An information-based underwater vehicle formation optimization method and system

Abstract

The application provides an information-based underwater vehicle formation shape optimization method and system, and belongs to the technical field of underwater vehicle formation control; using the collected sampling data of each vehicle in the queue, such as temperature and salinity data, a Gaussian process is used to construct an updated ocean feature field model, then under the formation constraint, the estimated feature field uncertainty of the sampling position of the queue is taken as an objective function, an optimization algorithm is used to optimize the objective function to obtain a formation with the maximum information degree, the formation parameters are output to a cooperative controller, the cooperative controller obtains the control parameters of the vehicle through control law calculation, the control parameters are output to the vehicle, the control of the vehicle is realized, and finally efficient formation cooperative sampling is realized. The method has the decision-making ability of formation optimization and the cooperative sampling ability of multiple vehicles, so that the underwater vehicle can perform efficient and high-quality sampling under the formation allowable error constraint.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater vehicle formation control, and in particular relates to an information-based underwater vehicle formation optimization method and system. Background Art

[0002] To obtain ocean data with sufficient temporal and spatial resolution, in situ ocean observation is a time-consuming, arduous, and costly method of collecting ocean data. This data collection is crucial for maintaining the marine environment, developing marine resources, and safeguarding national security. However, due to the vastness of the ocean, only limited in situ observation platforms are available for studying this vast area. Therefore, underwater vehicles require more efficient data collection methods. Formation optimization is a method for improving sampling efficiency while maintaining a certain temporal and spatial resolution.

[0003] The information-based underwater vehicle formation optimization method refers to using the sampling data collected by each vehicle in the formation to construct or update the ocean characteristic field model, using the estimated characteristic field uncertainty of the sampling position when the formation is about to advance or a mixed index of uncertainty and characteristic field value as the measurement criterion, and using the optimization algorithm to obtain the formation with the maximum information as the optimal formation.

[0004] Currently, underwater vehicles typically use fixed paths and fixed areas for ocean sampling, or use fleet-changing sampling or fleet-changing sampling. Previous methods lack consideration of the effectiveness of sampling when the entire fleet is in a specific formation. Summary of the Invention

[0005] In view of the above problems, the first aspect of the present invention provides an information-based underwater vehicle formation optimization method, which includes the following steps:

[0006] S1, collects ocean characteristic data in real time through sensors, and the sampled data is expressed as , N is the number of spacecraft, Refers to the aircraft The sampling location, specifically the latitude, longitude and depth coordinates, For sensors in position The sample values ​​are combined into a data set ;

[0007] S2, based on the sampled dataset , the ocean characteristic field is modeled based on the Gaussian process. The model includes the characteristic field value and variance. The variance is represented by the kernel function, and the hyperparameters of the kernel function are obtained using the likelihood function;

[0008] Based on the mean function and covariance obtained from the ocean characteristic field model, the unsampled areas of the characteristic field are Perform value estimation to obtain the estimated value and variance of the characteristic field;

[0009] S3, calculate the objective function, take the formation structure parameters as variables, use genetic algorithm as optimization tool, optimize the objective function, and obtain the optimal formation ;

[0010] Among them, in the early stage of sampling, the uncertainty of the constructed characteristic field is used as the objective function, and the optimal formation is the formation that minimizes the uncertainty; in the middle and late stages of sampling, the mixed index is used as the objective function, and the optimal formation is the formation that minimizes the mixed index;

[0011] S4, in formation The parameters are input, and the control parameters are obtained through the control law calculation formula , including forward thrust , steering thrust ;Thereby completing the optimization and adjustment of the underwater vehicle formation;

[0012] S5, after running for a certain period of time based on the adjusted formation, re-enters S1 to S4 to perform the optimization cycle until the task is completed.

[0013] Preferably, in S2, the ocean characteristic field is modeled according to the Gaussian process, and the characteristic field model is specifically:

[0014] (1)

[0015] in, Refers to the constructed characteristic field, represents a Gaussian process, is the sampling data, D is the formation, Refers to the first aircraft, Refers to the communication topology atlas;

[0016] GP consists of a mean function and a covariance, where the mean function is , the covariance function is , the covariance function is specifically:

[0017] (2)

[0018] (3)

[0019] in, and is the sampling position, is a hyperparameter, , is the dimension, where , , ， , and is a vector-valued function; Equation (2) is used for stationary fields, while Equation (3) is used for non-stationary fields.

