A safe motion control method for a deformable unmanned boat

By predicting and clustering the speed and course of unmanned ships, and combining adaptive deformation technology, the problem of unmanned ships crashing in narrow waterways is solved, achieving safety and success of navigation missions.

CN118859958BActive Publication Date: 2025-03-18CHINA UNIV OF PETROLEUM (EAST CHINA) +1
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Patent Information

Application Number
CN202411345493.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-09-26
Publication Date
2025-03-18
Estimated Expiration
2044-09-26

AI Technical Summary

Technical Problem

Existing unmanned ships are prone to collision and damage in narrow waterways, resulting in failure in navigation missions.

Method used

By training the Gaussian process regression forecast model and the improved k-means++ algorithm, predict and cluster the speed and heading of the unmanned ship, combined with the nonlinear reserve pool calculation algorithm, adaptive deformation of the unmanned ship, adjust the flange and tail to reduce the speed and improve heading.

Benefits of technology

Effectively reduce the collision risk of unmanned ships in narrow waterways and ensure the safety and success of navigation missions.

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Abstract

The present invention discloses a safe motion control method for a deformable unmanned boat, which relates to the technical field of unmanned boats. The speed vector is predicted by a mixed kernel function Gaussian process regression prediction model, and the predicted speed is clustered into a displacement state, a semi-planing state, and a planing state by an improved k-means++ algorithm; the heading is modeled and predicted by a nonlinear reserve pool calculation algorithm; the controller adaptively controls the deformation of the unmanned boat according to the surrounding environment, its own state, and the prediction of state information, formulates a safe motion strategy, realizes the transition of the navigation state, and safely and effectively completes the navigation task. The present invention can adaptively deform the unmanned boat according to the changes in the surrounding environment and the execution of the task, realize the transition of different navigation states, reduce the risk of collision of the unmanned boat at sea, and safely and effectively complete the navigation task.
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Description

Technical Field

[0001] The present invention relates to the technical field of unmanned ship motion control, and in particular to a safe motion control method for a deformable unmanned ship. Background Art

[0002] With the continuous advancement of science and technology, the rapid development of the field of unmanned ships has greatly liberated human and material resources in ocean observation, water quality monitoring and governance, and is suitable for many water-based work contents such as water quality sampling, underwater topography mapping, and surface garbage cleaning. In practical applications, the operation is flexible, and unmanned ships can replace manpower to complete the detection and sampling of dangerous environments. Most unmanned ships in the existing technology use automatic speed adjustment to complete the task. When adjusting the speed, the water flow detection structure, the speed adjustment structure, and the telescopic deformation of the side wings and tail of the unmanned ship cooperate with each other to achieve automatic speed adjustment. However, this adjustment method is prone to collision and damage to the unmanned ship when it runs into a narrow alley, thereby causing the navigation mission to fail. Summary of the invention

[0003] In order to overcome the above problems existing in the prior art, the present invention proposes a safe motion control method for a deformable unmanned boat.

[0004] The technical solution adopted by the present invention to solve the technical problem is: a safe motion control method for a deformable unmanned ship, comprising the following steps:

[0005] Step 1: Train the Gaussian process regression prediction model based on the speed and heading data collected by the unmanned ship in real time to predict the speed of the unmanned ship at future times. ;

[0006] Step 2: Cluster the speed data predicted by the Gaussian process regression prediction model using the improved k-means++ algorithm. There are three navigation state categories: displacement, semi-planing and planing. The speed is less than 3m / s for displacement, between 3-9m / s for semi-planing, and greater than 9m / s for planing.

[0007] Step 3: Model and predict the heading of the unmanned ship through the nonlinear reserve pool calculation algorithm to predict the heading of the unmanned ship at future times. ;

[0008] Step 4: The controller completes the deformation of the object ship according to the changes of its own state, surrounding environment, and execution task at the present and future time.

[0009] Step 4.1: When the unmanned ship is performing an operation in a narrow channel, if the predicted speed Higher than the speed range in displacement state , adjust the side wings and tail fins of the ship close to the hull, and only the main propeller provides power to help it slow down; if the predicted course and measuring heading Changes Above the narrow channel heading change threshold , then retract the rudder:

[0010] ;

[0011] ;

[0012] ;

[0013] Step 4.2: When the unmanned vessel approaches the narrow channel operation site, if the predicted speed Above the semi-planing speed range , adjust the side wings and tail fins of the ship close to the hull, and only the main propeller provides power to help it slow down. If the predicted course and measuring heading Changes Above heading change threshold , then retract the rudder:

[0014] ;

[0015] ;

[0016] ;

