A multi-aircraft safe formation control method under asynchronous communication

Abstract

This invention relates to the field of cluster command and control technology, and discloses a method for safe formation control of multiple aircraft under asynchronous communication. This method employs a cascaded distributed architecture of upper-level formation coordination and lower-level safety filtering: each aircraft, at its own independent sampling time, generates nominal control input based on the latest available states of the virtual leader and neighbors through an asynchronous formation consensus protocol; combining obstacles detected by airborne sensors and locally perceived neighbors, collision avoidance, obstacle avoidance, and communication maintenance safety functions are constructed; the safety constraints are linearized using higher-order control obstacle functions, and soft and hard constraints are set, combined with dynamic physical limiting to construct a quadratic programming safety filter; the actual safety control input is solved online to drive the aircraft's motion. This invention decouples coordination and safety control, eliminates dependence on a global synchronization clock, and improves formation stability and safety in weak communication environments.

Description

Technical Field

[0001] This invention relates to the field of cluster command and control technology, specifically to a method for safe formation control of multiple aircraft under asynchronous communication. Background Technology

[0002] Multi-vehicle systems can collaboratively perform reconnaissance and target search missions, offering advantages over single-vehicle systems such as wider coverage, higher mission efficiency, and stronger environmental adaptability. To achieve collaborative flight, each vehicle needs to exchange neighbor status information to achieve distributed collaborative control, enabling the entire system to form a preset formation and fly along a desired reference trajectory.

[0003] However, in actual flight environments, due to the inherent drift of the aircraft's local clock and the influence of external electromagnetic interference, wireless channel fluctuations, and limited communication bandwidth, it is difficult for each aircraft to synchronously acquire neighbor state information at a completely uniform sampling time. Under discrete and independent asynchronous communication conditions, existing safety cooperative control methods mainly face two shortcomings. Firstly, because the neighbor states acquired by each aircraft are delayed, highly coupled safety constraints are easily misestimated, leading to control input jumps, formation error fluctuations, and failures in collision and obstacle avoidance maneuvers. Secondly, under asynchronous sampling conditions, multiple constraints such as collision avoidance, obstacle avoidance, and communication connectivity maintenance among aircraft can create competition, easily leading to infeasibility in the optimization problem. Furthermore, traditional complex nonlinear solution methods have a high computational burden and cannot meet the real-time requirements of airborne control platforms.

[0004] Therefore, existing multi-aircraft safety cooperative control methods, in asynchronous communication environments without a global synchronization clock, struggle to balance distributed formation coordination performance with the feasibility and real-time performance of online multi-constraint solutions. This can easily lead to formation instability or even collision hazards, failing to meet the safety formation control requirements of multi-aircraft vehicles in complex engineering scenarios. To address this, a multi-aircraft safety formation control method under asynchronous communication is proposed, resolving the aforementioned problems. Summary of the Invention

[0005] The purpose of this invention is to provide a method for safe formation control of multiple aircraft under asynchronous communication, the method comprising: Acquire initial parameters for multi-aircraft system formation missions; At each independent discrete sampling moment of each aircraft, the latest available states of the virtual navigator and its neighboring aircraft are read from the local communication cache according to the initial parameters of the formation mission. The position state error and velocity state error between the aircraft and its neighboring aircraft are established. Based on the velocity and heading angle of the virtual navigator as a reference, the offset vector and velocity compensation vector of each aircraft in the time-varying formation are established. The nominal formation control input is generated through the asynchronous formation consistency protocol. During the flight mission, the aircraft uses onboard sensors to detect obstacle data within the local perception range of the aircraft to establish an obstacle set, and determines the local safety perception neighbor set based on the local safety perception radius of the onboard sensors. Based on the nominal formation control input, the obstacle set, the local safety-aware neighbor set, and the safety distance threshold in the initial parameters of the formation task, collision avoidance safety functions, obstacle avoidance safety functions, and communication connectivity maintenance safety functions are constructed respectively. The collision avoidance safety functions, obstacle avoidance safety functions, and communication connectivity maintenance safety functions are transformed into linear inequality constraints with respect to the control input using higher-order control obstacle functions. Collision avoidance and obstacle avoidance are treated as hard safety constraints, and communication connectivity maintenance is treated as a soft constraint that introduces non-negative relaxation variables. Combined with the dynamic physical amplitude limiting constraints of the aircraft, a quadratic programming model of the safety filter is constructed. The actual safety control input is obtained by solving the quadratic programming model of the safety filter online, and then the actual safety control input is applied to the power actuator of the corresponding aircraft to drive the aircraft to move.