[0020] Preferably, the hyperparameters of the kernel function are obtained using a likelihood function, and the specific learning process of the hyperparameters is:

[0021] (4)

[0022] (5)

[0023] is the prior distribution of the feature field. When the prior distribution of the feature field is unknown, then formula (4) is:

[0024]

[0025] in, is the estimated value of the hyperparameter, is a set of hyperparameters, is the likelihood function, is the sample value, n is the number of sampled data.

[0026] Preferably, the unsampled area of ​​the feature field Perform value estimation to obtain the estimated value and variance of the characteristic field. The specific calculation formula is:

[0027] (6)

[0028] (7)

[0029] in, is the unsampled position in the region of interest, yes The estimated value of the characteristic field at yes The variance of the characteristic field estimate at ; , ; It is a unit array. is the square of the measurement noise.

[0030] Preferably, in said S3, at the initial stage of sampling, the uncertainty of the constructed characteristic field is used as the objective function, and the specific function formula is:

[0031] (8)

[0032] In the middle and late stages of sampling, the mixed index is used as the objective function, and the specific function formula is:

[0033] (9)

[0034] wherein, is an optimization function, is the variance of the feature field obtained by sampling under the D formation, representing uncertainty, and is a weight coefficient, is the gradient value of the feature field of the D formation position, is the optimal formation.

[0035] Preferably, in S3, the formation structure parameters are taken as variables, a genetic algorithm is used as an optimization tool, and an objective function is optimized, and the specific process is as follows:

[0036] The formation is parameterized and expressed as D(a, b), a is a distance value in the longitude direction, and b is a distance value in the latitude direction, that is, a and b are optimization variables of the genetic algorithm; based on the vehicle dynamics model and the estimated value of the sea current, the control parameter is obtained by the cooperative control law formula, the control parameter is output to the dynamics model, the vehicle trajectory is obtained in combination with the estimated sea current velocity of the sea current, if the trajectory does not reach the expected trajectory length, the cooperative control is returned to the cooperative control law for cooperative control, if the trajectory reaches the expected position, the estimated value and the variance of the virtual sampling data set are calculated by calculating the feature field, and the objective function is calculated, and the genetic algorithm is used to optimize formula (10):

[0037] s.t. (10)

[0038] wherein represents the operation constraint of the D formation;

[0039] If the optimization cycle number or the optimization target value is reached, the optimization is ended, and the optimal formation is output, otherwise the genetic algorithm is used for continuous optimization.

[0040] Preferably, in S4, the formation parameters are taken as inputs, and the control parameter is obtained by the control law calculation formula, and the specific process is as follows:

[0041] The formula (11) and formula (12) are taken as the control law:

[0042] (11)

[0043] (12)

[0044] The control parameter is calculated, is the control input of the vehicle, including the forward direction thrust , the steering thrust ; Output to the aircraft; define the body coordinate system {X, Y, Z}, where the coordinate origin is at the center of mass, the X axis is the forward direction of the body axis, the Y axis is the sideslip direction, and the Z axis is perpendicular to the XY plane and points downward; and is the control gain, is the mass matrix of the spacecraft, 、 is the moment of inertia of the X and Z axes, , , , , are the additional mass of the spacecraft in the X, Y, and Z directions and the additional moment of inertia of the X and Z axes, and is the viscous damping force around the X and Z axes, 、 、 、 、 、 are the virtual speeds along each axis and corner respectively, is the combined velocity; and are the differences between the X-axis position and the Z-axis rotation angle of the neighboring spacecraft; and are the desired speeds along the X-axis and around the Z-axis respectively.