[0017] Step 4.3, when the unmanned ship is away from the narrow channel operation site, if the predicted speed Below the semi-planing speed range , adjust the electric push rod to push out the wing, the wing driver rotates to drive the propeller, the main propeller and wing propeller provide power to the hull at the same time to help increase the speed of the ship; if the predicted course and measuring heading Changes Above heading change threshold , then retract the rudder:

[0018] ;

[0019] ;

[0020] ;

[0021] Step 4.4: When the unmanned ship is performing an operation in a wide and unobstructed sea area, if the predicted speed Below the taxiing speed range , adjust the electric push rod to push out the side wing of the boat, and the electric telescopic rod to push out the tail wing. The tail wing driver rotates to drive the tail wing propeller to rotate. The main propeller, the side wing propeller, and the tail wing propeller provide power to the hull at the same time to help increase the speed of the ship. There is no special steering requirement:

[0022] .

[0023] In the above-mentioned safe motion control method for a deformable unmanned ship, the step 1 is specifically as follows:

[0024] Step 1.1, Gaussian process It can be completely determined by the mean function and covariance function To describe:

[0025] ;

[0026] Step 1.2, collect speed and heading information as the training set of Gaussian process regression prediction model:

[0027] ;

[0028] in, is the i-th input data, is the i-th output data;

[0029] Step 1.3, the mapping relationship between input and output in Gaussian process regression is:

[0030] ;

[0031] in, is subject to mean 0 and covariance is Independent Gaussian distributed noise;

[0032] The joint probability distribution of multidimensional Gaussian distribution is:

[0033] ;

[0034] Among them, the mean function of the training sample The a priori is given as 0, represents the output of the test sample, N represents Gaussian distribution, represents the mixed kernel function between the test sample and the training sample, represents the mixed kernel function between training samples, represents the mixed kernel function between test samples, represents the covariance of the noise, represents the identity matrix;

[0035] Step 1.4, derive from the Schulb formula:

[0036] m(f( x ∗ ))=E[f( x ∗ )∣ X , y , x ∗ ]=K( x ∗ , X ) [K( X , X )+ s n 2 I n ] −1 y cov (f( x ∗ ))=K( x ∗ , x ∗ )−K( x ∗ , X ) [K( X , X )+ s n 2 I n ] −1 K( X , x ∗ ) ;

[0037] in, Represents the mean function of the test sample output, that is, the predicted speed vector and heading of the unmanned ship, represents the covariance function, that is, the uncertainty of the predicted speed vector and speed of the unmanned ship, and y represents the output of the training sample;

[0038] Step 1.5, output the speed forecast information to the improved k-means++ algorithm module to cluster the speed.

[0039] In the above-mentioned safe motion control method for a deformable unmanned ship, the mixed kernel function in step 1.3 adopts a mixed kernel function of a square exponential kernel function and a polynomial kernel function, and the specific formula is:

[0040] ;

[0041] in, is a constant, and is the weight of the square exponential function and the polynomial kernel function, and the weight is adaptively adjusted according to the ocean sampling environment. , is the hyperparameter of the kernel function. The selection of hyperparameters is optimized through the maximum likelihood boundary function. The mathematical formula is:

[0042] ;

[0043] in, represents Gaussian noise with zero mean, is the hyperparameter vector;

[0044] In order to calculate the maximum likelihood boundary function, the partial derivative of the formula in step 1.4 is:

[0045] l = [K( X , X )+ s n 2 I n ] −1 y ∂ ∂ i j log (p( y X,θ )= 1 2 tr{[λ l T − (K+ s n 2 I n ) −1 ] ∂( K+ s n 2 I n ) ∂ i j } ;

[0046] in, represents a vector;

[0047] Output the forecast information of speed vector and heading.

[0048] In the above-mentioned safe motion control method for a deformable unmanned ship, the step 2 specifically comprises:

[0049] Step 2.1, the input is the speed data set predicted by the mixed kernel function Gaussian process regression: , ,in yes Axis sway speed, yes Axis sway speed, Axis speed is ignored and output data is divided into clusters ;

[0050] Step 2.2, from the dataset Select 3 as the initial centroid vectors: ,

[0051] The centroids are randomly initialized as:

[0052] ;

[0053] ;

[0054] ;

[0055] in, , is the length Froude number, is the waterline length of the ship, g is the acceleration due to gravity, Refers to the speed range under displacement state. Refers to the speed range in semi-planing state. Refers to the speed range in the planing state;

[0056] Step 2.3, at the maximum number of iterations , calculate the distance between each sample point and the randomly initialized centroid:

[0057] ;

[0058] in, is the number of centroids; the sample points with larger distance have a higher probability of becoming cluster centers, and the probability is calculated as follows:

[0059] ;

[0060] The larger it is, the greater the probability of being selected as the centroid. The sample point with the highest probability is set as the next centroid until three centroids are found. The initial k-means algorithm is used to assign each sample point to the nearest cluster, and finally the cluster classification is output.

