Methods, devices and electronic equipment for controlling underwater vehicle formations

Abstract

This invention relates to a method, device, and electronic equipment for underwater vehicle formation control. The method includes: constructing a formation configuration maintenance framework based on rigid graph theory, and determining the relative positional relationships between vehicles through distance constraints; establishing an obstacle avoidance control model based on the artificial potential field method, calculating the potential field force based on the distance between the vehicle and the obstacle and the distance between vehicles, thereby achieving obstacle avoidance and collision prevention between vehicles; performing online identification and compensation of unmodeled dynamics and external disturbances in the vehicle dynamics model based on a radial basis function neural network, using a Gaussian function as the activation function; and vector-fusing the formation maintenance control force, potential field force, and compensation output of the radial basis function neural network to generate control commands for each vehicle, thereby achieving formation control. This invention can achieve high-precision formation maintenance, effective obstacle avoidance, and adaptive disturbance compensation capabilities in complex underwater environments.

Description

Technical Field

[0001] This invention relates to the field of underwater vehicle formation control technology, and in particular to an underwater vehicle formation control method, device, and electronic equipment. Background Technology

[0002] Autonomous Underwater Vehicles (AUVs) play an irreplaceable role in missions such as seabed resource exploration, underwater search and rescue, and marine environmental monitoring. Faced with increasingly complex, time-sensitive, and large-scale mission requirements, multi-AUV collaborative operations significantly improve mission efficiency and system robustness compared to single-AUV operations. Stable and reliable formation control is the foundation for multi-AUV collaborative operations, and its core lies in: first, maintaining a preset geometric configuration in complex underwater environments to ensure the generation and maintenance of formations; and second, achieving coordinated control of the overall formation movement, enabling the swarm to navigate stably along the desired trajectory and adapt to environmental constraints.

[0003] The underwater environment is characterized by strong uncertainties, including ocean current disturbances, underwater obstacle distribution, and limited communication. These environmental factors pose severe challenges to the accuracy and stability of formation control. Specifically, existing formation control methods have the following shortcomings: First, traditional formation maintenance methods struggle to maintain a stable formation structure under external disturbances, resulting in large formation errors and slow convergence. Second, existing obstacle avoidance control strategies lack effective coordination with formation maintenance strategies, making formations prone to instability or trajectory deviation in environments with dense obstacles. Third, adaptive compensation mechanisms for underwater environmental uncertainties are inadequate, and fixed-gain control methods struggle to cope with the performance degradation caused by time-varying disturbances. Summary of the Invention

[0004] Therefore, it is necessary to provide an underwater vehicle formation control method, device, and electronic equipment that can achieve high-precision formation maintenance, effective obstacle avoidance, and disturbance adaptive compensation capabilities in complex underwater environments to address the aforementioned technical problems.

[0005] This invention provides a method for controlling underwater vehicle formations, the method comprising:

[0006] A formation maintenance framework is constructed based on rigid graph theory. The relative positional relationships between the vehicles are determined by constructing a rigid matrix and applying distance constraints, thereby generating formation maintenance control forces.

[0007] An obstacle avoidance control model is established based on the artificial potential field method. According to the distances between the vehicle and obstacles, and between the vehicles themselves, a fractional function structure that is continuously differentiable between the minimum safe distance and the maximum sensing radius is used to calculate the potential field force, thereby achieving obstacle avoidance and collision prevention between vehicles. Specifically, the fractional function structure is: the potential field function between vehicles. and the potential field function between the vehicle and the obstacle. ,in, This represents the Euclidean distance between the spacecraft. This represents the Euclidean distance between the vehicle and the obstacle. For minimum safe distance, For the maximum sensing radius, For the first The position vectors of the obstacles;

[0008] The radial basis function neural network is used to identify and adaptively compensate for unmodeled dynamics and external disturbances in the dynamic model of a vehicle. The radial basis function neural network uses a Gaussian function as the activation function and adjusts the network weights online through a weight adaptive update law.

[0009] The formation control force, the potential field force, and the compensation output of the radial basis function neural network are vector-fused to generate control commands for each vehicle, thereby achieving formation control.