[0006] Furthermore, the initial parameters for the formation mission include aircraft kinematic model parameters, reference trajectory parameters of the virtual navigator, communication topology matrix between follower aircraft, connection parameters between the virtual navigator and follower aircraft, sampling period, and the latest available state definition: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] A cluster second-order kinematic model consisting of one follower aircraft and one virtual navigator aircraft, where the first... The kinematic model of the aircraft is represented as follows: , In the formula, Indicates the first The first derivative of the position of the following aircraft with respect to time. Indicates the first Speed ​​information of the aircraft Indicates the first The first derivative of the velocity of the following aircraft with respect to time Indicates the first Control input information for each aircraft Indicates that it includes all A set of nodes for each follower aircraft is used to represent the second-order continuous particle motion state of each follower aircraft; the kinematic model of the virtual navigator aircraft is defined as follows: , In the formula, Indicates the reference position of the virtual navigator. The first derivative with respect to time Indicates the reference speed of the virtual navigator. The first derivative with respect to time The reference acceleration vector of the virtual navigator is used to provide a guide trajectory reference for the formation. The directed communication network topology between the following aircraft is represented as follows: , In the formula, This indicates the communication link relationship between aircraft. Represents the communication topology matrix between following aircraft, in the... The aircraft is able to reach the first In the case of an aircraft sending status information, determine yes The neighboring nodes are denoted as And communication weights In the The aircraft cannot reach the first Communication weights when an aircraft sends status information Thus, the first The communication neighbor set of each aircraft is: , The connection vector between the virtual navigator and follower aircraft is defined as follows: ,in Indicates the first The connection weight between each aircraft and the virtual navigator aircraft, in the th... When an aircraft can directly receive information from a virtual navigator aircraft In the When an aircraft cannot directly receive information from a virtual navigator aircraft ; Setting the first The sampling time of each aircraft is a real number sequence. Furthermore, the interval between adjacent sampling times satisfies the bounded condition: , In the formula, Represents the upper limit of the sampling period for positive real numbers; defined at any time... No. The latest sampling sequence number used by a neighbor for a given aircraft is represented as: , The corresponding latest available sampling time is defined as and define the first The abbreviated notation for the state of each neighboring spacecraft at the latest available sampling time is: , In the formula, Indicates the first The latest available position vector of each neighboring aircraft Indicates the latest available velocity vector. This represents the latest available control input vector, where .

[0007] Furthermore, the step of establishing an obstacle set by detecting obstacle data within the local perception range of the aircraft using airborne sensors, and determining a local safety perception neighbor set based on the local safety perception radius of the airborne sensors, includes: setting the minimum safety distance between aircraft as... The set of obstacles is For the first For each obstacle, an envelope model is used, with the circumcircle as the center. Envelope radius is And set a safe buffer distance outside the actual obstacle boundary. The maximum allowable communication distance between aircraft is set as follows: Construct a time-varying local security-aware topology: , In the formula, Represents a time-varying set of locally perceptual edges. This represents the local security-aware adjacency matrix, and its elements are defined as follows: , In the formula, This represents the local safety perception radius of the aircraft's onboard sensors. Indicates the first The aircraft obtained the first [data] through its onboard sensors. The estimated position of an aircraft under ideal perception conditions. , Represents Euclidean norm operations; determines the first [unit / group] based on the local security-aware adjacency matrix. The aircraft at time The local security-aware neighbor set is: , According to the minimum safe distance Obstacle envelope center Envelope radius Safety buffer distance and maximum communication distance Three types of safety constraints are established for safe formation flight of multiple aircraft: No. The aircraft and the first The physical distance between the aircraft satisfies the collision avoidance constraint: , No. The aircraft and its sensing range The physical distances between the obstacles satisfy the obstacle avoidance constraints: , No. The physical distance between an aircraft and its local security-aware neighbor aircraft satisfies the communication connectivity maintenance constraint: .

[0008] Furthermore, the calculation process of the time-varying formation bias and its derivative includes: The reference velocity vector of the virtual navigator is represented as... ,in This represents the horizontal component of the reference velocity vector. Representing the vertical component of the reference velocity vector, calculate the heading angle of the virtual navigator: , Construct a two-dimensional rotation matrix based on the heading angle to transform the navigator's motion coordinate system to the inertial coordinate system: , According to the The fixed formation offset vector of each aircraft in the navigator's motion coordinate system is preset. Calculate the first Time-varying formation offset vector of an aircraft in inertial coordinate system: , Differentiating the time-varying formation offset vector with respect to time yields the time-varying formation offset velocity compensation vector: , In the formula, the heading angular velocity is expressed as: ,in This is the reference acceleration vector for the virtual navigator.

[0009] Furthermore, the generation of nominal formation control input via the asynchronous formation consensus protocol includes: The target condition for the system to achieve asynchronous formation consistency is set as follows: , , In the Each aircraft's own sampling range Inside, based on the first The sampling position status of the individual aircraft With speed state The first Latest availability status of neighboring aircraft and The latest available reference position of the virtual navigator Compared with reference speed and the time-varying formation bias vector With time-varying formation offset velocity compensation vector The nominal formation control input is calculated according to the following asynchronous formation consensus protocol. : , In the formula, Indicates the position term gain. Indicates the gain of the velocity term. Indicates the first The neighboring aircraft at time The time-varying formation bias vector, Indicates the first A neighboring aircraft at a time The time-varying formation offset velocity compensation vector; driven by the asynchronous formation consensus protocol. Under discrete asynchronous communication conditions, each aircraft converges to the desired formation and tracking speed.

