0039] No. Each node adjusts its motion state according to the final total thrust command and the final disturbance rejection torque command.

[0040] A random-delay UAV formation control system based on an event-triggered mechanism, wherein the UAV formation control system is used to implement the above-mentioned UAV formation control method, including:

[0041] The data acquisition module is used to establish a global inertial coordinate system, acquire the original motion state of each node in the formation cluster in real time, and perform per-unit processing to obtain the standard motion state. The original motion state includes position, velocity, rotation angle and angular velocity.

[0042] The disturbance definition module is used to establish physical constraints based on the standard motion state using the Newton-Euler equations, construct heterogeneous dynamic constraint equations for translational and rotational channels, and define the true value of lumped disturbances.

[0043] The disturbance analysis module is used to design a dual-channel nonlinear disturbance observer by combining heterogeneous dynamic constraint equations. It introduces auxiliary variables to transform the differential operation on the motion state into an integral operation, and calculates the lumped disturbance estimate that approximates the true value of the lumped disturbance in real time through nonlinear iteration.

[0044] The event determination module is used to construct a fully coupled dynamic event triggering mechanism, calculate the dynamic triggering threshold, which is negatively correlated with the magnitude of the lumped disturbance estimate and includes a minimum interval protection term that decays exponentially over time. Communication is triggered when the state error exceeds the dynamic triggering threshold.

[0045] The communication module is used to correct the motion state of neighboring nodes with random communication delays based on the lumped interference estimate, so as to obtain the predicted motion state of the neighbors.

[0046] The formation correction module is used to construct a cascaded optimal disturbance rejection controller. It calculates the position and attitude coordination error of the nodes, inputs the position and attitude coordination error of the nodes into an offline trained stable manifold neural network to directly infer the optimal costate vector, solves to obtain the optimal nominal control law, and introduces the lumped disturbance estimate for feedforward compensation to generate the final physical control command and execute it.

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] This invention unifies the vastly different physical dimensions among heterogeneous nodes by establishing a global inertial coordinate system and standardizing the original motion state. Based on this, it constructs heterogeneous dynamic constraint equations using the Newton-Euler equations and defines the true value of lumped disturbances. Then, by introducing auxiliary variables, it transforms the differential operation on the motion state into an integral operation, designing a dual-channel nonlinear disturbance observer. This approach can obtain a lumped disturbance estimate approximating the true value of lumped disturbances in real time through nonlinear iteration without relying on accelerometers and avoiding differential noise amplification, thus accurately capturing nonlinear physical disturbances such as airflow and friction. Simultaneously, it directly infers the optimal costate vector by combining an offline-trained stable manifold neural network and solves for the optimal nominal control law. This method replaces the complex online solution process of the traditional HJB equations, improving the speed of control command generation. By introducing the lumped disturbance estimate into the optimal nominal control law for feedforward compensation, the final generated physical control command possesses both global convergence based on neural network optimization and the ability to actively cancel environmental disturbances, achieving a dual improvement in control accuracy and computational efficiency.

[0049] This invention also constructs a fully coupled dynamic event triggering mechanism, designing a dynamic triggering threshold that includes a minimum interval protection term that decays exponentially over time and is negatively correlated with the magnitude of the lumped interference estimate. This design allows the communication triggering condition to adaptively adjust its sensitivity based on the intensity of external interference, and triggers the minimum interval protection term in the initial stage when communication is first triggered, increasing the dynamic triggering threshold. This fundamentally avoids the phenomenon of unlimited triggering within a short period, significantly reducing the communication load while ensuring timely state updates. Furthermore, addressing the random latency problem in communication, the lumped interference estimate is used to perform interference correction on the motion state of neighboring nodes based on a dynamic model, obtaining the predicted motion state of neighbors. This prediction and compensation method based on physical force analysis corrects the trajectory deviation caused by simply extrapolating linear velocity, ensuring that the position and attitude coordination error calculation between nodes remains accurate and reliable even under random communication latency conditions, maintaining the dynamic stability of the formation in complex communication environments. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0051] Figure 2 This is a schematic diagram of the overall system structure of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0053] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0054] Example:

[0055] Please see Figure 1 The present invention provides a technical solution:

[0056] The random time-delay UAV formation control method based on event-triggered mechanism includes the following steps:

[0057] Step 1: Establish a global inertial coordinate system, acquire the original motion state of each node in the formation cluster in real time and perform per-unit processing to obtain the standard motion state, where the original motion state includes position, velocity, rotation angle and angular velocity;

[0058] In this embodiment, a three-dimensional rectangular coordinate system is established with the ground control base station as the origin, the horizontal plane as the XY axis plane, and the vertical plane as the XZ axis plane. Each device in the formation cluster is regarded as a different node. The original motion state of each node in the formation cluster is collected in real time by airborne sensors. The original motion state includes the original position vector, the original velocity vector, the original attitude angle vector, and the original angular velocity vector.

[0059] The original motion states of each node are normalized according to the standard unit length, standard unit speed, standard unit attitude angle and standard angular velocity units preset by relevant staff, so as to obtain the standard motion state of each node.

[0060] Position and velocity data are the fundamental feedback quantities for trajectory tracking and formation maintenance, determining the accuracy of outer-loop position coordination control. Attitude angles and angular velocities are crucial for underactuated systems like rotary-wing UAVs, as horizontal displacement must be achieved through attitude tilting, and angular velocity directly affects the stability of inner-loop flight, serving as a key input for subsequent disturbance rejection control. Heterogeneous nodes exhibit orders of magnitude differences in their physical properties. For example, two rotary-wing UAVs of different weights may perform different tasks and collaborate on a formation mission; the moments of inertia of nodes in such a heterogeneous formation cluster will differ. Directly using the collected raw data for joint calculations can lead to ill-conditioned matrix operations in the control algorithm, causing imbalances in weight updates or computational divergence. By introducing standard unit length, standard unit velocity and other benchmark values ​​for standardization, the influence of dimensions can be eliminated, and the state of each node in the formation cluster of different magnitudes can be mapped to a unified dimensionless mathematical space. This makes the same set of dynamic models and control parameters compatible with different types of hardware platforms, thereby ensuring the numerical stability and generalization ability of the system calculation. Specifically, standardization means expressing physical quantities as proportional values ​​based on benchmark values ​​preset by relevant personnel.

[0061] Step 2: Based on the standard motion state, establish physical constraints using the Newton-Euler equations, construct heterogeneous dynamic constraint equations for the translational and rotational channels, and define the true value of lumped disturbances;

[0062] In this embodiment, physical constraints are established using the Newton-Euler equations based on the standard motion states of each node.

