Multi-autonomous water surface vehicle formation control method and device

Abstract

The invention relates to a multi-autonomous water surface vehicle formation control method and device, and the method comprises the steps: taking the position information and speed information in the driving data of a plurality of autonomous water surface vehicles as state variables, and constructing a target mathematical model; setting an initial geometrical shape of the plurality of aircrafts for affine formation, and constructing a stress matrix according to the initial geometrical shape; according to the target mathematical model and the stress matrix, obtaining a tracking error of each aircraft in the affine formation; obtaining an affine formation control strategy of each aircraft according to the target mathematical model and the tracking error; a target mathematical model and a stress matrix are constructed to calculate a tracking error, so that an affine formation control strategy of each aircraft is determined in combination with the tracking error and the target mathematical model, the form of the affine formation is dynamically adjusted, communication resource allocation of each aircraft is optimized, the anti-interference capability is improved, and the service life of the aircraft is prolonged. The problem of formation control failure in a complex marine environment of a traditional method is effectively solved.

Description

Technical Field

[0001] This invention relates to the field of ship autopilot technology, and in particular to a method and apparatus for controlling a formation of multiple autonomous surface vehicles. Background Technology

[0002] In recent decades, unmanned surface vessels (USVs) have garnered widespread research attention due to their low maintenance costs, high adaptability, and superior maneuverability. The development of USVs relies on advancements in control theory, marine engineering, and communication technology. This technology has wide applications in many fields, including security patrol, maritime surveillance, and marine mapping. However, existing technologies suffer from the following problems: traditional formation control methods struggle to achieve real-time, continuous formation changes, are unable to adapt to complex marine environments, and have limited communication resources; fixed-time sampling mechanisms lead to bandwidth waste. Especially when facing denial-of-service attacks, communication congestion severely impacts control accuracy, while quantized control inputs and interference from unknown environments exacerbate system stability challenges. This results in multi-autonomous surface vehicle (MAV) systems being unable to withstand denial-of-service attacks in complex environments with network attacks and communication limitations, leading to wasted communication resources and inaccurate formation control.

[0003] Therefore, there is an urgent need to propose a method and device for controlling the formation of multiple autonomous surface vehicles (ASWs) to solve the problems of communication resource waste and inaccurate formation control caused by communication limitations and complex environments in existing ASW systems. Summary of the Invention

[0004] In view of this, it is necessary to provide a method and apparatus for controlling the formation of multiple autonomous surface vehicles (ASWs) to solve the problems of wasted communication resources and inaccurate formation control caused by communication limitations and complex environments in existing ASW systems.

[0005] To address the aforementioned problems, in a first aspect, the present invention provides a method for controlling a formation of multiple autonomous surface vehicles, comprising: A target mathematical model is constructed using position and velocity information from the driving data of multiple autonomous surface vehicles as state variables. The initial geometry of the multiple autonomous surface vehicles in affine formation is set, and a stress matrix is ​​constructed based on the initial geometry. Based on the target mathematical model and the stress matrix, the tracking error of each autonomous surface vehicle in the affine formation is obtained; Based on the target mathematical model and the tracking error, an affine formation control strategy for each autonomous surface vehicle is obtained.

[0006] In one possible implementation, the step of constructing a target mathematical model using position and velocity information from the driving data of multiple autonomous surface vessels as state variables includes: Based on the driving data, the velocity vector and state vector of each autonomous surface vehicle are obtained; Based on the state vector, the rotation matrix is ​​obtained; An initial mathematical model is constructed based on the velocity vector, state vector, control input of the driving data, and other parameters of each autonomous surface vehicle. Based on the other parameters and the velocity vector, the positive definite symmetric inertial matrix, centripetal matrix, and damping matrix of each autonomous surface vehicle are obtained; The inherent dynamic behavior is obtained based on the rotation matrix, the velocity vector, the positive definite symmetric inertia matrix, the centripetal matrix, and the damping matrix. After quantizing the control input, the initial mathematical model is simplified through the inherent dynamic behavior to construct the target mathematical model.

[0007] In one possible implementation, setting the initial geometry of the plurality of autonomous surface vehicles in affine formation and constructing a stress matrix based on the initial geometry includes: Establish the topological relationships between the multiple autonomous surface vehicles; A stress matrix is ​​constructed based on the relative positional constraints between the plurality of autonomous surface vehicles in the initial geometry and the topological relationships.

[0008] In one possible implementation, obtaining the tracking error of each autonomous surface vehicle in the affine formation based on the target mathematical model and the stress matrix includes: Based on the stress matrix, the relative constraint strength between each autonomous surface vehicle and its neighboring vehicles is obtained; The measurement error is obtained by comparing the historical state vector at the moment the dynamic event triggering mechanism was triggered in the historical driving data with the state vector. Based on the measurement error, determine whether each autonomous surface vehicle triggers the dynamic event triggering mechanism; If so, the tracking error of the corresponding autonomous surface vehicle in the affine formation is obtained based on the relative constraint strength, the state vector, and the state vector of the adjacent autonomous surface vehicle. If not, then the tracking error of the corresponding autonomous surface vehicle in the affine formation is obtained based on the relative constraint strength, the historical state vector, and the state vector.