[0010] In one embodiment, the formation configuration preservation framework constructed based on rigid graph theory includes:

[0011] Define an undirected graph This indicates the information exchange relationship between the aircraft, where For a set of nodes, Let be the set of edges. For the connection matrix;

[0012] Constructing a rigid matrix ,in The set of coordinates of all vertices. It is a side function;

[0013] Through the connection matrix Describe the relationships between the vertices, where .

[0014] In one embodiment, the vector fusion includes:

[0015] When the distance between the vehicle and the obstacle is less than the maximum sensing radius, the weight of the formation-keeping control force is dynamically reduced and the weight of the potential force is increased, so that the obstacle avoidance response takes precedence over formation maintenance; at the same time, the compensation output of the radial basis function neural network is used as a feedforward term and the feedback term composed of the potential force to form a composite control structure, which together corrects the vehicle trajectory.

[0016] In one embodiment, the online identification and adaptive compensation of unmodeled dynamics and external disturbances in the vehicle dynamics model based on a radial basis function neural network includes:

[0017] Constructing a radial basis function neural network approximation model ,in For the ideal weight matrix, For the first The input vector of each aircraft To approximate the error;

[0018] Using Gaussian functions as radial basis functions ,in As the center vector, For width parameters;

[0019] The perturbation compensation amount is output based on the approximation model.

[0020] In one embodiment, the vector fusion of the formation-keeping control force, the potential field force, and the compensation output of the radial basis function neural network to generate control commands for each aircraft includes:

[0021] Establish the dynamic equations of the aircraft ,in , These are the generalized matrices obtained after coordinate transformation of the inertia matrix and the Coriolis centripetal force matrix, respectively. For generalized velocity vectors, For generalized control input, For generalized external disturbances;

[0022] Design control law ,in These are approximate weights for the neural network. Here is the gain matrix. The given dynamics term is denoted as .

[0023] In one embodiment, the method further includes establishing a kinematic model of the aircraft. ,in This indicates the vehicle's position and heading angle. This indicates the speed information of the aircraft. It is a rotation matrix.

[0024] In one embodiment, the rotation matrix ,in This is the heading angle.

[0025] In one embodiment, the method further includes establishing a dynamic model of the aircraft. ,in The inertia matrix, The Coriolis centripetal force matrix, For hydrodynamic damping matrix, External disturbances For controlling input.

[0026] In one embodiment, the vector fusion further includes a dual-threshold-based intelligent switching mechanism, specifically:

[0027] Real-time monitoring of formation error and disturbance estimate; when the formation error is greater than a preset first threshold and the disturbance estimate is less than a preset second threshold, the weight of the formation maintaining control force is increased and the weight of the potential force is decreased, so as to prioritize the correction of the formation.

[0028] When the formation error is less than the first threshold and the distance between the vehicle and the obstacle is less than the maximum sensing radius, the weights of the potential force and the radial basis function neural network compensation output are increased and the weight of the formation holding control force is decreased to prioritize navigation safety.

[0029] In one embodiment, the online adjustment of network weights using a weight adaptive update law includes:

[0030] The weight update law is designed to include a product term of tracking error and hidden layer activation function output, plus a correction term to suppress parameter drift, so that under continuous external perturbation, the estimated network weight of the radial basis function neural network is always maintained within a preset bounded range.

[0031] The present invention also provides an underwater vehicle formation control device, the device comprising:

[0032] The formation maintenance control force generation module is used to construct a formation configuration maintenance framework based on rigid graph theory. It determines the relative positional relationship between each aircraft by constructing a rigid matrix and applying distance constraints, and generates the formation maintenance control force.

[0033] The potential field force calculation module is used to establish an obstacle avoidance control model based on the artificial potential field method. According to the distance between the vehicle and the obstacle and the distance between the vehicles, the potential field force is calculated using a fractional function structure that is continuously differentiable between the minimum safe distance and the maximum sensing radius, so as to realize obstacle avoidance and collision prevention between vehicles.

[0034] The compensation output module is used to identify and adaptively compensate for unmodeled dynamics and external disturbances in the vehicle dynamics model based on a radial basis function neural network. The radial basis function neural network uses a Gaussian function as the activation function and adjusts the network weights online through a weight adaptive update law.