[0063] Based on Newton's second law, and combined with the standard velocity vector in a standard state of motion, we construct the... The equation relating the translational acceleration and force at each node, the first node... The product of the standard mass and standard acceleration vector of each node is equal to the sum of the standard thrust vector, the standard gravity vector, and the true value of the translational lumped disturbance, thus obtaining the dynamic constraint equation of the translational channel.

[0064] The dynamic constraint equations for the translational channel are expressed as follows:

[0065]

[0066] In the formula, Indicates the node number. Indicates the preset first Standard quality of each node Indicates the first Standard velocity vector of each node The first derivative with respect to time, i.e., the standard acceleration vector, Indicates the first The standard thrust vector of each node is obtained from the physical control command output in the previous control cycle. Indicates the preset first The standard gravity vector of each node Indicates the first The true value of the translational lumped disturbance of each node;

[0067] The true value of translational lumped disturbance comprehensively reflects all unknown resultant forces acting on the UAV's position channel. Its magnitude directly characterizes the strength of disturbance factors such as gust drag, model error force, and unmodeled dynamic friction in the actual flight environment. The introduction of this parameter allows this method to quantify environmental disturbances that cannot be directly measured into explicit variables in the mathematical model, thus providing subsequent observers with accurate target approximations. The calculation results of the translational lumped disturbance true value have a close physical coupling relationship with the standard acceleration vector, standard thrust vector, and standard gravity vector. This is because, according to Newton's second law, the change in an object's state of motion is determined by the vector sum of all acting forces. Given the thrust and gravity, the deviation between the actual acceleration and the theoretical acceleration must originate from external disturbances. Specifically, the true value of translational lumped disturbance is positively correlated with the standard acceleration vector and negatively correlated with the standard thrust vector. This means that if the standard acceleration actually generated by the UAV increases under the same standard thrust, it indicates the presence of a positive disturbance force, and the true value of the disturbance increases. Conversely, if the thrust is large but the acceleration is small, it indicates the presence of a reverse drag force, and the true value of the disturbance decreases.

[0068] Based on Euler's equations of rigid body dynamics, and combined with the standard angular velocity vector in the standard motion state, an equation is constructed between standard angular acceleration and torque. The product of the standard moment of inertia matrix and the standard angular acceleration vector is equal to the sum of the standard control torque vector minus the gyroscopic effect torque term and the true value of the rotational lumped disturbance. The gyroscopic effect torque term is obtained by performing a cross product operation on the product of the standard angular velocity vector and the standard moment of inertia matrix and the standard angular velocity vector. The dynamic constraint equations of the rotation channel are then obtained.

[0069] The dynamic constraint equations for the rotating channel are expressed as follows:

[0070]

[0071] In the formula, Indicates the first The standard moment of inertia matrix of each node is obtained by recording motor torque commands and angular velocity response data, and then fitting it based on the rigid body dynamics equations using a frequency domain identification algorithm. Indicates the first Standard angular velocity of each node The first derivative with respect to time, i.e., the standard angular acceleration vector, Indicates the first The standard control torque vector for each node is obtained from the torque command output in the previous cycle. This represents the vector cross product operation. Indicates the first The true value of the lumped disturbance of the rotation of each node.

[0072] The true value of the rotational lumped disturbance specifically reflects the unknown torques acting on the UAV's attitude channel, encompassing factors such as aerodynamic yaw torque, center of gravity shift torque, and propeller airflow disturbance torque. This is achieved by introducing a gyro effect term into the equations. The dynamic constraint equations of the rotation channel can isolate the nonlinear physical characteristics unique to rotating rigid bodies from disturbances, ensuring that the calculated true value of the disturbance purely represents the torsional effect of the external environment on the fuselage attitude. This avoids misjudging the aircraft's own rotational inertia as a disturbance, thereby significantly improving the accuracy of attitude control. The true value of the rotational lumped disturbance is closely related to the standard angular acceleration, the standard control torque, and the gyroscopic effect term. This relationship is based on Euler's equations of rigid body dynamics, which describe how torque changes the angular momentum of an object. Numerically, the true value of the rotational lumped disturbance is positively correlated with the standard angular acceleration and negatively correlated with the standard control torque. That is, under the same control torque, if the actual angular acceleration of the UAV undergoes an abnormal abrupt change that cannot be explained by the gyroscopic effect, it will be reflected in a significant increase in the true value of the disturbance, indicating that there is an external airflow exerting an additional torsional torque on the fuselage.

[0073] Given that rotary-wing UAVs are underactuated systems with strong coupling between translation and rotation, and are susceptible to external airflow interference, high-precision disturbance rejection control is achieved by establishing translational channel constraints describing the relationship between force and linear motion, and rotational channel constraints describing the relationship between torque and angular motion, respectively, within a standardized space based on the Newton-Euler equations. These two dynamic constraint equations explicitly define the difference between the actual motion state and the theoretical model as the lumped disturbance truth value, thus providing a physical benchmark for the subsequent observer design. Particularly in the rotational channel, by explicitly introducing and removing the gyroscopic effect term, the coupling between external torque disturbance and the airframe's own rotational inertia is effectively decoupled, ensuring that the defined lumped disturbance truth value purely reflects the torsional effect of the external environment on the airframe. It should be noted that although the dynamic equations mathematically provide equations for directly calculating the disturbance truth value based on acceleration, mass, and thrust, in the actual engineering application of this embodiment, the acceleration is not directly obtained by differentiating the velocity signal to calculate this truth value. This is because differential operations have significant high-pass filtering characteristics in signal processing, which greatly amplifies high-frequency noise in sensor signals, causing the directly calculated interference values ​​to fluctuate drastically and become unusable for control feedback. Therefore, the core significance of this method lies in defining the approximation target of the observer, while the specific numerical acquisition will be achieved by a nonlinear interference observer with integral filtering characteristics in subsequent steps, thereby effectively avoiding the impact of differential noise on the stability of the control system while ensuring the accuracy of the physical model.