[0009] In one possible implementation, obtaining the affine formation control strategy for each autonomous surface vehicle based on the target mathematical model and the tracking error includes: Based on the tracking error and the velocity vector in the geodetic coordinate system of the target mathematical model, the sliding surface variables are obtained; The inherent dynamic behavior of the sliding surface variables and the target mathematical model is processed by a radial basis function neural network to obtain the affine formation control strategy for each autonomous surface vehicle.

[0010] In one possible implementation, the processing of the inherent dynamic behavior of the sliding surface variables and the target mathematical model based on a radial basis function neural network to obtain the affine formation control strategy for each autonomous surface vehicle includes: Based on the denial-of-service attack data in the historical driving data of the multiple autonomous surface vessels, an inactive denial-of-service attack set and an active denial-of-service attack set are obtained; the inactive denial-of-service attack set is the complement of the active denial-of-service attack set. The radial basis function neural network is used to calculate the preset basis function vector, the sliding mode surface variable, the relative constraint strength, and the measurement error for each autonomous surface vehicle to obtain the updated weights for each autonomous surface vehicle. Based on the driving data, the updated weights, and the inherent dynamic behavior in the target mathematical model, an affine formation control strategy is determined for each autonomous surface vehicle.

[0011] In one possible implementation, determining the affine formation control strategy for each autonomous surface vehicle based on the driving data, the updated weights, and the inherent dynamic behavior in the target mathematical model includes: When the current time in the driving data belongs to the set of inactive denial-of-service attacks, the first affine formation control strategy of the corresponding autonomous surface vehicle is obtained based on the inherent dynamic behavior, the preset basis function vector, the update weight, the tracking error and the sliding surface variable. When the current time in the driving data belongs to the set of active denial-of-service attacks, a second affine formation control strategy for the corresponding autonomous surface vehicle is obtained based on the inherent dynamic behavior.

[0012] In one possible implementation, after obtaining the affine formation control strategy for each autonomous surface vehicle based on the target mathematical model and the tracking error, the method further includes: After controlling the corresponding autonomous surface vehicle using the second affine formation control strategy, the corresponding autonomous surface vehicle is then controlled using the updated first affine formation control strategy for the current time.

[0013] In one possible implementation, the target mathematical model is:

[0014]

[0015] In the formula, ; ; ; ; ; This reflects the inherent dynamic behavior of autonomous surface vehicles; The velocity vector in the volume coordinate system; It is a rotation matrix; It is a centripetal matrix; Here is the damping matrix; It is a positive definite symmetric inertial matrix; For control input; Preset nonlinear bounded disturbance; For linearly bounded disturbances; It is a state vector; This is the velocity vector in the geodetic coordinate system; Affine formation control strategy; For environmental interference; This is the input quantization error.

[0016] Secondly, the present invention also provides a multi-autonomous surface vehicle formation control device, comprising: The model building module is used to construct a target mathematical model using the position and velocity information from the driving data of multiple autonomous surface vehicles as state variables. The matrix construction module is used to set the initial geometry of the multiple autonomous surface vehicles forming an affine formation, and to construct a stress matrix based on the initial geometry. The error calculation module is used to obtain the tracking error of each autonomous surface vehicle in the affine formation based on the target mathematical model and the stress matrix. The strategy determination module is used to obtain the affine formation control strategy for each autonomous surface vehicle based on the target mathematical model and the tracking error.

[0017] The beneficial effects of this invention are as follows: A target mathematical model is constructed using position and velocity information from the driving data of multiple autonomous surface vessels (ASWs) as state variables; an initial geometry is set for the affine formation of multiple ASWs, and a stress matrix is ​​constructed based on the initial geometry; the tracking error of each ASW in the affine formation is obtained based on the target mathematical model and the stress matrix; the affine formation control strategy for each ASW is obtained based on the target mathematical model and the tracking error; by constructing the target mathematical model and calculating the tracking error, the affine formation control strategy for each ASW is determined by combining the tracking error and the target mathematical model, thereby dynamically adjusting the morphology of the affine formation and optimizing the communication resource allocation for each ASW, improving anti-interference capabilities, and effectively solving the problem of formation control failure in complex marine environments using traditional methods. Attached Figure Description

[0018] Figure 1 A schematic flowchart of an embodiment of the multi-autonomous surface vehicle formation control method provided by the present invention; Figure 2 For the present invention Figure 1 A schematic diagram of an embodiment of step S101; Figure 3 For the present invention Figure 1 A schematic flowchart of an embodiment of step S103; Figure 4 This is a schematic diagram of an embodiment of the multi-autonomous surface vehicle formation control device provided by the present invention. Detailed Implementation

[0019] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0020] like Figure 1 As shown, a specific embodiment of the present invention discloses a method for controlling a formation of multiple autonomous surface vehicles, comprising: S101. Using the position and velocity information from the driving data of multiple autonomous surface vehicles as state variables, construct a target mathematical model.

[0021] The multi-autonomous surface vehicle (AUV) formation control method provided in this application can be applied to a multi-autonomous surface vehicle (AUV) formation control system. The AUV formation control system can be a software system running on a terminal device. The terminal device can be a server, tablet computer, augmented reality (AR) / virtual reality (VR) device, laptop computer, ultra-mobile personal computer (UMPC), netbook, personal digital assistant (PDA), mobile phone, or other terminal device. Multiple AUVs can be controlled through this terminal device. This application does not impose any restrictions on the specific type of terminal device.