[0035] The control command generation module is used to perform vector fusion of the formation holding control force, the potential field force, and the compensation output of the radial basis function neural network to generate control commands for each aircraft and realize formation control.

[0036] The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the underwater vehicle formation control method as described above.

[0037] The aforementioned underwater vehicle formation control method, device, and electronic equipment, through the combined effect of rigid matrix construction and distance constraints, ensure the global stability of the formation geometry, achieving effective formation maintenance under minimum communication topology requirements. By constructing an artificial potential field using a fractional function structure that is continuously differentiable between the minimum safe distance and the maximum sensing radius, the system jitter problem caused by force field abrupt changes during close-range obstacle avoidance in traditional potential field methods is overcome, enabling smooth obstacle avoidance and collision prevention control of the vehicle in dense obstacle environments. Online identification and compensation are achieved through the weight adaptive update law of the radial basis function neural network, utilizing the local approximation characteristics of the Gaussian function and the real-time adjustment capability of the weights to achieve adaptive suppression of time-varying ocean current disturbances and unmodeled dynamics. Finally, the formation maintenance control force, obstacle avoidance control force, and disturbance compensation force are unified and synthesized through a vector fusion mechanism, solving the control conflict problem among formation maintenance, obstacle avoidance, and disturbance resistance in complex underwater environments, and achieving multi-objective collaborative optimization. This solution significantly improves the robustness of multi-vehicle systems in complex underwater environments with dense obstacles and time-varying disturbances. Specifically, in an obstacle-free environment, the formation error convergence speed is accelerated and the steady-state error is significantly reduced; during obstacle avoidance, the speed fluctuation of the vehicles is significantly reduced, avoiding trajectory oscillations caused by sudden changes in potential field forces; in an obstacle environment, the formation can maintain geometric stability and smooth motion trajectory at the same time, significantly improving overall cooperation efficiency and operational safety. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0039] Figure 1 A flowchart of an underwater vehicle formation control method according to one embodiment;

[0040] Figure 2 This is a rendering of an aircraft formation in an unobstructed environment.

[0041] Figure 3 This is a rendering of a formation of aircraft in an environment with obstacles.

[0042] Figure 4 This is a diagram of a radial basis function neural network structure.

[0043] Figure 5 A comparison chart of formation errors for aircraft in an unobstructed environment;

[0044] Figure 6 A comparison chart of vehicle speed errors in an obstacle-free environment;

[0045] Figure 7 A comparison chart of formation errors for aircraft in obstacle-prone environments;

[0046] Figure 8 A comparison chart of vehicle speed errors in environments with obstacles;

[0047] Figure 9 This is an internal structural diagram of an electronic device according to one embodiment. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0049] The following is combined Figures 1-9 The present invention describes an underwater vehicle formation control method, apparatus, and electronic equipment.

[0050] This invention proposes an underwater vehicle formation control method based on the fusion of rigid graph theory, artificial potential field method and radial basis function neural network, aiming to solve the collaborative control problem of formation maintenance, obstacle avoidance and disturbance compensation in complex underwater environments.

[0051] First, establish the kinematic model of the aircraft. Consider the following... A formation system consisting of autonomous underwater vehicles, the first The kinematic model of a single aircraft can be represented as follows: ,in This indicates the vehicle's position and heading angle. This indicates the speed information of the aircraft. For rotation matrices, refer to Figure 1 The coordinate transformation relationship shown has the following specific form for the rotation matrix: ,in The rotation matrix represents the heading angle of the vehicle and enables velocity transformation between the vehicle's body coordinate system and the inertial coordinate system.

[0052] Secondly, a dynamic model of the aircraft is established. The dynamic model of the aircraft is ,in The inertial matrix of the aircraft. The Coriolis centripetal force matrix, For hydrodynamic damping matrix, This represents external disturbances (including ocean current disturbances, unmodeled dynamics, etc.). This dynamic model describes the motion characteristics of the vehicle in a complex underwater environment, providing a basis for subsequent control law design.