[0010] Furthermore, the construction of the inter-vehicle collision avoidance safety function, obstacle avoidance safety function, and communication connectivity maintenance safety function includes: Regarding the first An aircraft and its local security-aware neighbor set The first in For each neighboring aircraft, construct a collision avoidance safety function: , exist In the case of, characterizing the first The aircraft and the first The distance between each aircraft shall not be less than the minimum safe distance. To meet the collision avoidance requirements between aircraft; for the first The aircraft and its sensing range Given several obstacles, construct an obstacle avoidance safety function: , exist In the case of, characterizing the first The first aircraft is located outside the obstacle safety boundary; regarding the first... A set of aircraft and their communication neighbors The first in For each neighboring aircraft, establish a function to maintain secure communication connectivity: , exist In the case of, characterizing the first The aircraft and the first The distance between the aircraft did not exceed the communication radius. The corresponding communication link remains valid; the first security function constituted by the above security function All safety constraints for an aircraft are arranged vertically in column vector form as follows: .

[0011] Furthermore, the step of transforming the safety function into a linear inequality constraint with respect to the control input using a higher-order control barrier function includes: For any barrier function The conditions for the second-order higher-order control barrier function are set as follows: , In the formula, This represents the first total derivative of the security function with respect to time. This represents the second total derivative of the security function with respect to time. and All represent parameters of the higher-order control obstacle function, which transforms the aircraft safety constraints into parameters related to the actual control input vector. Linear inequality constraints ,in To control the input coefficient matrix, The corresponding lower bound of the constraint; the collision avoidance safety function Substituting the derivative into the given second-order higher-order control barrier function conditions, we obtain the following... Collision avoidance linear inequality hard constraints: , In the formula, , ,in and The parameters of the higher-order control obstacle function corresponding to collision avoidance; the obstacle avoidance safety function Substituting the derivative into the given second-order higher-order control barrier function conditions, we obtain the following... Obstacle avoidance linear inequality hard constraints: , In the formula, , ,in and The parameters for the higher-order control obstacle function corresponding to obstacle avoidance; the function for maintaining the safety of communication connectivity. Substituting the derivative into the given second-order higher-order control barrier function conditions, we obtain the following... The communication connectivity preservation linearity inequality constraint: , In the formula, , ,in and To maintain the corresponding higher-order control barrier function parameters for communication connectivity.

[0012] Furthermore, the construction of the quadratic programming model for the safety filter, which incorporates the dynamic physical limiting constraints of the aircraft, includes: The collision avoidance linear inequality constraint and the obstacle avoidance linear inequality constraint are used as hard safety constraints, and non-negative relaxation variables are introduced into the communication connectivity preservation linear inequality constraint. As a soft constraint, the optimization variables are expanded to: , The extended form of the three types of constraints is defined as follows: , The first All safety constraints corresponding to each aircraft are stacked row by row to obtain a unified safety constraint form: , In the formula, It is obtained by stacking the constraint matrices corresponding to all safety constraints row by row. Obtained by stacking the corresponding lower bound scalars column by column; according to the first The maximum control input component of each aircraft Maximum speed component limit and control step size Construct dynamic physical limiting constraints: , , In the formula, and They represent the first The components of the current velocity vector of an aircraft in the horizontal and vertical directions.

[0013] Furthermore, the online solution of the quadratic programming model of the security filter to obtain the actual security control input includes: Define the selection matrix as follows: , Make the optimization variables The part corresponding to the actual control input is represented as follows: Within each control cycle, the first Solve the following distributed quadratic programming problem for each aircraft: , , , In the formula, The nominal formation control input generated for the asynchronous formation consensus protocol. Penalize the weights for slack variables; solve online to obtain the globally optimal decision vector. Then, extract the actual safety control input: , And input the actual safety control As a low-level instruction, it is output to the... The aircraft's power actuators are used to update the aircraft's status.

[0014] Compared with the prior art, the present invention has the following advantages: (1) Based on the distributed control architecture of upper-level formation coordination and lower-level safety filtering, the nominal formation control input is generated by each aircraft using the latest available state of its neighbors at its own independent sampling time. The asynchronous sampling difference and information lag problem are concentrated in the upper-level nominal input generation link for processing, realizing the functional decoupling of formation coordination control and flight safety protection; effectively eliminating the dependence of traditional formation on global synchronization clock and centralized processing, preventing control command jumps and formation tracking error divergence caused by outdated states directly interfering with safety boundaries, and significantly improving the stability and engineering applicability of the formation system in weak communication and complex electromagnetic environments; (2) A soft and hard safety constraint hierarchical and relaxation mechanism is established, taking the collision avoidance between aircraft involving physical collisions and static obstacle avoidance as rigid hard safety constraints, and ensuring communication connectivity. The constraints are relaxed by introducing non-negative relaxation variables as soft constraints; when constraint competition occurs, the absolute physical safety of the aircraft is guaranteed first, which avoids the technical defect of no feasible solution in the optimization solution from the mechanism, and significantly improves the solution feasibility of online optimization and formation maneuver obstacle avoidance capability under multi-constraint environment; (3) Based on the high-order control obstacle function, the nonlinear safety constraint of the second-order aircraft system is transformed into a linear inequality constraint about the control input, and a quadratic programming safety filter model is constructed by combining the dynamic physical limit of the aircraft; only the nominal formation control input is subjected to the minimum correction that satisfies the safety boundary, which greatly reduces the computational complexity of the airborne embedded computing platform, realizes the millisecond-level high real-time online solution of control commands, and the optimized safety commands can be directly connected to the existing flight control execution mechanism, taking into account the formation accuracy, real-time safety and engineering deployment feasibility. Attached Figure Description

[0015] Figure 1 This is a diagram of the distributed cascaded architecture of multiple aircraft in this invention.