[0074] Step 3: Combining the heterogeneous dynamic constraint equations, introduce auxiliary variables to transform the differential operation on the motion state into an integral operation, design a dual-channel nonlinear disturbance observer, and calculate the lumped disturbance estimate that approximates the true value of the lumped disturbance in real time through nonlinear iteration;

[0075] In this embodiment, for the translational interference observer;

[0076] Based on the auxiliary variable transformation method in the design criteria for nonlinear disturbance observers in control theory, the first... The translational auxiliary variable of the nth node in the translational disturbance estimation calculation is defined as the nth node. The translational auxiliary variable of the nth node and the nth node The estimated translational lumped disturbance of the nth node satisfies a linear transformation relationship, specifically the nth node. The translational auxiliary variable of the nth node is equal to the nth node. The translational lumped disturbance estimate of the nth node minus the translational correction term, where the translational correction term is the preset translational observer gain matrix, the nth node, and the nth node, respectively. The product of the standard mass and standard velocity vector of each node:

[0077] No. The translational auxiliary variable of the nth node and the nth node The linear relationship between the estimated translational lumped disturbance values ​​of each node is as follows:

[0078]

[0079] In the formula, The first one represents the construction Translational auxiliary variables of each node, Indicates the first Estimates of translational lumped disturbance at each node This represents the preset translational observer gain matrix;

[0080] The first The translational auxiliary variable of the nth node and the nth node The linear relationship between the estimated translational lumped disturbance values ​​of the nodes is differentiated with respect to a preset unit time, and the nth node is set according to the negative feedback mechanism. The rate of change of the estimated translational lumped disturbance of the nth node and the 1st node The true value of the translational lumped disturbance of the nth node and the nth node The difference in the estimated translational lumped disturbance of the nth node is proportional to the difference in the estimated values ​​of the nth node. Combined with the dynamic constraint equations of the translational channel, the nth node is calculated. The sum of the standard thrust vector, standard gravity vector, translational auxiliary variable from the previous moment, and translational correction term for each node is then multiplied by the negative value of a preset translational observer gain matrix to obtain the result. The rate of change of the translational auxiliary variable of each node within a preset unit of time;

[0081] No. The expression for calculating the rate of change of the translational auxiliary variable of each node within a preset unit time is as follows:

[0082]

[0083] In the formula, Indicates the first The rate of change of the translational auxiliary variable of each node within a preset unit of time. This represents the output of the observer at the previous time step. Translational auxiliary variables of each node;

[0084] Combined with the The rate of change of the translational auxiliary variable at the nth node within a preset unit time is obtained by numerical integration iteration to obtain the nth node at the current time. The translational auxiliary variable of the nth node is substituted into the current time step of the nth node. The translational auxiliary variable of the nth node and the nth node The linear relationship between the estimated translational lumped disturbance values ​​of the n nodes is used to calculate the current time n. Estimates of the translational lumped disturbance of each node;

[0085] By taking the time derivative of both sides of the linear relationship of the translational auxiliary variable defined above, and simultaneously solving the translational channel dynamics constraint equations constructed in step two, the existing standard acceleration vector is replaced and algebraically eliminated using the known terms in the equations—the standard thrust vector, the standard gravity vector, and the disturbance term to be estimated. This derives the new formula that depends only on the standard thrust vector, the standard gravity vector, the standard velocity vector, and the translational auxiliary variable itself. By numerically integrating the rate of change of the translational auxiliary variable, the variable can be updated in real time, and then the estimated value of the translational lumped disturbance can be obtained by combining it with the standard velocity vector. Mathematically, this method transforms differential observations sensitive to high-frequency noise into integral observations with low-pass filtering characteristics, thus achieving high signal-to-noise ratio disturbance estimation under conditions without accelerometers.

[0086] The principle for the rotational disturbance observer is the same as that for the translational disturbance observer.

[0087] Construct the first The rotational auxiliary variable of the nth node in the rotational disturbance estimation operation is defined as the nth node. The rotation auxiliary variable of the nth node and the nth node The rotation lumped disturbance estimate of the nth node satisfies a linear transformation relationship, specifically the nth node. The rotation auxiliary variable of the nth node is equal to the nth node. The rotation lumped disturbance estimate of the nth node minus the rotation correction term, where the rotation correction term is the preset rotation observer gain matrix, the th node's rotation lumped disturbance estimate, the lumped disturbance estimate of the nth node, the rotation correction term is the preset rotation observer gain matrix ... The product of the standard moment of inertia matrix and the standard angular velocity vector of each node;

[0088] No. The rotation auxiliary variable of the nth node and the nth node The linear relationship between the estimated lumped disturbance values ​​of the rotation of each node is as follows:

[0089]

[0090] In the formula, The first one represents the construction Rotation auxiliary variables of each node, Indicates the first The estimated lumped disturbance of rotation at each node. This represents the preset rotation observer gain matrix;

[0091] The first The rotation auxiliary variable of the nth node and the nth node The linear relationship between the estimated lumped disturbance of the rotation at the nth node and the preset unit time is differentiated, and combined with the dynamic constraint equations of the rotation channel, the nth node is calculated. The vector sum of the standard control torque vector of each node, the rotation auxiliary variable of the previous moment, and the rotation correction term, minus the gyroscopic effect torque term, and then multiplying the final difference vector by the negative value of the preset rotation observer gain matrix, yields the result. The rate of change of the rotation auxiliary variable of each node within a preset unit of time;

[0092] No. The expression for calculating the rate of change of the rotational auxiliary variable of each node within a preset unit time is as follows:

[0093]

[0094] In the formula, Indicates the first The rate of change of the rotation auxiliary variable of each node within a preset unit of time. This represents the output of the observer at the previous time step. Rotation auxiliary variables for each node;

[0095] Combined with the The rate of change of the rotation auxiliary variable of the nth node within a preset unit time is obtained by numerical integration iteration to obtain the nth node at the current time. The rotation auxiliary variable of the nth node is substituted into the nth node. The rotation auxiliary variable of the nth node and the nth node The linear relationship between the estimated lumped disturbance of the rotation of the nth node is used to calculate the current time. Estimated lumped disturbance of rotation at each node.

[0096] The estimation of rotational lumped disturbance is also based on the aforementioned algebraic elimination logic, avoiding direct differentiation of the standard angular velocity vector. This formula explicitly introduces a gyroscopic torque term, fully reproducing the physical characteristics of the rotating rigid body in the observer's dynamics model. The observer automatically approximates the external disturbance torque by monitoring the residual between the applied standard control torque vector and the actual standard angular velocity vector in real time, utilizing an integral feedback mechanism. Since the standard angular acceleration vector term has been equivalently replaced using the rotational channel dynamics constraint equations during the algebraic derivation, the calculation process only requires the standard angular velocity vector and the standard control torque vector as input. This design not only solves the noise amplification problem caused by direct differentiation but also ensures that when the UAV performs rapid maneuvers, the observer can automatically deduct the influence of its own inertial torque, outputting a clean estimate of the external aerodynamic disturbance, providing a precise feedforward signal for subsequent attitude disturbance rejection control.