[0022] Among them, the state variables refer to the vehicle's position coordinates and velocity in three-dimensional space, which can be implemented using longitude, latitude, heading angle, and corresponding linear and angular velocities in a geodetic coordinate system, to comprehensively describe the vehicle's motion state. The target mathematical model refers to the dynamic equations that include the inertia matrix, centripetal force, and damping effects, which can be implemented through Lagrange mechanics modeling, to accurately characterize the dynamic characteristics of the vehicle's motion on the water surface.

[0023] S102. Set the initial geometry of multiple autonomous surface vehicles for affine formation, and construct the stress matrix based on the initial geometry.

[0024] The stress matrix refers to the weight matrix that describes the geometric constraints of the formation. Specifically, it can be constructed by combining the Laplace matrix with the relative position weight coefficients to maintain the rigidity requirements of the formation shape.

[0025] S103. Based on the target mathematical model and stress matrix, the tracking error of each autonomous surface vehicle in the affine formation is obtained.

[0026] Tracking error refers to the deviation between the actual position of an individual vehicle and the desired formation position. Specifically, it can be obtained by weighting the stress matrix and the state of neighboring vehicles, and is used to quantify the degree to which the control target is achieved.

[0027] S104. Based on the target mathematical model and tracking error, obtain the affine formation control strategy for each autonomous surface vehicle.

[0028] Specifically, this method first establishes a dynamic model using real-time position and velocity data of the vehicles, transforming complex hydrodynamic effects into a computable matrix form. A stress matrix is ​​generated by pre-setting the formation geometry, encoding the relative positional constraints between the vehicles. During control, the error of each vehicle relative to the desired formation position is dynamically calculated; this error includes not only its own motion deviation but also the state information of neighboring vehicles. An adaptive control law is designed based on the error signal. By quantizing the control input and introducing an event-triggered mechanism, control commands are updated only when the error exceeds a threshold, thereby significantly reducing communication frequency while maintaining formation accuracy.

[0029] Compared with existing technologies, this embodiment uses position and velocity information from the driving data of multiple autonomous surface vessels (ASWs) as state variables to construct a target mathematical model; sets the initial geometry of the ASWs in an affine formation and constructs a stress matrix based on the initial geometry; obtains the tracking error of each ASW in the affine formation based on the target mathematical model and the stress matrix; obtains the affine formation control strategy for each ASW based on the target mathematical model and the tracking error; calculates the tracking error by constructing the target mathematical model and the stress matrix, and then determines the affine formation control strategy for each ASW by combining the tracking error and the target mathematical model. This allows for dynamic adjustment of the affine formation's shape and optimization of the communication resource allocation for each ASW, improving anti-interference capabilities and effectively solving the problem of formation control failure in complex marine environments using traditional methods.

[0030] In some embodiments of the present invention, such as Figure 2 As shown, step S101 includes: S201. Based on the driving data, obtain the velocity vector and state vector of each autonomous surface vehicle.

[0031] The state vector refers to a multidimensional variable that contains position and velocity information. Specifically, it can be formed by combining coordinate values ​​in the geodetic coordinate system with velocity components to comprehensively describe the motion state of the vehicle.

[0032] S202. Obtain the rotation matrix based on the state vector.

[0033] The rotation matrix is ​​a mathematical tool used for coordinate transformation. Specifically, it can be generated by calculating the attitude angle to achieve the transformation between the body coordinate system and the geodetic coordinate system.

[0034] S203. Based on the velocity vector, state vector, driving data, control inputs, and other parameters of each autonomous surface vehicle, construct an initial mathematical model; S204. Based on other parameters and velocity vectors, obtain the positive definite symmetric inertial matrix, centripetal matrix, and damping matrix of each autonomous surface vehicle.

[0035] Among them, the positive definite symmetric inertia matrix refers to a symmetric matrix reflecting the inertial characteristics of a vehicle, which can be determined by mass distribution parameters and is used to characterize the inertial response of the vehicle in motion. The centripetal matrix refers to the set of parameters describing the centripetal effect when the vehicle is in curvilinear motion, which can be calculated by multiplying the velocity vector and the rotation matrix, and is used to correct dynamic deviations in nonlinear motion. The damping matrix is ​​a diagonal matrix characterizing the effect of fluid damping, which can be derived from experimental measurements or fluid dynamics models and is used to simulate the drag effect experienced by the vehicle in the marine environment.

[0036] S205. Based on the rotation matrix, velocity vector, positive definite symmetric inertia matrix, centripetal matrix, and damping matrix, the inherent dynamic behavior is obtained.

[0037] Among them, inherent dynamic behavior refers to the natural motion characteristics of a vehicle without external control input. Specifically, it can be derived through the interaction of the inertia matrix, centripetal matrix, and damping matrix, and is used to construct a simplified mathematical model.

[0038] S206. After quantizing the control input, the initial mathematical model is simplified through its inherent dynamic behavior to construct the target mathematical model.

[0039] Specifically, the velocity and state vectors are first extracted from the vehicle's flight data. The state vector integrates position and velocity information, providing fundamental parameters for subsequent modeling. The rotation matrix is ​​calculated using the attitude information from the state vector, enabling the transformation of motion parameters between different coordinate systems. An initial mathematical model is constructed based on the velocity vector, state vector, control input, and other environmental parameters. This model contains the vehicle's dynamic equations. Further, by combining the velocity vector with other parameters, the positive definite symmetric inertia matrix, centripetal matrix, and damping matrix are derived. These matrices collectively describe the vehicle's inherent dynamic characteristics. By combining the rotation matrix with the aforementioned matrices, the inherent dynamic behavior reflecting the vehicle's natural motion laws is obtained. The control input is quantized, for example, by using a piecewise constant function to approximate a continuous signal. This quantization, combined with the inherent dynamic behavior, reduces the order of the initial model, ultimately generating a simplified target mathematical model. This model retains key dynamic characteristics while reducing computational complexity.