[0016] Figure 2 This is a flowchart of the multi-aircraft safe formation control method of the present invention.

[0017] Figure 3 This is a flight trajectory diagram of multiple aircraft according to the present invention.

[0018] Figure 4 This is a diagram showing the formation changes of multiple aircraft at different times according to the present invention.

[0019] Figure 5 For the present invention, multiple aircraft Direction and position tracking error curve.

[0020] Figure 6 This invention relates to multiple aircraft Direction and position tracking error curve.

[0021] Figure 7 This is a graph showing the speed tracking error of multiple aircraft in this invention.

[0022] Figure 8 This is a graph showing the minimum safety function curve for collision avoidance constraints between aircraft in this invention.

[0023] Figure 9 This is a graph showing the minimum safety function curve for obstacle constraints in this invention.

[0024] Figure 10 This is a graph showing the minimum security function curve for communication connectivity constraints in this invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be described below with reference to the accompanying drawings. The embodiments described below are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] In this embodiment, the multi-vehicle system consists of six follower aircraft and one virtual navigator aircraft. The set of follower aircraft nodes is denoted as . The virtual navigator moves along a preset reconnaissance path. Six follower aircraft need to form a preset triangular formation under asynchronous sampling communication conditions and maintain this formation to complete the reconnaissance mission. At the same time, they must avoid collisions with other aircraft and obstacles during flight and maintain communication network connectivity.

[0027] like Figure 1 and Figure 2 As shown, this invention is based on a distributed control architecture that cascades upper-level formation coordination and lower-level safety filtering. This architecture centralizes the processing of neighbor information update differences and lags caused by asynchronous communication at the upper level, where nominal formation control commands are generated. The lower-level safety filter performs online safety filtering on the nominal control input, outputting the actual safety control input applied to the aircraft's underlying power actuators. This achieves functional decoupling between formation coordination control and flight physical safety. This invention provides a technical solution: a method for multi-aircraft safe formation control under asynchronous communication, comprising: A two-dimensional low-altitude flight plane is selected as the reconnaissance area, and the number of follower aircraft is set. A cluster second-order kinematic model is constructed, consisting of six follower aircraft and one virtual navigator aircraft, where the kinematic model is... The kinematic model of the following aircraft is represented as follows: , In the formula, Indicates the first The first derivative of the position of the following aircraft with respect to time. Indicates the first Speed ​​information of the aircraft Indicates the first The first derivative of the velocity of the following aircraft with respect to time Indicates the first The control input information of an aircraft, namely the acceleration control quantity. This represents the set of nodes containing all 6 follower aircraft, used to characterize the second-order continuous particle motion state of each follower aircraft.

[0028] The virtual navigation aircraft moves along a preset reconnaissance reference trajectory, and its kinematic model is represented as follows: , In the formula, Indicates the reference position of the virtual navigator. The first derivative with respect to time Indicates the reference speed of the virtual navigator. The first derivative with respect to time This represents the reference acceleration vector of the virtual navigator, used to provide a guide trajectory reference for the formation.

[0029] In this embodiment, the preset reconnaissance reference trajectory of the virtual navigation aircraft is set as follows: , In the formula, Indicates flight time. The virtual navigator's initial position is set to... The initial velocity is set to The initial positions of the six follower aircraft were set as follows: , , , , , The initial velocity is uniformly set to .

[0030] The directed communication network topology between the following aircraft is represented as follows: In the formula This indicates the communication link relationship between aircraft. This represents the communication topology matrix between following aircraft. In the... The aircraft is able to reach the first In the case of an aircraft sending status information, determine yes The neighboring nodes are denoted as And communication weights ; in the The aircraft cannot reach the first Communication weights when an aircraft sends status information Therefore, the first is defined. The communication neighbor set of each aircraft is The connection vector between the virtual navigator and follower aircraft is defined as follows: ,in Indicates the first The connection weight between each aircraft and the virtual navigator aircraft, in the th... When an aircraft can directly receive information from a virtual navigator aircraft In the When an aircraft cannot directly receive information from a virtual navigator aircraft .

[0031] Setting the first The sampling time of each aircraft is a real number sequence. And the interval between adjacent sampling times satisfies the bounded condition. In the formula This represents the upper limit of the sampling period for positive real numbers. Defined at any given time... No. The latest sampling sequence number used by the neighbor for each aircraft is represented as: The corresponding latest available sampling time is defined as Definition of the first The abbreviated notation for the state of each neighboring spacecraft at the latest available sampling time is: , In the formula, Indicates the first The latest available position vector of each neighboring aircraft Indicates the latest available velocity vector. This represents the latest available control input vector, where .

[0032] Let the minimum safe distance between aircraft be... The set of obstacles is For the first For each obstacle, an envelope model is used, with the circumcircle as the center. Envelope radius is And set a safe buffer distance outside the actual obstacle boundary. At this time, the overall protection radius of the obstacle is The maximum allowable communication distance between aircraft is set as follows. The centers of the four static obstacles are set as follows: , , , .