[0097] This method cleverly transforms the differential operations on velocity and angular velocity in the dynamic equations into integral operations on the auxiliary variables by introducing auxiliary variable technology. This approach is mathematically equivalent to low-pass filtering of the signal, effectively avoiding the noise amplification effect caused by directly differentiating the sensor velocity signal. Compared to directly using Newton's second law and Euler's equations for rigid body dynamics to calculate the true values ​​of translational and rotational lumped disturbances, the nonlinear disturbance observer designed in this method significantly improves the signal-to-noise ratio and smoothness of the estimated translational and rotational lumped disturbances while maintaining response speed, providing feedforward compensation signals for the stable operation of the subsequent controller. Specifically, the initial values ​​of the translational and rotational auxiliary variables are set using a zero initial disturbance assumption. At UAV startup, both the estimated translational and rotational lumped disturbances are set as zero vectors, and the initial values ​​are obtained through reverse calculation based on the established linear relationship.

[0098] Step 4: Construct a full-state coupled dynamic event triggering mechanism, calculate the dynamic triggering threshold. The dynamic triggering threshold is negatively correlated with the magnitude of the lumped interference estimate and includes a minimum interval protection term that decays exponentially with time. When the state error exceeds the dynamic triggering threshold, communication is triggered, sending its own standard motion state to neighboring nodes and sending a request to neighboring nodes to obtain the standard motion state.

[0099] In this embodiment, the calculation of the first... The magnitudes of the translational lumped interference estimates and rotational lumped interference estimates of each node are used to quantify the external interference intensity at the current moment, and the difference between the current time and the last triggered communication time is calculated as the elapsed time.

[0100] A fully coupled dynamic event triggering mechanism is constructed, and the dynamic triggering threshold at the current time is calculated. The specific calculation logic for the dynamic triggering threshold is as follows:

[0101] First, the interference adaptation component is calculated. The interference adaptation component is used to adaptively adjust the threshold according to environmental changes. The value is negatively correlated with the intensity of external interference. Specifically, it is obtained by dividing the preset basic error tolerance constant by the weighted sum of interference intensity. The weighted sum of interference intensity is composed of the weighted value of the magnitude of the translational lumped interference estimate, the weighted value of the magnitude of the rotational lumped interference estimate, and the sum of preset constant terms.

[0102] Secondly, the minimum interval protection term is calculated. The minimum interval protection term is used to prevent continuous triggering in a short period of time. Its value decays exponentially with the passage of time. Specifically, it is obtained by multiplying the preset protection term amplitude by the time decay factor. The time decay factor is calculated by performing a negative exponential operation based on the passage of time, so that the component reaches its maximum value at the moment after the communication is triggered and gradually approaches zero over time.

[0103] Finally, a threshold truncation determination is performed. The interference adaptation component is added to the minimum interval protection item to obtain a preliminary calculated threshold. This preliminary calculated threshold is compared with the preset lower limit of the dynamic trigger threshold, and the larger of the two values ​​is selected as the dynamic trigger threshold for the current time.

[0104] The design principle of the dynamic trigger threshold for the current time is as follows:

[0105]

[0106] In the formula, This represents the dynamic trigger threshold at the current time t. This represents the preset basic error tolerance constant. This indicates the translational interference sensitivity coefficient preset by the staff. This represents the magnitude of the translational lumped disturbance estimate. This indicates the rotational interference sensitivity coefficient preset by the staff. This represents the magnitude of the estimated value of the rotational lumped disturbance. This indicates the Zeno protection value preset by the staff. Represents the natural constant. This represents the time decay rate coefficient preset by the staff. Indicates the current time. This indicates the time when communication was last triggered, and it is automatically updated after each communication event is triggered. Indicates the lower limit of the dynamic trigger threshold;

[0107] The dynamic trigger threshold, serving as a quantitative standard for determining whether to execute a communication operation, represents the maximum tolerable state deviation limit at the current time. The calculation result of the dynamic trigger threshold is directly determined by the magnitudes of the estimated translational and rotational lumped interference, the elapsed time since the last communication, and the basic error tolerance. This design enables on-demand allocation of communication strategies: when external wind resistance or torque interference increases, leading to a larger interference magnitude, the dynamic trigger threshold automatically decreases due to its negative correlation with the interference magnitude, thereby increasing sensitivity to combat interference through high-frequency communication. Conversely, during stable flight, sensitivity is reduced to save bandwidth. Simultaneously, the minimum interval protection term included in the formula ensures that the dynamic trigger threshold reaches its maximum value immediately after each communication trigger. This positively correlated decay over time constructs a mandatory minimum event interval mechanism, effectively avoiding the possibility of the Zeno phenomenon from a mathematical perspective, and preventing communication congestion and computational resource exhaustion caused by computational noise or instantaneous error fluctuations.

[0108] Based on the error truncation principle, the magnitude of the deviation between the standard motion state and the expected motion state at the current time is calculated using Euclidean distance to obtain the comprehensive state error at the current time. The comprehensive state error at the current time is compared with the dynamic trigger threshold at the current time. If the comprehensive state error at the current time is less than the dynamic trigger threshold at the current time, communication is not triggered. If the comprehensive state error at the current time is greater than or equal to the dynamic trigger threshold at the current time, communication is triggered, and the standard motion state is sent to the neighboring nodes and a request to obtain the standard motion state is sent to the neighboring nodes. The expected motion state is the theoretical state at the current time calculated based on a preset spatiotemporal trajectory function, or the theoretical state at the current time deduced from the baseline state sent by the navigator node to other nodes.

[0109] The overall state error specifically reflects the degree to which the UAV's current actual flight state deviates from the predetermined trajectory or the target it is following. It encompasses both position tracking deviation and attitude maintenance deviation. The value of the overall state error is determined by the difference between the standard motion state and the expected motion state, and is positively correlated with the degree of deviation between the two. When the UAV deviates from its flight path due to interference or its flight rhythm deviates from the preset trajectory, the magnitude of the difference increases accordingly. Once this error exceeds a dynamic threshold determined by the current interference intensity, a trigger event is determined, and data broadcasting and updates are immediately executed to request neighboring nodes to coordinate adjustments. This triggering mechanism, based on trajectory tracking error rather than simple position changes, effectively eliminates redundant communication caused by normal maneuvers during consistent formation flight, occupying the channel only when unexpected deviations occur.

[0110] Step 5: Based on the lumped interference estimate, perform interference correction on the motion state of neighboring nodes with random communication delays to obtain the predicted neighbor motion state;

[0111] In this embodiment, when the first When a node receives a status data packet sent by a neighboring node, it calculates the difference between the timestamp in the data packet and the current time to obtain the random communication delay, and then normalizes it to obtain the standard random communication delay.