[0040] In a specific embodiment of the present invention, using the collected single-ship information and considering the quantized control input, an initial mathematical model of the multi-autonomous surface vehicle is constructed as shown in formulas (1) and (2): (1) (2) In the formula, ; It is a state vector; They are the first An autonomous surface vehicle (ASV) in a three-dimensional coordinate system x , y , z Position and direction; It is a velocity vector; Indicates control input; It is an unknown, nonlinear, bounded disturbance. Note that due to the physical limitations of autonomous surface vessels, and It is bounded.

[0041] Indicates the first A rotation matrix for an autonomous surface vehicle, used for coordinate transformation. The description is as shown in formula (3): (3) It is a positive definite symmetric inertia matrix as shown in formula (4), where and It is an inertial parameter.

[0042] (4) The Coriolis matrix and the centripetal matrix are shown in formula (5). The meaning is as follows: (5) In the formula, and . Indicates the first The damping matrix of an autonomous surface vessel (ASV) can be defined as shown in formula (6): (6) In the formula, and These are hydrodynamic damping parameters. This represents the quantized control input signal. Quantized control input is more suitable for practical engineering applications because it significantly reduces communication resource consumption compared to transmitting high-precision continuous control signals. The hysteresis quantizer can be described as shown in equation (7): (7) In the formula, and It is a positive integer. In a hysteresis quantizer, the key parameter is... and Smaller This can reduce quantization error and make the control input closer to a continuous signal, but it requires more quantization levels and increases data transmission. Smaller quantization levels make the hysteresis quantizer more sensitive to input changes, making it easier to switch between different levels. For ease of calculation, It can be linearly decomposed into ,in Bounded and .

[0043] The initial data model can be simplified into the target mathematical model using the above methods, as shown in formulas (8) and (9): (8) (9) In the formula, ; ; ; ; ; This reflects the inherent dynamic behavior of autonomous surface vehicles; The velocity vector in the volume coordinate system; It is a rotation matrix; It is a centripetal matrix; Here is the damping matrix; It is a positive definite symmetric inertial matrix; For control input; Preset nonlinear bounded disturbance; For linearly bounded disturbances; It is a state vector; This is the velocity vector in the geodetic coordinate system; Affine formation control strategy; For environmental interference; This is the input quantization error.

[0044] In some embodiments of the present invention, step S102 includes: Establish the topological relationships between multiple autonomous surface vehicles; The stress matrix is ​​constructed based on the relative positional constraints and topological relationships between multiple autonomous surface vehicles in the initial geometry.

[0045] The topology refers to the logical structure of communication connections between aircraft, which can be implemented using adjacency matrices or Laplace matrices in graph theory. It describes the range of information exchange and data transmission paths between aircraft. The stress matrix is ​​a weight matrix reflecting the strength of relative positional constraints between aircraft. It is generated by calculating the difference between the expected and actual distances between adjacent aircraft in the initial geometry, and is used to quantify the positional deviation compensation requirements between each aircraft and its neighbors in the formation.

[0046] Specifically, after setting the initial geometry, the topology is first determined by defining communication links between the aircraft, for example, using an undirected graph structure to represent bidirectional communication connections between aircraft. Then, based on the pre-planned relative positions of the aircraft in the initial geometry, such as a desired distance of 5 meters or a navigation angle of 60 degrees between two aircraft, positional constraints are extracted. Adjacent aircraft pairs with direct communication connections are selected based on the topology, and the relative positional constraints of each pair are converted into corresponding weight elements in the stress matrix. For example, if aircraft A and aircraft B are defined as neighbors in the topology, the element value corresponding to the intersection of A and B in the stress matrix can be calculated by the ratio of the deviation between their desired relative position and their actual position. The resulting stress matrix serves as the basis for calculating tracking errors in subsequent formation control, ensuring the stability of the formation geometry during dynamic adjustments.

[0047] In a specific embodiment of the present invention, to make formation feasible, a stress matrix is ​​used to implement the affine transformation of the autonomous surface vehicle formation. Let... Denotes a set of elements in the stress matrix, where The weight of each edge represents an element in the stress matrix used to describe the aircraft. i with neighboring aircraft j The relative constraint strength between them Represented as a vehicle i with neighboring aircraft k The relative constraint strength between them. This coefficient reflects the tightness of the relative positional relationship between the vehicles under affine transformation, and has... Established. The set of edges representing a vehicle formation is the set of all pairs of vehicles that have communication links or relative positional constraints. When the condition is satisfied... The stress can be called equilibrium stress. Before determining the stress matrix, it is necessary to set the nominal formation of the unmanned surface vessel (USV) formation, i.e., the initial geometry, and confirm the topological relationships between the various USVs. Based on the relative positional constraints and topological relationships between the individuals in this nominal formation, a suitable stress matrix is ​​constructed. The stress matrix is ​​shown in equation (10): (10) In some embodiments of the present invention, such as Figure 3 As shown, step S103 includes: S301. Based on the stress matrix, obtain the relative constraint strength between each autonomous surface vehicle and its neighboring vehicles.