[0053] like Figure 1 As shown, in one embodiment, an underwater vehicle formation control method includes the following steps:

[0054] Step S110: Construct a formation configuration maintenance framework based on rigid graph theory, determine the relative positional relationship between each vehicle by constructing a rigid matrix and applying distance constraints, and generate formation maintenance control force.

[0055] Specifically, a two-stage process is used to achieve formation control. The first stage constructs a formation configuration preservation framework based on rigid graph theory, defining an undirected graph. This indicates the information exchange relationship between air vehicles (AUVs), where Let be the set of all nodes in the graph. Let be the set of edges. To construct a rigid matrix for the connection matrix to represent the communication relationships between nodes in a graph. The formation framework is composed of Implementation, in which Represents the set of coordinates of all vertices. Let be the edge function, where each term Corresponding to the connection number and The edges of each vertex are connected by a matrix. Describe the relationships between the vertices, where The above theories can solve the formation construction problem of aircraft. By utilizing the distance constraint characteristics of rigid graph theory, the global stability of the formation configuration can be ensured, and the formation can be effectively maintained.

[0056] Step S120: Establish an obstacle avoidance control model based on the artificial potential field method. According to the distance between the vehicle and the obstacle and the distance between the vehicles, the potential field force is calculated using a fractional function structure that is continuously differentiable between the minimum safe distance and the maximum sensing radius, so as to realize obstacle avoidance and collision prevention between vehicles.

[0057] The second stage establishes an obstacle avoidance control model based on the artificial potential field method to achieve obstacle avoidance and collision prevention between vehicles, referring to... Figure 2 and Figure 3 The formation motion trajectory, the mathematical model of the artificial potential field method includes the potential field function between the aircraft. and the potential field function between the vehicle and the obstacle ,in This represents the Euclidean distance between the various spacecraft. This represents the Euclidean distance between the vehicle and the obstacle. This indicates the minimum safe distance, which ensures that the vehicles will not collide with each other or with obstacles. This indicates the maximum detection radius of a target that the vehicle can detect, when the distance between vehicles or between a vehicle and an obstacle is less than [a certain value]. When the potential field function generates a repulsive force, it propels the vehicle away from obstacles or other vehicles, achieving safe obstacle avoidance. To prevent excessive potential force amplitude during obstacle avoidance from disrupting the formation topology, the potential force is processed by a saturation function before vector fusion. When the calculated potential force amplitude exceeds a preset safety threshold, the saturation function limits it to a reasonable range, ensuring compatibility between obstacle avoidance control and formation maintenance.

[0058] It is important to emphasize that the two-stage process is not executed completely independently, but rather forms a closed-loop coupling mechanism through vector fusion. The second stage, based on the control output generated by the artificial potential field method and radial basis function neural network, corrects the rigid distance constraint parameters of the first stage in real time through the feedback channel. This allows the virtual navigator trajectory to be dynamically adjusted according to actual obstacle avoidance requirements and disturbance compensation, achieving adaptive maintenance of the formation configuration in complex environments.

[0059] Step S130: Based on the radial basis function neural network, the unmodeled dynamics and external disturbances in the vehicle dynamics model are identified and adaptively compensated online. The radial basis function neural network uses the Gaussian function as the activation function and adjusts the network weights online through the weight adaptive update law.

[0060] Online identification and compensation of unmodeled dynamics and external disturbances in the vehicle dynamics model based on radial basis function neural networks, referencing Figure 4 The radial basis function (RBF) neural network structure is described. This network is a three-layer feedforward neural network, consisting of an input layer, a hidden layer, and an output layer. The input layer is composed of source nodes. Each neuron in the hidden layer calculates its output using radial basis functions. The output layer linearly sums the outputs of the hidden layer neurons, and the network ultimately provides the corresponding response. The RBF neural network uses a Gaussian function as the activation function to construct an approximate model. ,in For the ideal weight matrix, Indicates the first The input vector of each aircraft To approximate the error, the Gaussian function is in the form of: ,in As the center vector, For width parameter, This radial basis function neural network, with its local approximation characteristics, simple network structure, and fast convergence speed, can identify unmodeled dynamics and external disturbances in the aircraft formation system in real time online. By estimating the disturbance terms in real time, it provides a compensation basis for the design of control laws.