[0045] A second aspect of the present invention provides an information-based underwater vehicle formation optimization system, comprising a sampling module, a learning module, a planner module, and a collaborative control module; wherein the sampling module and the collaborative control module are the control layer, which is the inner loop for underwater vehicle control; the learning module and the planning module are the planning layer, which is the outer loop;

[0046] The sampling module is used to collect ocean feature data in real time. The sampling data is expressed as , N is the number of spacecraft, Refers to the aircraft The sampling location, specifically the latitude, longitude and depth coordinates, For sensors in position The sample values ​​are combined into a data set ;

[0047] The learning module is based on a sampled data set , the ocean characteristic field is modeled based on the Gaussian process. The model includes the characteristic field value and variance. The variance is represented by the kernel function, and the hyperparameters of the kernel function are obtained using the likelihood function;

[0048] Based on the mean function and covariance obtained from the ocean characteristic field model, the unsampled areas of the characteristic field are Perform value estimation to obtain the estimated value and variance of the characteristic field;

[0049] The planner module is used to calculate the objective function, take the formation structure parameters as variables, use genetic algorithm as optimization tool, optimize the objective function, and obtain the optimal formation. ;

[0050] Among them, in the early stage of sampling, the uncertainty of the constructed characteristic field is used as the objective function, and the optimal formation is the formation that minimizes the uncertainty; in the middle and late stages of sampling, the mixed index is used as the objective function, and the optimal formation is the formation that minimizes the mixed index;

[0051] The cooperative control module is in formation The parameters are input, and the control parameters are obtained through the control law calculation formula , including forward thrust , steering thrust ; thereby completing the optimization and adjustment of the underwater vehicle formation.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention provides an information-based underwater vehicle formation optimization method and system. These methods combine formation optimization decision-making capabilities with multi-vehicle collaborative sampling capabilities, enabling efficient and high-quality sampling within the constraints of formation tolerances. This method utilizes an optimized formation for multi-vehicle collaborative sampling, enabling real-time, three-dimensional, and high-resolution simultaneous acquisition of ocean environmental information. This significantly improves the precision and accuracy of ocean feature field construction.

[0054] In particular, a planner with formation as a parameter based on environmental information was designed to obtain the optimal formation. This optimal formation takes into account the motion constraints of multiple aircraft and the overall sampling efficiency of the formation. Compared with previous path optimization methods, it achieves an improvement in the quality of sampling information under formation control. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a structural diagram of the underwater vehicle formation optimization system of the present invention.

[0056] Figure 2 This is a flow chart of the underwater vehicle formation optimization method of the present invention.

[0057] Figure 3 This is the optimization flow chart of the planner module of the present invention. DETAILED DESCRIPTION

[0058] The invention will be further described below with reference to specific embodiments.

[0059] Implementation method: This method is embedded in the offshore control system. The sampling data of each spacecraft is sent to the offshore control system via a communication satellite. The offshore control system calculates the optimal formation based on the sampling data using the formation optimization method. The parameters of the optimal formation are sent to the cooperative controller. The cooperative controller calculates the cooperative control parameters. The control parameters are sent to each spacecraft via satellite. The spacecraft controls its own operation based on the control parameters. Figure 1 shown.

[0060] The method of the present invention includes four modules: a sampling module, a learning module, a planner module, and a collaborative control module. The sampling and collaborative control modules form the control layer, representing the inner loop for underwater vehicle control and a high execution frequency. The learning and planning module forms the planning layer, which is executed less frequently and forms the outer loop.

[0061] The specific process of the information-based underwater vehicle formation optimization method of the present invention is as follows: Figure 2 shown.

[0062] 1. Sampling module for data collection:

[0063] The vehicles are equipped with sensors that collect ocean characteristic data. For example, thermohaline sensors collect ocean temperature and salinity data, and chlorophyll sensors collect chlorophyll concentration data. The information-based underwater vehicle formation optimization method uses the sampled data collected by each vehicle in the formation, such as temperature and salinity data, to construct or update an ocean characteristic field model using a Gaussian process. Then, under formation constraints, the estimated characteristic field uncertainty (or a combination of uncertainty and characteristic field values) at the sampling positions of the formation is used as the objective function. An optimization algorithm is used to optimize the objective function to obtain the formation with the highest information content. This formation is considered the optimal formation, and the formation parameters are output to a collaborative controller. The collaborative controller calculates the control parameters of the vehicles through control laws and outputs these control parameters to the vehicles to control them, ultimately achieving efficient formation collaborative sampling.

[0064] The sampled data is represented as , N is the number of spacecraft, is the number of sampling points, Refers to the aircraft The sampling location, specifically the latitude, longitude and depth coordinates, For sensors in position The sampling module filters the data collected by each aircraft and combines them into a data set And output to the learning module.