[0048] The stress matrix describes the relative positional constraints between multiple autonomous surface vessels (ASWs). It can be constructed using topological relationships and pre-defined vessel spacing in the initial geometry, and is used to quantify the interaction strength among formation members. Relative constraint strength refers to the degree of positional coupling between vessels, expressed through the elements of the stress matrix; for example, it can be the numerical value at corresponding positions in the matrix. This feature is used to dynamically adjust the weighting of formation tracking errors.

[0049] S302. The measurement error is obtained by comparing the historical state vector and the state vector at the moment the dynamic event triggering mechanism is triggered in the historical driving data.

[0050] The dynamic event triggering mechanism refers to a logical rule that determines whether to update the control signal based on a measurement error threshold. For example, communication is triggered when the deviation between the real-time state vector and the historical state vector exceeds a preset threshold. This mechanism can reduce unnecessary data transmission. Measurement error refers to the difference between the current state vector and the state vector at the most recent trigger moment. It can be calculated using Euclidean distance or vector norm and is used to assess whether the control strategy needs to be updated.

[0051] Specifically, the dynamic event triggering mechanism is shown in formula (11): (11) In the formula, and It is a positive parameter, and ,parameter It is the initial measurement error threshold. Controlling the exponential decay of the threshold, The larger the value, the faster the threshold decreases. When the triggering condition is met, the event is triggered immediately, and at the instant of triggering, the measurement error is reset to zero. Indicates measurement error. Indicates the first An autonomous surface vehicle (ASV) in The measurement state at time, where It is the first The first ASV The trigger time and .

[0052] S303. Determine whether each autonomous surface vehicle triggers the dynamic event triggering mechanism based on the measurement error.

[0053] Specifically, it determines whether the absolute value of the measurement error in formula (11) is less than or equal to .

[0054] S304. If so, then based on the relative constraint strength, state vector and the state vector of the adjacent autonomous surface vehicle, the tracking error of the corresponding autonomous surface vehicle in the affine formation is obtained.

[0055] In the case of triggering the dynamic event triggering mechanism, the tracking error is calculated as shown in formula (12): (12) In the formula, To track errors, This represents the weight of each edge.

[0056] S305. If not, then based on the relative constraint strength, historical state vector, and state vector, the tracking error of the corresponding autonomous surface vehicle in the affine formation is obtained.

[0057] In the absence of a dynamic event triggering mechanism, the tracking error is calculated as shown in formula (13): (13) Specifically, in affine formation control, the relative constraint strength between each vehicle and its neighbors is first determined by analyzing the stress matrix. This strength value can be the numerical value of the corresponding element in the matrix. Then, the difference between the current state vector and the historical state vector saved at the time of the last triggered event is calculated in real time as the measurement error. When the measurement error exceeds a preset threshold, a dynamic event is triggered. At this point, the latest state vector is combined with the state vectors of adjacent vehicles, along with the relative constraint strength, to calculate the tracking error. If the trigger condition is not met, the historical state vector is used for calculation. For example, when no event is triggered, the tracking error calculation can be represented as a weighted combination of the historical state vector and the current state of adjacent vehicles, where the weights are determined by the relative constraint strength.

[0058] In some embodiments of the present invention, step S104 includes: Based on the tracking error and the velocity vector in the geodetic coordinate system of the target mathematical model, the sliding mode surface variables are obtained.

[0059] Among them, the sliding surface-like variable refers to the control variable formed by the linear combination of tracking error and velocity vector. Specifically, it can be realized by the weighted sum of error and velocity, and is used to characterize the deviation between the system state and the desired trajectory. The calculation of the sliding surface-like variable is shown in formula (14): (14) In the formula, It is a positive control gain. It is worth noting that the sliding surface-like variable constructed in this embodiment of the invention depends only on the position state information, heading state information, and local velocity information of its neighbors. It does not require velocity information from neighboring autonomous surface vehicles, which makes practical implementation easier.

[0060] By processing the inherent dynamic behavior of sliding mode surface variables and target mathematical models using radial basis function neural networks, an affine formation control strategy for each autonomous surface vehicle is obtained.

[0061] Radial basis function neural networks (RBNs) are neural network models built using Gaussian functions as basis functions. Specifically, they can be implemented using a multi-layer feedforward network structure to approximate nonlinear dynamic behavior and generate control strategies. Inherent dynamic behavior refers to the motion laws determined by the vehicle's own dynamic characteristics. It can be described by the interaction of the inertia matrix, centripetal matrix, and damping matrix, reflecting the system's inherent physical constraints.

[0062] Specifically, a sliding mode surface variable is constructed as a control reference by linearly combining the tracking error with the velocity vector in the geodetic coordinate system. This variable reflects the dynamic deviation between the actual motion state of the aircraft and the desired trajectory. Subsequently, a radial basis function neural network is used to nonlinearly map the sliding mode surface variable and the inherent dynamic behavior. Unknown disturbances and dynamic characteristics are approximated by preset basis function vectors, and the network weights are updated in conjunction with a dynamic event triggering mechanism. During neural network processing, the quantization range of the control input is adjusted according to the relative constraint strength and measurement error, ultimately generating an affine formation control strategy adapted to complex environmental disturbances. For example, when a denial-of-service attack is detected, the system switches to a simplified control strategy based on inherent dynamic behavior to ensure formation stability.