[0061] To further ensure the convergence and boundedness of the neural network weight estimation, a correction term is introduced into the radial basis function neural network during the adaptive weight update process. Specifically, the weight update law is designed to include a product term of the tracking error and the output of the hidden layer activation function, and is superimposed with a correction term to suppress parameter drift. This ensures that under continuous external disturbances, the network weight estimate remains within a reasonable bounded range, avoiding the weight divergence problem caused by the traditional gradient descent method. Based on Lyapunov stability theory, the stability of the designed control law is verified. A composite Lyapunov function containing formation error, velocity error, and neural network weight estimation error is constructed. Through rigorous mathematical derivation, it is proven that under the action of the control law, the formation error and velocity error of the closed-loop system can converge to a bounded neighborhood near the zero point, ensuring the global asymptotic stability of the multi-vehicle system in complex underwater environments.

[0062] Step S140 involves vector fusion of the formation holding control force, potential field force, and compensation output of the radial basis function neural network to generate control commands for each aircraft, thereby achieving formation control.

[0063] By combining the aforementioned formation configuration preservation framework, obstacle avoidance control model, and radial basis function neural network compensation, control commands for each vehicle are generated. To achieve a unified design of the control law, the dynamic equations in the vehicle coordinate system are transformed using a rotation matrix. Transform to the inertial coordinate system. Define the coordinate transformation relationship as follows:

[0064]

[0065] ,

[0066] in, For rotation matrix, express The transpose of the inverse matrix, Let be the time derivative of the rotation matrix.

[0067] At the same time, a generalized velocity vector is defined. For the velocity tracking error of the vehicle in the inertial coordinate system: ,in, This represents the actual velocity of the vehicle in the inertial coordinate system. Let be the desired trajectory velocity. After the coordinate transformation described above, the original dynamic equations can be transformed into a generalized form: ,in, The comprehensive expression, after coordinate transformation, includes the known parts of the hydrodynamic damping term and the Coriolis term, as well as the known dynamic terms related to the desired trajectory acceleration. By substituting the approximation model into the dynamic equations, we obtain... Based on this, the control law is designed. ,in, , These are the generalized matrices obtained after coordinate transformation of the inertia matrix and the Coriolis centripetal force matrix, respectively. For generalized velocity vectors, For generalized control input, For generalized external disturbances, These are approximate weights for the neural network. Here is the gain matrix. Given the dynamics, this control law integrates the formation-keeping constraints of rigid graph theory, the obstacle avoidance guidance of the artificial potential field method, and the disturbance compensation of the radial basis function neural network, achieving coordinated optimization of formation control, obstacle avoidance, and disturbance resistance.

[0068] During vector fusion, the formation-keeping control force, obstacle avoidance control force, and disturbance compensation force are not simply linearly superimposed, but dynamically adjusted in weight according to real-time mission requirements. When the distance between the vehicle and the obstacle is less than the maximum sensing radius, the system automatically reduces the weight of the formation-keeping control force and increases the weight of the potential force, prioritizing obstacle avoidance response over formation maintenance. After escaping the obstacle, the system automatically restores the preset geometric configuration through rigid matrix constraints. Simultaneously, the compensation output of the radial basis function neural network, as a feedforward term, forms a composite control structure with the potential force as a feedback term, jointly correcting the vehicle's trajectory. Furthermore, vector fusion intelligently switches based on real-time formation error and disturbance estimate: when the formation error is greater than a first threshold and the disturbance estimate is less than a second threshold, the weight of the formation-keeping control force is increased to prioritize formation correction; when the formation error is less than the first threshold and the vehicle is approaching an obstacle, the weights of the potential force and compensation output are increased to prioritize navigation safety, achieving multi-objective adaptive optimization.

[0069] For practical applications where underwater communication is limited, the method of this invention can be extended to a distributed implementation. Each vessel interacts only with its neighboring nodes for local rigid constraint information, and the radial basis function neural network runs independently on each vessel, synchronizing weight updates only through intermittent underwater acoustic communication. This distributed architecture reduces reliance on global communication, significantly improving the system's robustness and practicality in communication-constrained environments while maintaining formation control performance.