[0112] For the The translational state delay compensation prediction of each node's neighbor nodes is combined with the translational lumped interference estimate sent by the neighbor nodes and the dynamic constraint equations of the translational channel. Based on the kinematic Taylor expansion principle, the predicted neighbor standard position vector after interference compensation is calculated. The specific calculation logic is as follows: taking the standard position vector in the state data packet sent by the neighbor nodes as the reference, firstly, the linear displacement generated by the standard velocity vector of the neighbor nodes within the standard random communication delay is superimposed, and then the second-order dynamic correction displacement generated by the resultant external force is superimposed. The calculation method of the second-order dynamic correction displacement is as follows: calculate the vector sum of the standard thrust vector of the neighbor nodes and the translational lumped interference estimate, divide it by the standard mass of the neighbor nodes to obtain the equivalent acceleration, and then multiply the equivalent acceleration by half of the square of the standard random communication delay to obtain the predicted neighbor standard position vector.

[0113] The principle behind calculating the standard location vector of predicted neighbors is as follows:

[0114]

[0115] In the formula, Indicates neighboring nodes, Indicates neighboring nodes after interference compensation The predicted standard position vector, Representing neighboring nodes Standard position vector, Representing neighboring nodes The standard velocity vector, Indicates the first Each node and its neighboring nodes Standard random communication delay between them Indicates the preset neighbor nodes Standard quality Representing neighboring nodes Standard thrust vector Representing neighboring nodes Estimates of translational lumped disturbance;

[0116] The predicted neighbor standard position vector specifically reflects the true physical position of neighbor nodes at the current moment. It means extrapolating the received positions from past moments to the current moment based on physical laws. Obtaining this prediction eliminates time deviations caused by random delays, enabling the local controller to perform collaborative calculations based on the real-time state of neighbors, thereby avoiding formation collisions or formation divergence caused by information asynchrony. The predicted neighbor standard position vector mainly depends on the historical state, delay duration, and current force conditions of the neighbor nodes in the data packets they send. This is based on the Taylor expansion principle of kinematics: position updates depend not only on the linear extrapolation of velocity but also on the second-order correction of acceleration. Acceleration is determined by both thrust and disturbance force. In particular, the introduction of translational lumped disturbance estimates allows the prediction model to fully consider the nonlinear effects of environmental factors such as wind resistance on the neighbor's trajectory during the delay interval. Numerically, the predicted location vector is positively correlated with the delay duration and also positively correlated with the estimated translational lumped interference. That is, if the neighbor is in a downwind state, even within a small gap of communication interruption, its actual location will be farther than that calculated based solely on speed. This formula can accurately capture this dynamic deviation.

[0117] For the The rotation state delay compensation prediction of each node's neighbor nodes is combined with the rotation lumped interference estimate sent by the neighbor nodes and the dynamic constraint equation of the rotation channel. Based on the Taylor expansion principle of rotational dynamics, the predicted standard attitude angle vector of the neighbor nodes after interference compensation is calculated. The specific calculation logic is as follows: taking the standard attitude angle vector in the state data packet sent by the neighbor nodes as the reference, firstly, the angular displacement generated by the standard angular velocity vector of the neighbor nodes within the standard random communication delay is superimposed, and then the second-order angular dynamic correction displacement generated by the resultant torque is superimposed. The calculation method of the second-order angular dynamic correction displacement is as follows: calculate the vector sum of the standard control torque vector of the neighbor nodes and the rotation lumped interference estimate, use the inverse matrix of the standard rotational inertia matrix of the neighbor nodes to transform the vector sum to obtain the equivalent angular acceleration, and then multiply the equivalent angular acceleration by half of the square of the standard random communication delay to obtain the predicted standard attitude angle vector of the neighbor nodes.

[0118] The principle behind calculating the predicted standard attitude angle vector of neighbors is as follows:

[0119]

[0120] In the formula, Indicates neighboring nodes after interference compensation The predicted standard pose angle vector of the neighbor. Representing neighboring nodes The standard attitude angle vector in the sent status data packet, Representing neighboring nodes The standard angular velocity vector, Representing neighboring nodes The standard moment of inertia matrix, Representing neighboring nodes Standard thrust vector Representing neighboring nodes The estimated value of rotational lumped disturbance;

[0121] The predicted neighbor standard attitude angle vector accurately reconstructs the fuselage attitude of neighbor nodes at the current moment, providing a lag-free reference benchmark for cooperative attitude control. This prediction is also based on a second-order expansion of rotational dynamics, with the inclusion of a rotational lumped disturbance estimate ensuring that the torsional effect of airflow disturbances on the neighbor's attitude is factored into the prediction calculation under random time delays. The rotational lumped disturbance estimate is positively correlated with the predicted attitude angle vector, meaning that if a neighbor is subjected to a sudden external torque disturbance, the prediction algorithm can immediately calculate the accumulated attitude offset caused by the disturbance within the time delay period the moment the data packet arrives, thus guiding the local machine to make accurate avoidance or cooperative responses.

[0122] Step 6: Construct a cascaded optimal disturbance rejection controller, calculate the position and attitude coordination error of the nodes, input the position and attitude coordination error of the nodes into an offline trained stable manifold neural network to directly infer the optimal costate vector, solve to obtain the optimal nominal control law, introduce the lumped disturbance estimate for feedforward compensation, generate the final physical control command and execute it.

[0123] In this embodiment, the comprehensive position error of the current node is calculated in a three-dimensional Cartesian coordinate system. The comprehensive position error of the current node is composed of a weighted sum of the cooperative error with neighboring nodes and the tracking error of the expected motion state at the current moment. The cooperative error is calculated by... The tracking error is obtained by calculating the difference between the standard position vector of the nth node, the predicted standard position vector of the neighboring nodes, and the expected distance vector, and then weighting the calculated differences. The difference between the standard position vector of the nth node and the expected motion state at the current moment is used to calculate the weighted sum. The combined position error of the nth node is input into a pre-trained position loop-stabilized manifold neural network to obtain the nth node's position error. The optimal co-state vector of the position loop in the HJB equation is the standard motion state of each node. Based on the optimal co-state vector of the position loop, combined with the optimal feedback control law formula and the difference between the estimated value of the translational set disturbance, the three-dimensional disturbance-resistant virtual resultant force vector is obtained.