[0065] 2. Learning and model reconstruction:

[0066] Based on the sampled data set , the ocean characteristic field is modeled based on the Gaussian process. The model includes the characteristic field value and variance. The variance is represented by the kernel function, and the hyperparameters of the kernel function are obtained using the likelihood function. The characteristic field model is:

[0067] (1-1)

[0068] in, Refers to the constructed characteristic field, represents a Gaussian process, is the sampling data, D is the formation, Refers to the first aircraft, Refers to the communication topology atlas.

[0069] GP consists of a mean function and a covariance, where the mean function is , the covariance function is , the covariance function is specifically:

[0070] (1-2)

[0071] (1-3)

[0072] in, and is the sampling position, is a hyperparameter, , is the dimension, where , , ， , and is a vector-valued function; Equation (1-2) is used for stationary fields, while Equation (1-3) is used for non-stationary fields.

[0073] The hyperparameter learning process of the Gaussian process of the feature field is:

[0074] (1-4)

[0075] (1-5)

[0076] is the prior distribution of the feature field. When the prior distribution of the feature field is unknown, then formula (1-4) is:

[0077]

[0078] in, is the estimated value of the hyperparameter, is a set of hyperparameters, is the likelihood function, is the sampling value, and n is the number of sampling data.

[0079] According to formula 1-1, the unsampled area of ​​the feature field can be calculated using the following formula: By performing value estimation, we can obtain the estimated value and variance of the characteristic field:

[0080] (1-6)

[0081] (1-7)

[0082] in, is the unsampled position in the region of interest, yes The estimated value of the characteristic field at yes The variance of the characteristic field estimate at ; , ; It is a unit array. is the square of the measurement noise.

[0083] 3. Planner performs formation optimization:

[0084] After obtaining the characteristic field model, simulated sampling is performed according to the coordinated control law and the sampling formation, and the sampling values ​​are obtained according to formulas 1-6 and 1-7. The objective function is further calculated. In the early stage of sampling, the uncertainty of the constructed characteristic field is used as the objective function, that is, formula 1-8, and the optimal formation is the formation that minimizes the uncertainty; in the middle and late stages of sampling, the mixed index is used as the objective function, that is, formula 1-9, and the optimal formation is the formation that minimizes the mixed index. The formation optimization process uses the formation structure parameters as variables and the genetic algorithm as the optimization tool to optimize the objective function, that is, formula 1-10, to obtain the optimal formation. .

[0085] At the beginning of sampling, the uncertainty of the constructed characteristic field is used as the objective function, and the specific function formula is:

[0086] (1-8)

[0087] In the middle and late stages of sampling, the mixed index is used as the objective function, and the specific function formula is:

[0088] (1-9)

[0089] in, is the optimization function, is the variance of the characteristic field obtained by sampling under the D formation, representing uncertainty, and is the weight coefficient, is the characteristic field gradient value of the D formation position, The optimal formation.

[0090] The optimization process is as follows Figure 3 As shown: the formation is parameterized, specifically D(a, b), where a is the distance value in the longitude direction and b is the distance value in the latitude direction, that is, a and b are the optimization variables of the genetic algorithm; based on the vehicle dynamics model and the estimated ocean current value, the cooperative control law formula (Equations 1-11 and 1-12) obtains the control parameters, which are output to the dynamics model. The vehicle trajectory is obtained by combining the estimated ocean current velocity. If the trajectory does not reach the desired trajectory length, it returns to the cooperative control law for cooperative control. If the trajectory reaches the desired position, the estimated value and variance of the virtual sampling data set are calculated by using Equations 1-6 and 1-7 on the characteristic field, and the objective function is calculated according to Equations 1-8 and 1-9. The genetic algorithm is used to optimize Equation (10):

[0091] st (1-10)

[0092] in Indicates the operational constraints of the D formation;

[0093] If the number of optimization cycles or the optimization target value is reached, the optimization ends and the optimal formation is output; otherwise, the genetic algorithm is used to continue the optimization.