[0063] In some embodiments of the present invention, the inherent dynamic behavior of sliding mode surface variables and target mathematical models is processed based on radial basis function neural networks to obtain an affine formation control strategy for each autonomous surface vehicle, including: Based on denial-of-service attack data from the historical driving data of multiple autonomous surface vessels, a set of inactive denial-of-service attacks and a set of active denial-of-service attacks are obtained; the set of inactive denial-of-service attacks is the complement of the set of active denial-of-service attacks.

[0064] The inactive denial-of-service attack set refers to the set of time periods during which no denial-of-service attacks occurred. This can be achieved using offline data analysis or online monitoring techniques, and is used to optimize the computational efficiency of control strategies under normal communication conditions. The active denial-of-service attack set refers to the set of time periods during which denial-of-service attacks occurred. This can be achieved through network traffic anomaly detection or packet loss rate analysis, and is used to switch to a more robust control mode when communication is restricted.

[0065] Specifically, denial-of-service attacks are modeled as a series of attack intervals, the cumulative duration of which has an upper limit. Each attack interval can be defined as shown in formula (15): (15) In the formula, Represented as an attack interval, it is the first... N The interval between attack moments, and the duration of each attack moment. The duration is from... Beginning, to Finish, This represents the duration of an attack.

[0066] Each and Defined as the duration during which a denial-of-service attack is active or inactive. and The determination of is shown in formulas (16) and (17): (16) (17) In the formula, and Let these represent the start and end times of any given time interval, respectively, satisfying... ... yes The supplement to .

[0067] Assumption 1: Assume that there is no overlap between each denial-of-service attack range. For There are positive numbers and This results in the following as shown in formula (18): (18) In the formula, and ; This represents a regularization parameter that guarantees the existence of denial-of-service attacks. Used to limit the duration of a denial-of-service attack.

[0068] Limiting the duration of a denial-of-service (DoS) attack is necessary. If Large enough, a DoS attack could occur at intervals. The attack persists within the system. In this scenario, autonomous surface vessels (ASVs) cannot receive any state updates from their neighbors, all attempts to transmit information between ASVs will fail, and control performance cannot be guaranteed. Assumption 1 limits the cumulative duration of a DoS attack, which is reasonable because attackers must consume energy to launch a DoS attack, and DoS attacks rarely disrupt all communication for an extended period. After a period of DoS attack, the attacker needs to enter a dormant period to accumulate energy for the next attack. Furthermore, the DoS attack model used in this paper is aperiodic because the timing of attacks is often unpredictable in real-world scenarios, and ASVs cannot predict when a DoS attack will occur. Therefore, this denial-of-service attack method is realistic, feasible, and universally applicable.

[0069] The radial basis function neural network is used to calculate the preset basis function vector, sliding mode surface variable, relative constraint strength and measurement error of each autonomous surface vehicle to obtain the updated weight of each autonomous surface vehicle.

[0070] In this context, a radial basis function (RBF) neural network is a nonlinear function approximator with local approximation capabilities. It can be implemented using Gaussian functions as basis functions to handle system dynamic uncertainties and environmental disturbances. The preset basis function vectors refer to pre-defined combinations of radial basis function parameters, which can be determined empirically or through offline training, and are used to construct the basic structure of the neural network. Updated weights refer to the connection weights that the neural network dynamically adjusts based on real-time data. This can be implemented using gradient descent or adaptive laws to compensate for system model errors and external disturbances online.

[0071] Specifically, the update law of the radial basis function neural network is calculated as shown in formulas (19) and (20): (19) (20) In the formula, Represented as The renewal law; For the first i A preset basis function vector for an autonomous surface vehicle; Relative constraint strength; For measurement error; It is a positive constant. It is a variable similar to continuous sliding mode.

[0072] Based on driving data, updated weights, and the inherent dynamic behavior in the target mathematical model, an affine formation control strategy is determined for each autonomous surface vehicle.

[0073] Specifically, within the time period corresponding to the inactive denial-of-service attack set, the control strategy adapts to the dynamic changes of the aircraft by continuously updating the neural network weights, while maintaining the stability of the network structure using preset basis function vectors. When it is detected that the current time belongs to the active denial-of-service attack set, the control strategy switches to a calculation mode based on inherent dynamic behavior, avoiding reliance on real-time communication data. In this process, relative constraint strength is used to quantify the cooperative relationship between the aircraft, and measurement errors are used to trigger weight update conditions. By alternately using neural network compensation and inherent dynamic models, control accuracy is improved when communication is normal, and basic formation stability is maintained when communication is interrupted.

[0074] In some embodiments of the present invention, an affine formation control strategy for each autonomous surface vehicle is determined based on driving data, updated weights, and the inherent dynamic behavior in the target mathematical model, including: When the current time in the driving data belongs to the set of non-activated denial-of-service attacks, the first affine formation control strategy of the corresponding autonomous surface vehicle is obtained based on the inherent dynamic behavior, preset basis function vector, update weight, tracking error and sliding mode surface variable. When the current time in the driving data belongs to the set of active denial-of-service attacks, the second affine formation control strategy for the corresponding autonomous surface vehicle is obtained based on the inherent dynamic behavior.