[0124] The core purpose of constructing a cascaded optimal disturbance rejection controller is to solve the technical challenge of traditional control methods in simultaneously achieving computational real-time performance, global optimality, and disturbance rejection robustness. While the traditional HJB equations theoretically provide the globally optimal control solution for nonlinear systems, as high-dimensional nonlinear partial differential equations, their online solution incurs an extremely high computational load, making them difficult to directly apply to the highly dynamic airborne control of unmanned aerial vehicles (UAVs). Therefore, this method, based on the stable manifold theory of the HJB equations, employs a data-driven approximation solution strategy, utilizing an offline-trained stable manifold neural network to fit the solution structure of the HJB equations. During online operation, this neural network can replace the complex equation-solving process, directly mapping the optimal costate vector from the input error state through forward inference. The combined position error, including the cooperative error of neighboring nodes and the tracking error of the expected motion state at the current moment, is calculated and input into the offline-trained position loop stable manifold neural network. The neural network outputs the optimal position loop costate vector that minimizes the system cost function within milliseconds, thereby solving for the optimal nominal virtual force. Based on this, the controller incorporates the translational lumped disturbance estimate output from step three for feedforward compensation, that is, superimposing the disturbance value on the optimal nominal force in the opposite direction. The technical effect of this combined strategy is that the UAV can not only plan the most energy-efficient and fastest-converging flight trajectory, but also maintain trajectory rigidity when encountering sudden airflow or model parameter disturbances, thus achieving the fusion of optimal control and active disturbance rejection.

[0125] The magnitude of the three-dimensional anti-disturbance virtual resultant force vector is calculated to obtain the final total thrust command of the UAV rotor. Based on the three-dimensional anti-disturbance virtual resultant force vector and the preset reference yaw angle, the first thrust is obtained by combining backstepping control. The desired attitude angle vector of the nth node is calculated. The difference between the standard attitude vector and the desired attitude angle vector in the standard motion state of the nth node is used to obtain the attitude tracking deviation vector. The combined position error of the nth node is input into the pre-trained attitude loop stable manifold neural network to obtain the nth node. The optimal co-state vector of the attitude loop in the HJB equation is the standard motion state of each node. Based on the optimal co-state vector of the attitude loop, combined with the optimal feedback control law formula and the difference between the estimated value of the rotation set disturbance, the final disturbance rejection torque command is obtained.

[0126] Since quadcopter UAVs are underactuated systems and cannot directly generate horizontal thrust, this step utilizes a vector mapping function to decompose the disturbance-resistant virtual resultant force calculated in the outer loop into a total thrust command and a desired attitude angle. Subsequently, in the inner loop attitude control, a control architecture that uses neural network inference of optimal torque and rotational disturbance feedforward compensation is also adopted. By inputting the attitude tracking error into the attitude loop neural network to obtain the optimal torque and subtracting the estimated value of rotational lumped disturbance, the system can resist the risk of rollover caused by aerodynamic yaw torque or center of gravity shift in real time. The final technical effect is that it generates a final physical control command containing total thrust and three-axis torque, directly driving the motor speed adjustment. This allows the UAV formation to maintain a tight cooperative formation like a rigid body even in complex high-dynamic environments and accurately track the preset spatiotemporal trajectory, achieving closed-loop control from decision-making algorithm to physical execution.

[0127] No. Each node adjusts its motion state according to the final total thrust command and the final disturbance rejection torque command.

[0128] Please see Figure 2 The present invention also provides a random delay UAV formation control system based on an event-triggered mechanism. The UAV formation control system is used to implement the above-mentioned UAV formation control method, comprising:

[0129] The data acquisition module is used to establish a global inertial coordinate system, acquire the original motion state of each node in the formation cluster in real time, and perform per-unit processing to obtain the standard motion state. The original motion state includes position, velocity, rotation angle and angular velocity.

[0130] The disturbance definition module is used to establish physical constraints based on the standard motion state using the Newton-Euler equations, construct heterogeneous dynamic constraint equations for translational and rotational channels, and define the true value of lumped disturbances.

[0131] The disturbance analysis module is used to design a dual-channel nonlinear disturbance observer by combining heterogeneous dynamic constraint equations. It introduces auxiliary variables to transform the differential operation on the motion state into an integral operation, and calculates the lumped disturbance estimate that approximates the true value of the lumped disturbance in real time through nonlinear iteration.

[0132] The event determination module is used to construct a fully coupled dynamic event triggering mechanism, calculate the dynamic triggering threshold, which is negatively correlated with the magnitude of the lumped disturbance estimate and includes a minimum interval protection term that decays exponentially over time. Communication is triggered when the state error exceeds the dynamic triggering threshold.

[0133] The communication module is used to correct the motion state of neighboring nodes with random communication delays based on the lumped interference estimate, so as to obtain the predicted motion state of the neighbors.

[0134] The formation correction module is used to construct a cascaded optimal disturbance rejection controller. It calculates the position and attitude coordination error of the nodes, inputs the position and attitude coordination error of the nodes into an offline trained stable manifold neural network to directly infer the optimal costate vector, solves to obtain the optimal nominal control law, and introduces the lumped disturbance estimate for feedforward compensation to generate the final physical control command and execute it.

[0135] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0136] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0137] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0138] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A random time delay UAV formation control method based on an event trigger mechanism, characterized in that, The specific steps include: A global inertial coordinate system is established to acquire the original motion state of each node in the formation cluster in real time and perform per-unit processing to obtain the standard motion state. The original motion state includes position, velocity, rotation angle and angular velocity. Based on the standard motion state, physical constraints are established using the Newton-Euler equations, heterogeneous dynamic constraint equations for translational and rotational channels are constructed, and the true value of lumped disturbance is defined. By combining heterogeneous dynamic constraint equations and introducing auxiliary variables, the differential operation on the motion state is transformed into an integral operation. A dual-channel nonlinear disturbance observer is designed, and the lumped disturbance estimate approximates the true value of the lumped disturbance is calculated through nonlinear iteration. A full-state coupled dynamic event triggering mechanism is constructed, and a dynamic triggering threshold is calculated. The dynamic triggering threshold is negatively correlated with the magnitude of the lumped interference estimate and includes a minimum interval protection term that decays exponentially with time. When the comprehensive state error exceeds the dynamic triggering threshold, communication is triggered, and the standard motion state is sent to the neighboring nodes and a request to obtain the standard motion state is sent to the neighboring nodes. Based on the lumped interference estimate, the motion state of neighboring nodes with random communication delays is corrected for interference to obtain the predicted neighbor motion state. Construct a cascaded optimal disturbance rejection controller, calculate the position and attitude coordination error of the nodes, input the position and attitude coordination error of the nodes into an offline trained stable manifold neural network to directly infer the optimal costate vector, solve to obtain the optimal nominal control law, introduce the lumped disturbance estimate for feedforward compensation, generate the final physical control command and execute it. Calculate the first The magnitudes of the translational lumped interference estimates and rotational lumped interference estimates of each node are used to quantify the external interference intensity at the current moment, and the difference between the current time and the last triggered communication time is calculated as the elapsed time. A fully coupled dynamic event triggering mechanism is constructed, and the dynamic triggering threshold at the current time is calculated. The specific calculation logic for the dynamic triggering threshold is as follows: First, the interference adaptation component is calculated. The interference adaptation component is used to adaptively adjust the threshold according to environmental changes. The value is negatively correlated with the intensity of external interference. Specifically, it is obtained by dividing the preset basic error tolerance constant by the weighted sum of interference intensity. The weighted sum of interference intensity is composed of the weighted value of the magnitude of the translational lumped interference estimate, the weighted value of the magnitude of the rotational lumped interference estimate, and the sum of preset constant terms. Secondly, the minimum interval protection term is calculated. The minimum interval protection term is used to prevent continuous triggering in a short period of time. Its value decays exponentially with the passage of time. Specifically, it is obtained by multiplying the preset protection term amplitude by the time decay factor. The time decay factor is calculated by performing a negative exponential operation based on the passage of time, so that the component reaches its maximum value at the moment after the communication is triggered and gradually approaches zero over time. Finally, a threshold truncation determination is performed. The interference adaptation component is added to the minimum interval protection item to obtain a preliminary calculated threshold. This preliminary calculated threshold is compared with the preset lower limit of the dynamic trigger threshold, and the larger of the two values ​​is selected as the dynamic trigger threshold for the current time. The Euclidean distance is used to calculate the magnitude of the deviation between the standard motion state and the expected motion state at the current time, resulting in the comprehensive state error at the current time. This comprehensive state error is then compared with the dynamic trigger threshold at the current time. If the comprehensive state error at the current time is less than the dynamic trigger threshold, communication is not triggered. If the comprehensive state error at the current time is greater than or equal to the dynamic trigger threshold, communication is triggered, and the standard motion state is sent to neighboring nodes, along with a request to obtain the standard motion state from neighboring nodes. The expected motion state is either the theoretical state at the current time calculated based on a preset spatiotemporal trajectory function, or the theoretical state at the current time derived from the baseline state sent to other nodes by a designated leader node.