[0094] 4. Collaborative Controller:

[0095] Take the formation parameters as input and use equations 1-11 and 1-12 as control laws to calculate the control parameters , is the control input of the spacecraft, including the forward thrust , steering thrust . Output to the aircraft. Define the aircraft coordinate system {X, Y, Z}, where the origin is at the center of mass, the X axis is the forward direction of the aircraft axis, the Y axis is the sideslip direction, and the Z axis is perpendicular to the XY plane and points downward.

[0096] (1-11)

[0097] (1-12)

[0098] in, and is the control gain, is the mass matrix of the spacecraft, 、 is the moment of inertia of the X and Z axes, , , , , are the additional mass of the spacecraft in the X, Y, and Z directions and the additional moment of inertia of the X and Z axes, and is the viscous damping force around the X and Z axes, 、 、 、 、 、 are the virtual speeds along each axis and corner respectively, It is the combined speed. and are the differences in the X-axis position and the Z-axis rotation angle of the neighboring spacecraft. and are the desired speeds along the X-axis and around the Z-axis respectively.

[0099] The above description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

[0100] Although the above describes the specific implementation methods of the present invention, it does not limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. An information-based underwater vehicle formation optimization method, characterized in that: The following processes are included: S1, collects ocean characteristic data in real time through sensors, and the sampled data is expressed as , N is the number of spacecraft, Refers to the aircraft The sampling location, specifically the latitude, longitude and depth coordinates, For sensors in position The sample values ​​are combined into a data set ; S2, based on the sampled dataset , the ocean characteristic field is modeled based on the Gaussian process. The model includes the characteristic field value and variance. The variance is represented by the kernel function, and the hyperparameters of the kernel function are obtained using the likelihood function; Based on the mean function and covariance obtained from the ocean characteristic field model, the unsampled areas of the characteristic field are Perform value estimation to obtain the estimated value and variance of the characteristic field; S3, calculate the objective function, take the formation structure parameters as variables, use genetic algorithm as optimization tool, optimize the objective function, and obtain the optimal formation ; Among them, in the early stage of sampling, the uncertainty of the constructed characteristic field is used as the objective function, and the optimal formation is the formation that minimizes the uncertainty; in the middle and late stages of sampling, the mixed index is used as the objective function, and the optimal formation is the formation that minimizes the mixed index; specifically: At the beginning of sampling, the uncertainty of the constructed characteristic field is used as the objective function, and the specific function formula is: （8） In the middle and late stages of sampling, the mixed index is used as the objective function, and the specific function formula is: （9） in, is the optimization function, is the variance of the characteristic field obtained by sampling under the D formation, representing uncertainty, and is the weight coefficient, is the characteristic field gradient value of the D formation position, is the optimal formation; S4, in formation The parameters are input, and the control parameters are obtained through the control law calculation formula , including forward thrust , steering thrust ;Thereby completing the optimization and adjustment of the underwater vehicle formation; S5, after running for a certain period of time based on the adjusted formation, re-enters S1 to S4 to perform the optimization cycle until the task is completed.

2. The information-based underwater vehicle formation optimization method according to claim 1, characterized in that: In S2, the ocean characteristic field is modeled based on the Gaussian process. The characteristic field model is specifically: （1） in, Refers to the constructed characteristic field, represents a Gaussian process, is the sampling data, D is the formation, Refers to the first aircraft, Refers to the communication topology atlas; GP consists of a mean function and a covariance, where the mean function is , the covariance function is , the covariance function is specifically: （2） （3） in, and is the sampling position, is a hyperparameter, , is the dimension, where , , ， , and is a vector-valued function; Equation (2) is used for stationary fields, while Equation (3) is used for non-stationary fields.

3. The information-based underwater vehicle formation optimization method according to claim 2, characterized in that: The hyperparameters of the kernel function are obtained using the likelihood function. The specific learning process of the hyperparameters is as follows: （4） （5） is the prior distribution of the feature field. When the prior distribution of the feature field is unknown, then formula (4) is: in, is the estimated value of the hyperparameter, is a set of hyperparameters, is the likelihood function, is the sample value, n is the number of sampled data.

4. The information-based underwater vehicle formation optimization method according to claim 2, characterized in that: The unsampled area of ​​the feature field Perform value estimation to obtain the estimated value and variance of the characteristic field. The specific calculation formula is: （6） （7） in, is the unsampled position in the region of interest, yes The estimated value of the characteristic field at yes The variance of the characteristic field estimate at ; , ; It is a unit array. is the square of the variance of the measurement noise; is the sampled value.