[0070] To verify the effectiveness of the method of the present invention, a simulation experiment was conducted. The simulation environment was set to a two-dimensional plane, and the initial positions and heading angles of the three vehicles were set as follows: , , The desired formation is a triangle, represented by a relative position vector. and , refer to Figure 2 In an unobstructed environment, the aircraft formation can navigate stably along the desired path (straight lines and curves) and maintain a preset triangular formation.

[0071] Further verification was conducted in an obstacle environment, with obstacle positions set as obstacle 1. Obstacle 2 3 obstacles All three are modeled as circles with a radius of 2, referring to... Figure 3 The aircraft formation was able to effectively avoid obstacles and maintain its formation when encountering them, verifying the effectiveness of the method of the present invention in environments with dense obstacles.

[0072] To quantitatively evaluate the performance of the method of this invention, the formation control effects of the method of this invention (RGT-APF-RBF) without using radial basis function neural networks (i.e., the RGT-APF method that only uses rigid graph theory and artificial potential field method) and the method of this invention were compared. (Refer to...) Figure 5 In an obstacle-free environment, the formation error of the method of this invention (red curve) is significantly reduced compared to the RGT-APF method (blue curve), especially in the steady-state phase (150-200s), where the formation error of the method of this invention remains at a lower level. Figure 6 In the comparison of speed errors in an obstacle-free environment, the speed fluctuation of the method of the present invention is significantly reduced, and the movement of the aircraft is more stable.

[0073] Reference Figure 7 In obstacle-prone environments, when the vehicle approaches an obstacle (300-400s), the peak formation error of the method described in this invention is significantly lower than that of the RGT-APF method, and the error convergence speed is faster. (Refer to...) Figure 8 In the comparison of speed errors in obstacle environments, the method of the present invention significantly reduces speed fluctuations during obstacle avoidance, avoids drastic speed changes caused by obstacle avoidance, and improves the smoothness of formation movement.

[0074] In summary, this invention achieves coordinated control of formation holding, obstacle avoidance, and disturbance compensation by organically integrating rigid graph theory, artificial potential field method, and radial basis function neural network. It solves the technical problems of low formation control accuracy, poor obstacle avoidance effect, and weak anti-disturbance capability in complex underwater environments. Simulation results show that the method of this invention has smaller formation error and speed fluctuation in both obstacle-free and obstacle-prone environments, and significantly improves the mission execution robustness and overall cooperation efficiency of multi-vehicle systems in complex scenarios.

[0075] Figure 9 This example illustrates a schematic diagram of the physical structure of an electronic device, which can be a smart terminal. Its internal structure diagram can be as follows: Figure 9 As shown, the electronic device includes a processor, memory, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements any of the aforementioned underwater vehicle formation control methods.

[0076] Those skilled in the art will understand that Figure 9The structure shown is merely a block diagram of a portion of the structure related to the present invention and does not constitute a limitation on the electronic device to which the present invention is applied. A specific electronic device may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0077] On the other hand, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, implements any of the above-described underwater vehicle formation control methods.

[0078] In another aspect, a computer program product or computer program is provided, which includes computer instructions stored in a computer-readable storage medium. A processor of an electronic device reads the computer instructions from the computer-readable storage medium, and when the processor executes the computer instructions, it implements any of the aforementioned underwater vehicle formation control methods.

[0079] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory.

[0080] By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0081] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0082] The above-described embodiments are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. An underwater vehicle formation control method, characterized by, The method includes: A formation maintenance framework is constructed based on rigid graph theory. The relative positional relationships between the vehicles are determined by constructing a rigid matrix and applying distance constraints, thereby generating formation maintenance control forces. An obstacle avoidance control model is established based on the artificial potential field method. According to the distances between the vehicle and obstacles, and between the vehicles themselves, a fractional function structure that is continuously differentiable between the minimum safe distance and the maximum sensing radius is used to calculate the potential field force, thereby achieving obstacle avoidance and collision prevention between vehicles. Specifically, the fractional function structure is: the potential field function between vehicles. and the potential field function between the vehicle and the obstacle. ,in, This represents the Euclidean distance between the spacecraft. This represents the Euclidean distance between the vehicle and the obstacle. For minimum safe distance, For the maximum sensing radius, For the first The position vectors of the obstacles; The radial basis function neural network is used to identify and adaptively compensate for unmodeled dynamics and external disturbances in the dynamic model of a vehicle. The radial basis function neural network uses a Gaussian function as the activation function and adjusts the network weights online through a weight adaptive update law. The formation control force, the potential field force, and the compensation output of the radial basis function neural network are vector-fused to generate control commands for each vehicle, thereby achieving formation control.