2. The random time delay UAV formation control method based on event trigger mechanism according to claim 1, characterized in that: Using the ground control base station as the origin, the horizontal plane is set as the XY axis plane, and the vertical plane is set as the XZ axis plane to establish a three-dimensional rectangular coordinate system. Each device in the formation cluster is regarded as a different node. The original motion state of each node in the formation cluster is collected in real time through airborne sensors. The original motion state includes the original position vector, the original velocity vector, the original attitude angle vector, and the original angular velocity vector. The original motion states of each node are normalized according to the standard unit length, standard unit speed, standard unit attitude angle and standard angular velocity units preset by the relevant staff, so as to obtain the standard motion state of each node.

3. The random time-delay UAV formation control method based on event triggering mechanism according to claim 2, characterized in that: Based on the standard motion state of each node, physical constraints are established using the Newton-Euler equations. Based on Newton's second law, and combined with the standard velocity vector in a standard state of motion, we construct the... The equation relating the translational acceleration and force at each node, the first node... The product of the standard mass and standard acceleration vector of each node is equal to the sum of the standard thrust vector, the standard gravity vector, and the true value of the translational lumped disturbance, thus obtaining the dynamic constraint equation of the translational channel. Based on Euler's equations for rigid body dynamics, and combined with the standard angular velocity vector in the standard motion state, an equation is constructed between standard angular acceleration and torque. The product of the standard moment of inertia matrix and the standard angular acceleration vector is equal to the sum of the standard control torque vector minus the gyroscopic effect torque term and the true value of the rotational lumped disturbance. The gyroscopic effect torque term is obtained by performing a cross product operation on the standard angular velocity vector and the product of the standard moment of inertia matrix and the standard angular velocity vector. The dynamic constraint equations of the rotation channel are then obtained.

4. The random time-delay UAV formation control method based on event triggering mechanism according to claim 3, characterized in that: For translational interference observers; Based on the auxiliary variable transformation method in the design criteria for nonlinear disturbance observers in control theory, the first... The translational auxiliary variable of the nth node in the translational disturbance estimation calculation is defined as the nth node. The translational auxiliary variable of the nth node and the nth node The estimated translational lumped disturbance of the nth node satisfies a linear transformation relationship, specifically the nth node. The translational auxiliary variable of the nth node is equal to the nth node. The translational lumped disturbance estimate of the nth node minus the translational correction term, where the translational correction term is the preset translational observer gain matrix, the nth node, and the nth node, respectively. The product of the standard mass and standard velocity vector of each node; The first The translational auxiliary variable of the nth node and the nth node The linear relationship between the estimated translational lumped disturbance values ​​of the nodes is differentiated with respect to a preset unit time, and the nth node is set according to the negative feedback mechanism. The rate of change of the estimated translational lumped disturbance of the nth node and the 1st node The true value of the translational lumped disturbance of the nth node and the nth node The difference in the estimated translational lumped disturbance of the nth node is proportional to the difference in the estimated values ​​of the nth node. Combined with the dynamic constraint equations of the translational channel, the nth node is calculated. The sum of the standard thrust vector, standard gravity vector, translational auxiliary variable from the previous moment, and the translational correction term at each node is multiplied by the negative value of a preset translational observer gain matrix to obtain the first node. The rate of change of the translational auxiliary variable of each node within a preset unit of time; Combined with the The rate of change of the translational auxiliary variable at the nth node within a preset unit time is obtained by numerical integration iteration to obtain the nth node at the current time. The translational auxiliary variable of the nth node is substituted into the current time step of the nth node. The translational auxiliary variable of the nth node and the nth node The linear relationship between the estimated translational lumped disturbance values ​​of the n nodes is used to calculate the current time n. Estimates of the translational lumped disturbance of each node; The principle for the rotational disturbance observer is the same as that for the translational disturbance observer. Construct the first The rotational auxiliary variable of the nth node in the rotational disturbance estimation operation is defined as the nth node. The rotation auxiliary variable of the nth node and the nth node The rotation lumped disturbance estimate of the nth node satisfies a linear transformation relationship, specifically the nth node. The rotation auxiliary variable of the nth node is equal to the nth node. The rotation lumped disturbance estimate of the nth node minus the rotation correction term, where the rotation correction term is the preset rotation observer gain matrix, the th node's rotation lumped disturbance estimate, the lumped disturbance estimate of the nth node, the rotation correction term is the preset rotation observer gain matrix ... The product of the standard moment of inertia matrix and the standard angular velocity vector of each node; The first The rotation auxiliary variable of the nth node and the nth node The linear relationship between the estimated lumped disturbance of the rotation at the nth node and the preset unit time is differentiated, and combined with the dynamic constraint equations of the rotation channel, the nth node is calculated. The sum of the standard control torque vector of each node, the rotation auxiliary variable of the previous moment, and the rotation correction term, minus the gyroscopic effect torque term, and then multiplying the final difference vector by the negative value of the preset rotation observer gain matrix, yields the result. The rate of change of the rotation auxiliary variable of each node within a preset unit of time; Combined with the The rate of change of the rotation auxiliary variable of the nth node within a preset unit time is obtained by numerical integration iteration to obtain the nth node at the current time. The rotation auxiliary variable of the nth node is substituted into the nth node. The rotation auxiliary variable of the nth node and the nth node The linear relationship between the estimated lumped disturbance of the rotation of the nth node is used to calculate the current time. Estimated lumped disturbance of rotation at each node.