[0061] In the above-mentioned safe motion control method for a deformable unmanned ship, the step 3 is specifically as follows:

[0062] Step 3.1: Take the measured heading at the historical moment as input , The output at time is recorded as , reserve pool The state at the moment is recorded as , in At this moment, the relationship between the internal state of the reserve pool and the input of the reserve pool at the historical moment is:

[0063] ;

[0064] for , is the sparsity of the integrating neuron, is the activation function , is the strong nonlinear coefficient in the marine environment, is a hyperparameter, is the connection weight matrix from the input layer to the reserve pool, is the connection weight matrix from the reservoir state to the next reservoir state, is the connection weight matrix from the reserve pool to the output layer;

[0065] Step 3.2, in At this moment, the state equation of the output layer is:

[0066] ;

[0067] Represents vector connection;

[0068] Step 3.3: Use the ridge regression method to train and solve :

[0069] ;

[0070] is the state matrix of the reserve pool, is the regularization coefficient, For one dimensional identity matrix, is the target output matrix;

[0071] Step 3.4: Output the unmanned ship’s heading information at the future moment .

[0072] The beneficial effect of the present invention is that the present invention can adaptively deform the unmanned ship according to changes in the surrounding environment and the tasks to be performed, realize the transition of different navigation states, reduce the risk of collision of the unmanned ship at sea, and complete the navigation mission safely and effectively. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a schematic diagram of the present invention. DETAILED DESCRIPTION

[0074] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0075] This embodiment discloses a safe motion control method for a deformable unmanned ship. Figure 1 As shown, the following steps are included:

[0076] Step 1: Train a Gaussian process regression prediction model based on the speed and heading data collected by the unmanned ship in real time to predict the speed change trend of the unmanned ship in the future.

[0077] Step 1 specifically includes:

[0078] Step 1.1, Gaussian process It can be completely determined by the mean function and covariance function To describe:

[0079] ;

[0080] Step 1.2: The state information (speed, heading) collected by the ship speed collector is the training set of the Gaussian process regression prediction model: ;

[0081] in, is the i-th input data, is the i-th output data;

[0082] Step 1.3, the mapping relationship between input and output in Gaussian process regression is:

[0083] ;

[0084] in, is subject to mean 0 and covariance is Independent Gaussian distributed noise;

[0085] The joint probability distribution of multidimensional Gaussian distribution is:

[0086] ;

[0087] Among them, the mean function of the training sample The a priori is given as 0, represents the output of the test sample, N represents Gaussian distribution, represents the mixed kernel function between the test sample and the training sample, represents the mixed kernel function between training samples, represents the mixed kernel function between test samples, represents the covariance of the noise, Represents the identity matrix.

[0088] The hybrid kernel function adopts a hybrid kernel function of the square exponential kernel function and the polynomial kernel function. The specific formula is:

[0089] ;

[0090] in, is a constant, and is the weight of the square exponential function and the polynomial kernel function, and the weight is adaptively adjusted according to the ocean sampling environment. , is the hyperparameter of the kernel function. The selection of hyperparameters is optimized through the maximum likelihood boundary function. The mathematical formula is:

[0091] ;

[0092] in, represents Gaussian noise with zero mean, is the hyperparameter vector;

[0093] In order to calculate the maximum likelihood boundary function, the partial derivative of the formula in step 1.5 is:

[0094] λ= [K( X , X )+ s n 2 I n ] −1 y ∂ ∂ i j log (p( y X,θ )= 1 2 tr{[λ l T − (K+ s n 2 I n ) −1 ] ∂( K+ s n 2 I n ) ∂ i j } ;

[0095] in, Represents a vector.

[0096] Output the forecast information of speed vector and heading.

[0097] Step 1.4, derive from the Schulb formula:

[0098] m(f( x ∗ ))=E[f( x ∗ )∣ X , y , x ∗ ]=K( x ∗ , X ) [K( X , X )+ s n 2 I n ] −1 y cov (f( x ∗ ))=K( x ∗ , x ∗ )−K( x ∗ , X ) [K( X , X )+ s n 2 I n ] −1 K( X , x ∗ ) ;

[0099] in, Represents the mean function of the test sample output, that is, the predicted speed vector and heading of the unmanned ship, represents the covariance function, that is, the uncertainty of the predicted speed vector and speed of the unmanned ship, and y represents the output of the training sample;

[0100] Step 1.5, output the speed forecast information to the improved k-means++ algorithm module to cluster the speed.