2. The underwater vehicle formation control method according to claim 1, characterized in that, The formation configuration preservation framework based on rigid graph theory includes: Define an undirected graph This indicates the information exchange relationship between the aircraft, where For a set of nodes, Let be the set of edges. For the connection matrix; Constructing a rigid matrix ,in The set of coordinates of all vertices. It is a side function; Through the connection matrix Describe the relationships between the vertices, where .

3. The underwater vehicle formation control method according to claim 1, characterized in that, The vector fusion includes: When the distance between the vehicle and the obstacle is less than the maximum sensing radius, the weight of the formation-keeping control force is dynamically reduced and the weight of the potential force is increased, so that the obstacle avoidance response takes precedence over formation maintenance; at the same time, the compensation output of the radial basis function neural network is used as a feedforward term and the feedback term composed of the potential force to form a composite control structure, which together corrects the vehicle trajectory.

4. The underwater vehicle formation control method according to claim 1, characterized in that, The online identification and adaptive compensation of unmodeled dynamics and external disturbances in the vehicle dynamics model based on radial basis function neural networks includes: Constructing a radial basis function neural network approximation model ,in For the ideal weight matrix, For the first The input vector of each aircraft To approximate the error; Using Gaussian functions as radial basis functions ,in As the center vector, For width parameters; The perturbation compensation amount is output based on the approximation model.

5. The underwater vehicle formation control method according to claim 4, characterized in that, The process of vector-fusing the formation-keeping control force, the potential field force, and the compensation output of the radial basis function neural network to generate control commands for each aircraft includes: Establish the dynamic equations of the aircraft ,in , These are the generalized matrices obtained after coordinate transformation of the inertia matrix and the Coriolis centripetal force matrix, respectively. For generalized velocity vectors, For generalized control input, For generalized external disturbances; Design control law ,in These are approximate weights for the neural network. Here is the gain matrix. The given dynamics term is denoted as .

6. The underwater vehicle formation control method according to claim 1, characterized in that, The method also includes establishing a kinematic model of the aircraft. ,in This indicates the vehicle's position and heading angle. This indicates the speed information of the aircraft. It is a rotation matrix.

7. The underwater vehicle formation control method according to claim 6, characterized in that, The rotation matrix ,in This is the heading angle.

8. The underwater vehicle formation control method according to claim 1, characterized in that, The method also includes establishing a dynamic model of the aircraft. ,in The inertia matrix, The Coriolis centripetal force matrix, For hydrodynamic damping matrix, External disturbances To control the input.

9. The underwater vehicle formation control method according to claim 1, characterized in that, The vector fusion also includes a dual-threshold-based intelligent switching mechanism, specifically: Real-time monitoring of formation error and disturbance estimate; when the formation error is greater than a preset first threshold and the disturbance estimate is less than a preset second threshold, the weight of the formation maintaining control force is increased and the weight of the potential force is decreased, so as to prioritize the correction of the formation. When the formation error is less than the first threshold and the distance between the vehicle and the obstacle is less than the maximum sensing radius, the weights of the potential force and the radial basis function neural network compensation output are increased and the weight of the formation holding control force is decreased to prioritize navigation safety.

10. The underwater vehicle formation control method according to claim 4, characterized in that, The online adjustment of network weights through a weight adaptive update law includes: The weight update law is designed to include a product term of tracking error and hidden layer activation function output, plus a correction term to suppress parameter drift, so that under continuous external perturbation, the estimated network weight of the radial basis function neural network is always maintained within a preset bounded range.

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