5. The random time-delay UAV formation control method based on event triggering mechanism according to claim 1, characterized in that: When the When a node receives a status data packet sent by a neighboring node, it calculates the difference between the timestamp in the data packet and the current time to obtain the random communication delay, and then normalizes it to obtain the standard random communication delay. For the The translational state delay compensation prediction of each node's neighbor nodes is combined with the translational lumped interference estimate sent by the neighbor nodes and the dynamic constraint equations of the translational channel. Based on the kinematic Taylor expansion principle, the predicted neighbor standard position vector after interference compensation is calculated. The specific calculation logic is as follows: taking the standard position vector in the state data packet sent by the neighbor nodes as the reference, firstly, the linear displacement generated by the standard velocity vector of the neighbor nodes within the standard random communication delay is superimposed, and then the second-order dynamic correction displacement generated by the resultant external force is superimposed. The calculation method of the second-order dynamic correction displacement is as follows: calculate the vector sum of the standard thrust vector of the neighbor nodes and the translational lumped interference estimate, divide it by the standard mass of the neighbor nodes to obtain the equivalent acceleration, and then multiply the equivalent acceleration by half of the square of the standard random communication delay to obtain the predicted neighbor standard position vector. For the The rotation state delay compensation prediction of each node's neighbor nodes is combined with the rotation lumped interference estimate sent by the neighbor nodes and the dynamic constraint equation of the rotation channel. Based on the Taylor expansion principle of rotational dynamics, the predicted standard attitude angle vector of the neighbor nodes after interference compensation is calculated. The specific calculation logic is as follows: taking the standard attitude angle vector in the state data packet sent by the neighbor nodes as the reference, firstly, the angular displacement generated by the standard angular velocity vector of the neighbor nodes within the standard random communication delay is superimposed, and then the second-order angular dynamic correction displacement generated by the resultant torque is superimposed. The calculation method of the second-order angular dynamic correction displacement is as follows: calculate the vector sum of the standard control torque vector of the neighbor nodes and the rotation lumped interference estimate, use the inverse matrix of the standard rotational inertia matrix of the neighbor nodes to transform the vector sum to obtain the equivalent angular acceleration, and then multiply the equivalent angular acceleration by half of the square of the standard random communication delay to obtain the predicted standard attitude angle vector of the neighbor nodes.

6. The random time-delay UAV formation control method based on an event-triggered mechanism according to claim 5, characterized in that: The comprehensive position error of the current node is calculated in a three-dimensional Cartesian coordinate system. This comprehensive position error is a weighted sum of the cooperative error with neighboring nodes and the tracking error for the expected motion state at the current moment. The cooperative error is calculated by... The tracking error is obtained by calculating the difference between the standard position vector of the nth node, the predicted standard position vector of the neighboring nodes, and the expected distance vector, and then weighting the calculated differences. The difference between the standard position vector of the nth node and the expected motion state at the current moment is used to calculate the weighted sum. The combined position error of the nth node is input into a pre-trained position loop-stabilized manifold neural network to obtain the nth node's position error. The optimal co-state vector of the position loop in the HJB equation is the standard motion state of each node. Based on the optimal co-state vector of the position loop, combined with the optimal feedback control law formula and the difference between the estimated value of the translational set disturbance, the three-dimensional disturbance-resistant virtual resultant force vector is obtained. The magnitude of the three-dimensional anti-disturbance virtual resultant force vector is calculated to obtain the final total thrust command of the UAV rotor. Based on the three-dimensional anti-disturbance virtual resultant force vector and the preset reference yaw angle, the first thrust is obtained by combining backstepping control. The expected attitude angle vector of the nth node is calculated. The difference between the standard attitude vector and the desired attitude angle vector in the standard motion state of the nth node is used to obtain the attitude tracking deviation vector. The combined position error of the nth node is input into the pre-trained attitude loop stable manifold neural network to obtain the nth node. The optimal co-state vector of the attitude loop in the HJB equation is the standard motion state of each node. Based on the optimal co-state vector of the attitude loop, combined with the optimal feedback control law formula and the difference between the estimated value of the rotation set disturbance, the final disturbance rejection torque command is obtained. No. Each node adjusts its motion state according to the final total thrust command and the final disturbance rejection torque command.

7. A random time-delay UAV formation control system based on an event-triggered mechanism, characterized in that: The drone formation control system is used to implement the drone formation control method according to any one of claims 1-6, including: The data acquisition module is used to establish a global inertial coordinate system, acquire the original motion state of each node in the formation cluster in real time, and perform per-unit processing to obtain the standard motion state. The original motion state includes position, velocity, rotation angle and angular velocity. The disturbance definition module is used to establish physical constraints based on the standard motion state using the Newton-Euler equations, construct heterogeneous dynamic constraint equations for translational and rotational channels, and define the true value of lumped disturbances. The disturbance analysis module is used to design a dual-channel nonlinear disturbance observer by combining heterogeneous dynamic constraint equations. It introduces auxiliary variables to transform the differential operation on the motion state into an integral operation, and calculates the lumped disturbance estimate that approximates the true value of the lumped disturbance in real time through nonlinear iteration. The event determination module is used to construct a fully coupled dynamic event triggering mechanism, calculate the dynamic triggering threshold, which is negatively correlated with the magnitude of the lumped disturbance estimate and includes a minimum interval protection term that decays exponentially over time. Communication is triggered when the state error exceeds the dynamic triggering threshold. The communication module is used to correct the motion state of neighboring nodes with random communication delays based on the lumped interference estimate, so as to obtain the predicted motion state of the neighbors. The formation correction module is used to construct a cascaded optimal disturbance rejection controller. It calculates the position and attitude coordination error of the nodes, inputs the position and attitude coordination error of the nodes into an offline trained stable manifold neural network to directly infer the optimal costate vector, solves to obtain the optimal nominal control law, and introduces the lumped disturbance estimate for feedforward compensation to generate the final physical control command and execute it.

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