[0075] The first affine formation control strategy refers to a dynamic control strategy generated based on a radial basis function neural network. Specifically, it combines tracking error with inherent dynamic behavior for online adjustment, aiming to achieve precise formation control under normal communication conditions. The second affine formation control strategy refers to a simplified control strategy that relies solely on inherent dynamic behavior. For example, it calculates the control input using a preset damping matrix and centripetal matrix, aiming to maintain the basic motion stability of the aircraft during communication interruptions.

[0076] Specifically, when not under a denial-of-service attack, the autonomous surface vehicle (ASW) calculates control inputs using real-time updated neural network weights, dynamically adjusting its formation strategy based on sliding mode surface variables and tracking errors to adapt to environmental disturbances and maintain formation accuracy. When a denial-of-service attack is detected causing communication interruption, the system switches to a control strategy based on inherent dynamic behavior, using damping and centripetal matrices to maintain the vehicle's basic motion and prevent control failure due to communication blockage. After the attack ends, the system reacquires updated neural network parameters and resumes high-precision formation control. For example, at the instant communication is restored, the vehicle recalculates the tracking error based on the latest state vector and the relative position constraints of neighboring vehicles, generating optimized control inputs.

[0077] In a specific embodiment of the present invention, When the denial-of-service attack is not activated, the first affine formation control strategy is calculated as shown in formula (21): (twenty one) In the formula, For control strategies; The tracking error was rewritten due to the influence of the event-triggered mechanism. , To control the gain coefficient; It is an inherent dynamic behavior; T This is the transpose of the matrix; It is an estimate of the adaptive weight vector. It is updated online using some adaptive law (such as gradient descent) to learn the unknown parts of the system.

[0078] When a denial-of-service attack is activated, the first affine formation control strategy is calculated as shown in formula (22): (twenty two) In some embodiments of the present invention, after step S104, the method further includes: After controlling the corresponding autonomous surface vehicle using the second affine formation control strategy, the corresponding autonomous surface vehicle is then controlled using the updated first affine formation control strategy for the current time.

[0079] The updated first affine formation control strategy for the current time refers to a strategy recalculated based on the latest environmental conditions. This can be achieved by periodically refreshing the neural network weight parameters to ensure the matching of the control strategy with the current navigation state.

[0080] Specifically, when a denial-of-service attack is detected, the system automatically switches to a second affine formation control strategy, which relies solely on local sensor data and a preset dynamic model for control decisions. After the attack ends, the system immediately acquires the current aircraft status data, recalculates the weight parameters using a neural network, and generates an updated first affine formation control strategy. This switching mechanism uses timestamps to determine changes in the attack status, prioritizes strategy updates after communication is restored, and then applies the new strategy to achieve rapid reconstruction of the formation.

[0081] Through the above technical solution, this application can quickly rebuild precise control after a denial-of-service attack ends, avoiding the accumulation of formation deviations caused by the simplification of control strategies during the attack. The synergy between the policy update mechanism and real-time status data significantly reduces the redundant consumption of communication resources while ensuring the continuity and stability of formation control.

[0082] This invention ensures real-time, continuous formation changes. The strategy considers input quantization, interference from unknown environments, and potential non-periodic denial-of-service attacks. Furthermore, to address the issue of limited communication resources, a dynamic event-triggered mechanism is deployed to reduce communication resource consumption. Compared to fixed autonomous surface vehicle formations and periodic denial-of-service models, these considerations aim to improve the system's practical relevance.

[0083] To better implement the multi-autonomous surface vehicle (MAV) formation control method in the embodiments of the present invention, the embodiments of the present invention also provide a multi-MAV formation control device, such as... Figure 4 As shown, the multi-autonomous surface vehicle formation control device 400 includes: The model building module 401 is used to construct a target mathematical model using the position and velocity information from the driving data of multiple autonomous surface vehicles as state variables. The matrix construction module 402 is used to set the initial geometry of multiple autonomous surface vehicles forming an affine formation, and to construct a stress matrix based on the initial geometry. Error calculation module 403 is used to obtain the tracking error of each autonomous surface vehicle in the affine formation based on the target mathematical model and stress matrix; The strategy determination module 404 is used to obtain the affine formation control strategy for each autonomous surface vehicle based on the target mathematical model and tracking error.

[0084] The multi-autonomous surface vehicle formation control device 400 provided in the above embodiments can realize the technical solutions described in the above embodiments of the multi-autonomous surface vehicle formation control method. The specific implementation principles of each module or unit can be found in the corresponding content in the above embodiments of the multi-autonomous surface vehicle formation control method, which will not be repeated here.

[0085] The multi-autonomous surface vehicle formation control method and device provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for controlling a formation of multiple autonomous surface vehicles, characterized in that, include: A target mathematical model is constructed using position and velocity information from the driving data of multiple autonomous surface vehicles as state variables. The initial geometry of the multiple autonomous surface vehicles in affine formation is set, and a stress matrix is ​​constructed based on the initial geometry. Based on the target mathematical model and the stress matrix, the tracking error of each autonomous surface vehicle in the affine formation is obtained; Based on the target mathematical model and the tracking error, an affine formation control strategy for each autonomous surface vehicle is obtained.