[0033] Typical parameter settings for this embodiment are shown in Table 1: Table 1 Typical parameter settings In Table 1, the fixed formation offset The relative spatial positions of each aircraft in the navigator's motion coordinate system were defined. Sampling period. This demonstrates that each aircraft has its own independent discrete sampling timing, without relying on a global synchronization clock.

[0034] Based on the speed and heading angle of the virtual navigator aircraft, the offset vector and velocity compensation vector of each aircraft in the time-varying formation are established: The reference velocity vector of the virtual navigator is represented as: ,in This represents the horizontal component of the reference velocity vector. Representing the vertical component of the reference velocity vector, calculate the heading angle of the virtual navigator: , Construct a two-dimensional rotation matrix to transform the navigator's moving coordinate system to the inertial coordinate system based on the heading angle: , According to the The fixed formation offset vector of each aircraft in the navigator's motion coordinate system is preset. Calculate the first Time-varying formation offset vector of an aircraft in inertial coordinate system: , Taking the derivative of the time-varying formation bias vector with respect to time, we obtain the time-varying formation bias velocity compensation vector: , In the formula, the heading angular velocity is expressed as: ,in This is the reference acceleration vector for the virtual navigator.

[0035] At each aircraft's independent discrete sampling time, after reading the latest available state of neighboring aircraft from the local communication buffer, the position state error and velocity state error between the aircraft and its neighbors are established. Combining the time-varying formation offset vector and the time-varying formation offset velocity compensation vector, the first... The aircraft and the first A communication neighbor aircraft at time The relative position error of the formation is , define the first The aircraft and the first A communication neighbor aircraft at time The formation relative velocity state error is .

[0036] The target condition for the system to achieve asynchronous formation consistency is set as follows: , , In the Each aircraft's own sampling range Inside, based on the established first The aircraft and the first The position and velocity errors between the communicating neighboring aircraft are combined with the latest available reference position of the virtual navigator aircraft. Compared with reference speed The nominal formation control input is calculated according to the following asynchronous formation consensus protocol. : In the formula, Indicates the position term gain. Indicates the gain of the velocity term. Indicates the first A neighboring aircraft at a time The time-varying formation bias vector, Indicates the first A neighboring aircraft at a time The time-varying formation offset velocity compensation vector. In this embodiment, the position term gain is set to... The speed gain is set to The result calculated through this protocol As a reference input for the next-level security filter.

[0037] During the flight mission, the aircraft uses onboard sensors to detect obstacle data within its local perception range to establish a time-varying obstacle set, and determines the local safety perception neighbor set based on the local safety perception radius of the onboard sensors.

[0038] Constructing a time-varying local security-aware topology In the formula Represents a time-varying set of locally perceptual edges. This represents the local security-aware adjacency matrix, and its elements are defined as follows: , In the formula, This represents the local safety perception radius of the aircraft's onboard sensors. Indicates the first The aircraft obtained the first [data] through its onboard sensors. The estimated position of an aircraft under ideal perception conditions. , This represents the Euclidean norm operation. The first [unit / group] is determined based on the local security-aware adjacency matrix. The aircraft at time The local security-aware neighbor set is .

[0039] No. The aircraft at time All detected obstacle information is stored in a local cache to build an obstacle set. : , In the formula, For the first The aircraft at time Number of obstacles detected.

[0040] Based on the nominal formation control input, obstacle set, local safety-aware neighbor set, and safety distance threshold in the initial parameters of the formation mission, collision avoidance safety function, obstacle avoidance safety function, and communication connectivity maintenance safety function are constructed respectively: Regarding the first An aircraft and its local security-aware neighbor set The first in For each neighboring aircraft, construct a collision avoidance safety function: , exist In the case of, characterizing the first The aircraft and the first The distance between each aircraft shall not be less than the minimum safe distance. This meets the requirements for collision avoidance between aircraft.

[0041] Regarding the first The aircraft and its sensing range Given several obstacles, construct an obstacle avoidance safety function: , exist In the case of, characterizing the first The aircraft is located at the obstacle safety boundary. In addition.

[0042] Regarding the first A set of aircraft and their communication neighbors The first in For each neighboring aircraft, establish a function to maintain secure communication connectivity: , exist In the case of, characterizing the first The aircraft and the first The distance between the aircraft did not exceed the communication radius. The corresponding communication link remains valid.

[0043] The first security function constituted by the above All safety constraints for an aircraft are arranged vertically in column vector form as follows: , For any barrier function The second-order higher-order control barrier function condition is set as follows: In the formula This represents the first total derivative of the security function with respect to time. This represents the second total derivative of the security function with respect to time. and All represent parameters of the higher-order control obstacle function, which transforms the aircraft safety constraints into parameters related to the actual control input vector. Linear inequality constraints ,in To control the input coefficient matrix, The corresponding lower bound of the constraint: Collision avoidance safety function After differentiating and substituting the second-order higher-order control barrier function conditions, we obtain the following about Collision avoidance linear inequality hard constraints: In the formula , ,in and The parameters of the higher-order control obstacle function for collision avoidance; Obstacle avoidance safety function After differentiating and substituting the second-order higher-order control barrier function conditions, we obtain the following about Obstacle avoidance linear inequality hard constraints: In the formula , ,in and The parameters for the higher-order obstacle avoidance control function; Function to maintain communication connectivity After differentiating and substituting the second-order higher-order control barrier function conditions, we obtain the following about The communication connectivity preservation linearity inequality constraint: In the formula , ,in and To maintain the corresponding higher-order control barrier function parameters for communication connectivity.