5. The information-based underwater vehicle formation optimization method according to claim 1, characterized in that: In S3, the formation structure parameters are used as variables and the genetic algorithm is used as the optimization tool to optimize the objective function. The specific process is as follows: The formation is parameterized as D(a, b), where a is the distance value in the longitude direction and b is the distance value in the latitude direction. That is, a and b are the optimization variables of the genetic algorithm. Based on the dynamic model of the vehicle and the estimated ocean current, the control parameters are obtained from the cooperative control law formula. The control parameters are output to the dynamic model. The vehicle trajectory is obtained by combining the estimated ocean current velocity. If the trajectory does not reach the desired trajectory length, the cooperative control law is returned to for cooperative control. If the trajectory reaches the desired position, the estimated value and variance of the virtual sampling data set are obtained by calculating the characteristic field, and the objective function is calculated. The genetic algorithm is used to optimize Equation (10): s.t. (10) in Represents the operational constraints of the D formation; If the number of optimization cycles or the optimization target value is reached, the optimization ends and the optimal formation is output; otherwise, the genetic algorithm is used to continue the optimization.

6. The information-based underwater vehicle formation optimization method according to claim 1, characterized in that: In the S4, the formation The parameters are input, and the control parameters are obtained through the control law calculation formula The specific process is: Taking formula (11) and formula (12) as control law: （11） （12） Calculation control parameters , is the control input of the spacecraft, including the forward thrust , steering thrust ; Output to the aircraft; define the body coordinate system {X, Y, Z}, where the coordinate origin is at the center of mass, the X axis is the forward direction of the body axis, the Y axis is the sideslip direction, and the Z axis is perpendicular to the XY plane and points downward; and is the control gain, is the mass matrix of the spacecraft, 、 is the moment of inertia of the X and Z axes, , , , , are the additional mass of the spacecraft in the X, Y, and Z directions and the additional moment of inertia of the X and Z axes, and is the viscous damping force around the X and Z axes, 、 、 、 、 、 are the virtual speeds along each axis and corner respectively, is the combined velocity; and are the differences between the X-axis position and the Z-axis rotation angle of the neighboring spacecraft; and are the desired speeds along the X-axis and around the Z-axis respectively.

7. An information-based underwater vehicle formation optimization system, characterized by: It includes a sampling module, a learning module, a planner module, and a collaborative control module. The sampling module and the collaborative control module are the control layer, which is the inner loop for underwater vehicle control. The learning module and the planning module are the planning layer, which is the outer loop. The sampling module is used to collect ocean feature data in real time. The sampling data is expressed as , N is the number of spacecraft, Refers to the aircraft The sampling location, specifically the latitude, longitude and depth coordinates, For sensors in position The sample values ​​are combined into a data set ; The learning module is based on a sampled data set , the ocean characteristic field is modeled based on the Gaussian process. The model includes the characteristic field value and variance. The variance is represented by the kernel function, and the hyperparameters of the kernel function are obtained using the likelihood function; Based on the mean function and covariance obtained from the ocean characteristic field model, the unsampled areas of the characteristic field are Perform value estimation to obtain the estimated value and variance of the characteristic field; The planner module is used to calculate the objective function, taking the formation structure parameters as variables and using genetic algorithm as the optimization tool to optimize the objective function and obtain the optimal formation. ; Among them, in the early stage of sampling, the uncertainty of the constructed characteristic field is used as the objective function, and the optimal formation is the formation that minimizes the uncertainty; in the middle and late stages of sampling, the mixed index is used as the objective function, and the optimal formation is the formation that minimizes the mixed index; At the beginning of sampling, the uncertainty of the constructed characteristic field is used as the objective function, and the specific function formula is: In the middle and late stages of sampling, the mixed index is used as the objective function, and the specific function formula is: in, is the optimization function, is the variance of the characteristic field obtained by sampling under the D formation, representing uncertainty, and is the weight coefficient, is the characteristic field gradient value of the D formation position, is the optimal formation; The cooperative control module is in formation The parameters are input, and the control parameters are obtained through the control law calculation formula , including forward thrust , steering thrust ; thereby completing the optimization and adjustment of the underwater vehicle formation.

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