2. The multi-autonomous surface vehicle formation control method according to claim 1, characterized in that, The method of constructing a target mathematical model using position and velocity information from the driving data of multiple autonomous surface vehicles as state variables includes: Based on the driving data, the velocity vector and state vector of each autonomous surface vehicle are obtained; Based on the state vector, the rotation matrix is ​​obtained; An initial mathematical model is constructed based on the velocity vector, state vector, control input of the driving data, and other parameters of each autonomous surface vehicle. Based on the other parameters and the velocity vector, the positive definite symmetric inertial matrix, centripetal matrix, and damping matrix of each autonomous surface vehicle are obtained; The inherent dynamic behavior is obtained based on the rotation matrix, the velocity vector, the positive definite symmetric inertia matrix, the centripetal matrix, and the damping matrix. After quantizing the control input, the initial mathematical model is simplified through the inherent dynamic behavior to construct the target mathematical model.

3. The multi-autonomous surface vehicle formation control method according to claim 1, characterized in that, The process of setting the initial geometry for the affine formation of the multiple autonomous surface vehicles and constructing a stress matrix based on the initial geometry includes: Establish the topological relationships between the multiple autonomous surface vehicles; A stress matrix is ​​constructed based on the relative positional constraints between the plurality of autonomous surface vehicles in the initial geometry and the topological relationships.

4. The multi-autonomous surface vehicle formation control method according to claim 2, characterized in that, The tracking error of each autonomous surface vehicle in the affine formation is obtained based on the target mathematical model and the stress matrix, including: Based on the stress matrix, the relative constraint strength between each autonomous surface vehicle and its neighboring vehicles is obtained; The measurement error is obtained by comparing the historical state vector at the moment the dynamic event triggering mechanism was triggered in the historical driving data with the state vector. Based on the measurement error, determine whether each autonomous surface vehicle triggers the dynamic event triggering mechanism; If so, the tracking error of the corresponding autonomous surface vehicle in the affine formation is obtained based on the relative constraint strength, the state vector, and the state vector of the adjacent autonomous surface vehicle. If not, then the tracking error of the corresponding autonomous surface vehicle in the affine formation is obtained based on the relative constraint strength, the historical state vector, and the state vector.

5. The multi-autonomous surface vehicle formation control method according to claim 4, characterized in that, The step of obtaining the affine formation control strategy for each autonomous surface vehicle based on the target mathematical model and the tracking error includes: Based on the tracking error and the velocity vector in the geodetic coordinate system of the target mathematical model, the sliding surface variables are obtained; The inherent dynamic behavior of the sliding surface variables and the target mathematical model is processed by a radial basis function neural network to obtain the affine formation control strategy for each autonomous surface vehicle.

6. The multi-autonomous surface vehicle formation control method according to claim 5, characterized in that, The process of processing the inherent dynamic behavior of the sliding surface variables and the target mathematical model based on the radial basis function neural network to obtain the affine formation control strategy for each autonomous surface vehicle includes: Based on the denial-of-service attack data in the historical driving data of the multiple autonomous surface vessels, an inactive denial-of-service attack set and an active denial-of-service attack set are obtained; the inactive denial-of-service attack set is the complement of the active denial-of-service attack set. The radial basis function neural network is used to calculate the preset basis function vector, the sliding mode surface variable, the relative constraint strength, and the measurement error for each autonomous surface vehicle to obtain the updated weights for each autonomous surface vehicle. Based on the driving data, the updated weights, and the inherent dynamic behavior in the target mathematical model, an affine formation control strategy is determined for each autonomous surface vehicle.

7. The multi-autonomous surface vehicle formation control method according to claim 6, characterized in that, The step of determining the affine formation control strategy for each autonomous surface vehicle based on the driving data, the updated weights, and the inherent dynamic behavior in the target mathematical model includes: When the current time in the driving data belongs to the set of inactive denial-of-service attacks, the first affine formation control strategy of the corresponding autonomous surface vehicle is obtained based on the inherent dynamic behavior, the preset basis function vector, the update weight, the tracking error and the sliding surface variable. When the current time in the driving data belongs to the set of active denial-of-service attacks, a second affine formation control strategy for the corresponding autonomous surface vehicle is obtained based on the inherent dynamic behavior.

8. The multi-autonomous surface vehicle formation control method according to claim 7, characterized in that, After obtaining the affine formation control strategy for each autonomous surface vehicle based on the target mathematical model and the tracking error, the method further includes: After controlling the corresponding autonomous surface vehicle using the second affine formation control strategy, the corresponding autonomous surface vehicle is then controlled using the updated first affine formation control strategy for the current time.

9. The multi-autonomous surface vehicle formation control method according to claim 2, characterized in that, The target mathematical model is: In the formula, ; ; ; ; ; This reflects the inherent dynamic behavior of autonomous surface vehicles; The velocity vector in the volume coordinate system; It is a rotation matrix; It is a centripetal matrix; Here is the damping matrix; It is a positive definite symmetric inertial matrix; For control input; Preset nonlinear bounded disturbance; For linearly bounded disturbances; It is a state vector; This is the velocity vector in the geodetic coordinate system; Affine formation control strategy; For environmental interference; This is the input quantization error.

10. A multi-autonomous surface vehicle formation control device, characterized in that, include: The model building module is used to construct a target mathematical model using the position and velocity information from the driving data of multiple autonomous surface vehicles as state variables. The matrix construction module is used to set the initial geometry of the multiple autonomous surface vehicles forming an affine formation, and to construct a stress matrix based on the initial geometry. The error calculation module is used to obtain the tracking error of each autonomous surface vehicle in the affine formation based on the target mathematical model and the stress matrix. The strategy determination module is used to obtain the affine formation control strategy for each autonomous surface vehicle based on the target mathematical model and the tracking error.

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