[0044] Collision avoidance linear inequality constraints and obstacle avoidance linear inequality constraints are used as hard safety constraints, and non-negative relaxation variables are introduced into the communication connectivity preservation linear inequality constraints. As a soft constraint, and by expanding the optimization variables to The extended form of the three types of constraints is defined as follows: , The first All safety constraints corresponding to each aircraft are stacked row by row to obtain a unified safety constraint form. In the formula It is obtained by stacking the constraint matrices corresponding to all safety constraints row by row. It is obtained by stacking the corresponding lower bound scalars in columns.

[0045] During the control cycle, it is determined whether the current moment is the sampling moment of the aircraft itself: if the current moment is determined to be the sampling moment of the aircraft itself... In this case, read the current location of the local machine. With speed Virtual Navigator Status and And the latest availability status of neighboring aircraft stored in the local communication cache. , Time-varying bias and its derivative , and thus establish the first The aircraft and the first The position and state error of each neighboring aircraft at the current sampling time and speed state error It broadcasts its own status information to the outside world, including the gain parameter. and Calculate nominal formation control input : If the current time is determined not to be the sampling time of the aircraft itself, the nominal formation control input calculated at the previous sampling time is retained.

[0046] According to the The maximum control input component of each aircraft Maximum speed component limit and control step size Construct dynamic physical limiting constraints: , , In the formula, and They represent the first The components of the current velocity vector of an aircraft in the horizontal and vertical directions.

[0047] Define the selection matrix as This makes the optimization variables The part corresponding to the actual control input is represented as follows: Within each control cycle, the first... Each aircraft is introduced into a slack variable penalty weight. Solve the following distributed quadratic programming problem online: , , , Online solution to obtain the global optimal decision vector Then, extract the actual safety control input. And output the actual safety control input as the underlying instruction to the first The power actuators of an aircraft drive its movement and update its status.

[0048] The above steps are used to perform simulation verification of asynchronous safe formation control for multiple aircraft: like Figure 3 and Figure 4As shown, the follower aircraft gradually converges from a dispersed state to a preset triangular formation configuration in the initial stage; when approaching the obstacle area, the formation configuration is locally adaptively adjusted according to safety constraints to smoothly maneuver around obstacles; after passing the obstacle, the system can quickly restore and maintain the preset formation configuration and fly stably following the virtual navigator's trajectory.

[0049] like Figure 5 , Figure 6 and Figure 7 As shown, under asynchronous communication conditions, the position tracking error and velocity tracking error of each aircraft in the horizontal and vertical directions converge to a minimum neighborhood near zero during the stable cruise phase. When encountering strong constraint obstacles, although there are brief fluctuations due to safety filtering intervention, the tracking remains bounded and quickly recovers stability throughout the entire process, demonstrating good tracking accuracy and convergence.

[0050] like Figure 8 , Figure 9 and Figure 10 As shown, throughout the entire flight mission cycle, the minimum safety function curves for collision avoidance, obstacle avoidance, and communication connectivity maintenance all remain strictly above the zero line, indicating that no collisions or obstacle crossings occurred, and the communication network maintained the preset connectivity level. At the same time, no unsolvable phenomena caused by multiple constraint conflicts occurred, fully verifying the safety, adaptability, and engineering feasibility of the present invention under asynchronous communication conditions.

[0051] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0052] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for safe formation control of multiple aircraft under asynchronous communication, characterized in that, The method includes: Acquire initial parameters for multi-aircraft system formation missions; At each independent discrete sampling moment of each aircraft, the latest available states of the virtual navigator and its neighboring aircraft are read from the local communication cache according to the initial parameters of the formation mission. The position state error and velocity state error between the aircraft and its neighboring aircraft are established. Based on the velocity and heading angle of the virtual navigator as a reference, the offset vector and velocity compensation vector of each aircraft in the time-varying formation are established. The nominal formation control input is generated through the asynchronous formation consistency protocol. During the flight mission, the aircraft uses onboard sensors to detect obstacle data within the local perception range of the aircraft to establish an obstacle set, and determines the local safety perception neighbor set based on the local safety perception radius of the onboard sensors. Based on the nominal formation control input, the obstacle set, the local safety-aware neighbor set, and the safety distance threshold in the initial parameters of the formation task, collision avoidance safety functions, obstacle avoidance safety functions, and communication connectivity maintenance safety functions are constructed respectively. The collision avoidance safety functions, obstacle avoidance safety functions, and communication connectivity maintenance safety functions are transformed into linear inequality constraints with respect to the control input using higher-order control obstacle functions. Collision avoidance and obstacle avoidance are treated as hard safety constraints, and communication connectivity maintenance is treated as a soft constraint that introduces non-negative relaxation variables. Combined with the dynamic physical amplitude limiting constraints of the aircraft, a quadratic programming model of the safety filter is constructed. The actual safety control input is obtained by solving the quadratic programming model of the safety filter online, and then the actual safety control input is applied to the power actuator of the corresponding aircraft to drive the aircraft to move.

2. The method for safe formation control of multiple aircraft under asynchronous communication according to claim 1, characterized in that, The initial parameters for the formation mission include aircraft kinematic model parameters, reference trajectory parameters of the virtual navigator, communication topology matrix between follower aircraft, connection parameters between the virtual navigator and follower aircraft, sampling period, and the latest available state definition, which are constructed by... A cluster second-order kinematic model consisting of one follower aircraft and one virtual navigator aircraft, where the first... The kinematic model of the aircraft is represented as follows: ， In the formula, Indicates the first The first derivative of the position of the following aircraft with respect to time. Indicates the first Speed ​​information of the aircraft Indicates the first The first derivative of the velocity of the following aircraft with respect to time Indicates the first Control input information for each aircraft Indicates that it includes all A set of nodes for each follower aircraft is used to represent the second-order continuous particle motion state of each follower aircraft; the kinematic model of the virtual navigator aircraft is defined as follows: ， In the formula, Indicates the reference position of the virtual navigator. The first derivative with respect to time Indicates the reference speed of the virtual navigator. The first derivative with respect to time The reference acceleration vector of the virtual navigator is used to provide a guide trajectory reference for the formation. The directed communication network topology between the following aircraft is represented as follows: ， In the formula, This indicates the communication link relationship between aircraft. Represents the communication topology matrix between following aircraft, in the... The aircraft is able to reach the first In the case of an aircraft sending status information, determine yes The neighboring nodes are denoted as And communication weights In the The aircraft cannot reach the first Communication weights when an aircraft sends status information Thus, the first The communication neighbor set of each aircraft is: ， The connection vector between the virtual navigator and follower aircraft is defined as follows: ,in Indicates the first The connection weight between each aircraft and the virtual navigator aircraft, in the th... When an aircraft can directly receive information from a virtual navigator aircraft In the When an aircraft cannot directly receive information from a virtual navigator aircraft ; Setting the first The sampling time of each aircraft is a real number sequence. Furthermore, the interval between adjacent sampling times satisfies the bounded condition: ， In the formula, Represents the upper limit of the sampling period for positive real numbers, defined at any time. No. The latest sampling sequence number used by a neighbor for a given aircraft is represented as: ， The corresponding latest available sampling time is defined as and define the first The abbreviated notation for the state of each neighboring spacecraft at the latest available sampling time is: ， In the formula, Indicates the first The latest available position vector of each neighboring aircraft Indicates the latest available velocity vector. This represents the latest available control input vector, where .

3. The method for safe formation control of multiple aircraft under asynchronous communication according to claim 2, characterized in that, The process of detecting obstacle data within the local perception range of an aircraft using airborne sensors to establish an obstacle set, and determining a local safety perception neighbor set based on the local safety perception radius of the airborne sensors, includes: setting the minimum safety distance between aircraft as... The set of obstacles is For the first For each obstacle, an envelope model is used, with the circumcircle as the center. Envelope radius is And set a safe buffer distance outside the actual obstacle boundary. The maximum allowable communication distance between aircraft is set as follows: Construct a time-varying local security-aware topology: ， In the formula, Represents a time-varying set of locally perceptual edges. This represents the local security-aware adjacency matrix, and its elements are defined as follows: ， In the formula, This represents the local safety perception radius of the aircraft's onboard sensors. Indicates the first The aircraft obtained the first [data] through its onboard sensors. The estimated position of an aircraft under ideal perception conditions. , Represents Euclidean norm operations; determines the first [unit / group] based on the local security-aware adjacency matrix. The aircraft at time The local security-aware neighbor set is: ， According to the minimum safe distance Obstacle envelope center Envelope radius Safety buffer distance and maximum communication distance Three types of safety constraints are established for safe formation flight of multiple aircraft: No. The aircraft and the first The physical distance between the aircraft satisfies the collision avoidance constraint: ， No. The aircraft and its sensing range The physical distances between the obstacles satisfy the obstacle avoidance constraints: ， No. The physical distance between an aircraft and its local security-aware neighbor aircraft satisfies the communication connectivity maintenance constraint: 。 4. The method for safe formation control of multiple aircraft under asynchronous communication according to claim 3, characterized in that, The calculation process of the time-varying formation bias and its derivative includes: The reference velocity vector of the virtual navigator is represented as... ,in This represents the horizontal component of the reference velocity vector. Representing the vertical component of the reference velocity vector, calculate the heading angle of the virtual navigator: ， Construct a two-dimensional rotation matrix based on the heading angle to transform the navigator's motion coordinate system to the inertial coordinate system: ， According to the The fixed formation offset vector of each aircraft in the navigator's motion coordinate system is preset. Calculate the first Time-varying formation offset vector of an aircraft in inertial coordinate system: ， Differentiating the time-varying formation offset vector with respect to time yields the time-varying formation offset velocity compensation vector: ， In the formula, the heading angular velocity is expressed as: ,in This is the reference acceleration vector for the virtual navigator.

5. The method for safe formation control of multiple aircraft under asynchronous communication according to claim 4, characterized in that, The generation of nominal formation control input via asynchronous formation consensus protocol includes: The target condition for the system to achieve asynchronous formation consistency is set as follows: ， ， In the Each aircraft's own sampling range Inside, based on the first The sampling position status of the individual aircraft With speed state The first Latest availability status of neighboring aircraft and The latest available reference position of the virtual navigator Compared with reference speed and the time-varying formation bias vector With time-varying formation offset velocity compensation vector The nominal formation control input is calculated according to the following asynchronous formation consensus protocol. : ， In the formula, Indicates the position term gain. Indicates the gain of the velocity term. Indicates the first The neighboring aircraft at time The time-varying formation bias vector, Indicates the first The neighboring aircraft at time The time-varying formation offset velocity compensation vector; driven by the asynchronous formation consensus protocol. Under discrete asynchronous communication conditions, each aircraft converges to the desired formation and tracking speed.

6. The method for safe formation control of multiple aircraft under asynchronous communication according to claim 3, characterized in that, The construction of the inter-vehicle collision avoidance safety function, obstacle avoidance safety function, and communication connectivity maintenance safety function includes: Regarding the first An aircraft and its local security-aware neighbor set The first in For each neighboring aircraft, construct a collision avoidance safety function: ， exist In the case of, characterizing the first The aircraft and the first The distance between each aircraft shall not be less than the minimum safe distance. To meet the collision avoidance requirements between aircraft; for the first The aircraft and its sensing range Given several obstacles, construct an obstacle avoidance safety function: ， exist In the case of, characterizing the first The first aircraft is located outside the obstacle safety boundary; regarding the first... A set of aircraft and their communication neighbors The first in For each neighboring aircraft, establish a function to maintain secure communication connectivity: ， exist In the case of, characterizing the first The aircraft and the first The distance between the aircraft did not exceed the communication radius. The corresponding communication link remains valid; the first security function constructed above constitutes the second security function. All safety constraints of an aircraft are arranged vertically in column vector form as follows: 。 7. The method for safe formation control of multiple aircraft under asynchronous communication according to claim 6, characterized in that, The process of transforming the safety function into a linear inequality constraint with respect to the control input using a higher-order control barrier function includes: For any barrier function The conditions for the second-order higher-order control barrier function are set as follows: ， In the formula, This represents the first total derivative of the security function with respect to time. This represents the second total derivative of the security function with respect to time. and All represent parameters of the higher-order control obstacle function, which transforms the aircraft safety constraints into parameters related to the actual control input vector. Linear inequality constraints ,in To control the input coefficient matrix, The corresponding lower bound of the constraint; the collision avoidance safety function Substituting the derivative into the given second-order higher-order control barrier function conditions, we obtain the following... Collision avoidance linear inequality hard constraints: ， In the formula, , ,in and The parameters of the higher-order control obstacle function corresponding to collision avoidance; the obstacle avoidance safety function Substituting the derivative into the given second-order higher-order control barrier function conditions, we obtain the following... Obstacle avoidance linear inequality hard constraints: ， In the formula, , ,in and The parameters for the higher-order control obstacle function corresponding to obstacle avoidance; the function for maintaining the safety of communication connectivity. Substituting the derivative into the given second-order higher-order control barrier function conditions, we obtain the following... The communication connectivity preservation linearity inequality constraint: ， In the formula, , ,in and To maintain the corresponding higher-order control barrier function parameters for communication connectivity.

8. The method for safe formation control of multiple aircraft under asynchronous communication according to claim 7, characterized in that, The construction of a quadratic programming model for the safety filter, which incorporates the dynamic physical limiting constraints of the aircraft, includes: The collision avoidance linear inequality constraint and the obstacle avoidance linear inequality constraint are used as hard safety constraints, and non-negative relaxation variables are introduced into the communication connectivity preservation linear inequality constraint. As a soft constraint, the optimization variables are expanded to: ， The extended form of the three types of constraints is defined as follows: ， The first All safety constraints corresponding to each aircraft are stacked row by row to obtain a unified safety constraint form: ， In the formula, It is obtained by stacking the constraint matrices corresponding to all safety constraints row by row. Obtained by stacking the corresponding lower bound scalars column by column; according to the first The maximum control input component of each aircraft Maximum speed component limit and control step size Construct dynamic physical limiting constraints: ， ， In the formula, and They represent the first The components of the current velocity vector of an aircraft in the horizontal and vertical directions.

9. The method for safe formation control of multiple aircraft under asynchronous communication according to claim 8, characterized in that, The online solution of the quadratic programming model of the security filter yields the actual security control input, including: Define the selection matrix as follows: ， Make the optimization variables The part corresponding to the actual control input is represented as follows: Within each control cycle, the first Solve the following distributed quadratic programming problem for each aircraft: ， ， ， In the formula, The nominal formation control input generated for the asynchronous formation consensus protocol. Penalize the weights for slack variables; solve online to obtain the globally optimal decision vector. Then, extract the actual safety control input: ， And input the actual safety control As a low-level instruction, it is output to the... The aircraft's power actuators are used to update the aircraft's status.

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