[0101] Step 2: The speed data predicted by the Gaussian process regression prediction model are clustered by the improved k-means++ algorithm. There are three navigation state categories: displacement, semi-planing and planing. The speed is less than 3m / s for displacement state, between 3-9m / s for semi-planing state, and greater than 9m / s for planing state.

[0102] Step 2 specifically includes:

[0103] Step 2.1, the input is the speed data set predicted by the mixed kernel function Gaussian process regression:

[0104] , ,in yes Axis sway speed, yes Axis sway speed, Axis speed is ignored and the output is cluster division ;

[0105] Step 2.2, from the dataset Select 3 as the initial centroid vectors: ,

[0106] The centroids are randomly initialized as:

[0107] ;

[0108] ;

[0109] ;

[0110] in, , is the length Froude number, is the waterline length of the ship, g is the acceleration due to gravity, Refers to the speed range under displacement state. Refers to the speed range in semi-planing state. Refers to the speed range in the gliding state.

[0111] Step 2.3, at the maximum number of iterations , calculate the distance between each sample point and the randomly initialized centroid:

[0112] ;

[0113] in, is the number of centroids. The probability of a sample point with a larger distance becoming a cluster center is higher, and the probability is calculated as follows:

[0114] ;

[0115] The larger the value, the greater the probability of being selected as the centroid. The sample point with the highest probability is set as the next centroid until three centroids are found. Then, the initial k-means algorithm is used to classify each sample point into the nearest cluster, and finally the classification of the cluster is output.

[0116] Step 3, the heading of the unmanned ship is modeled and predicted through a nonlinear reserve pool calculation algorithm to predict the heading change trend of the unmanned ship at future moments.

[0117] Step 3 is as follows: Step 3.1: Take the measured heading at the historical moment as input , The output at time is recorded as , reserve pool The state at the moment is recorded as In the At this moment, the relationship between the internal state of the reserve pool and the input of the reserve pool at the historical moment is:

[0118] ;

[0119] for , is the sparsity of the integrating neuron, is the activation function ( ), is the strong nonlinear coefficient in the marine environment, is a hyperparameter. is the connection weight matrix from the input layer to the reserve pool. is the connection weight matrix from the reservoir state to the reservoir state at the next moment. is the connection weight matrix from the reserve pool to the output layer.

[0120] Step 3.2, in At this moment, the state equation of the output layer is:

[0121] ;

[0122] Represents vector connection.

[0123] Step 3.3: Use the ridge regression method to train and solve :

[0124] ;

[0125] is the state matrix of the reserve pool, is the regularization coefficient, is a dimensional identity matrix, is the target output matrix.

[0126] Step 3.4: Output the unmanned ship’s heading information at the future moment .

[0127] Step 4: The controller completes the deformation of the object hull according to the changes in its own state, surrounding environment, and execution tasks at the present and future times.

[0128] Step 4 is as follows: Step 4.1: When the unmanned ship is performing an operation task in a narrow channel, if the predicted speed Higher than the speed range in displacement state , adjust the side wings and tail fins of the ship close to the hull, and only the main propeller provides power to help it slow down; if the predicted course and measuring heading Changes Above the narrow channel heading change threshold (30°), then pull in the rudder to reduce the risk of collision during operation:

[0129] ;

[0130] ;

[0131] .

[0132] Step 4.2: When the unmanned vessel approaches the narrow channel operation site, if the predicted speed Above the semi-planing speed range , adjust the side wings and tail fins close to the hull, and only the main propeller provides power to help it slow down. and measuring heading Changes Above heading change threshold (30°), then pull in the rudder to reduce the risk of collision during operation.

[0133] ;

[0134] ;

[0135] .

[0136] Step 4.3, when the unmanned ship is away from the narrow channel operation site, if the predicted speed Below the semi-planing speed range , adjust the electric push rod to push out the wing, the wing driver rotates to drive the propeller, the main propeller and wing propeller provide power to the hull at the same time to help increase the speed of the ship. and measuring heading Changes Above heading change threshold (40°), then pull in the rudder to reduce the risk of collision during operation:

[0137] ;

[0138] ;

[0139] .

[0140] Step 4.4: When the unmanned ship is performing an operation in a wide and unobstructed sea area, if the predicted speed Below the taxiing speed range , adjust the electric push rod to push out the side wing of the boat, and the electric telescopic rod to push out the tail wing. The tail wing driver rotates to drive the tail wing propeller to rotate. The main propeller, the side wing propeller, and the tail wing propeller provide power to the hull at the same time to help increase the speed of the ship. There is no special steering requirement:

[0141] .

[0142] The deformable unmanned boat involved in this embodiment is the deformable unmanned boat disclosed in the publication number CN116620492A and the name is a deformable unmanned boat and a deformation method, which belongs to the prior art and the specific structure of the deformable unmanned boat will not be described in detail here.

[0143] The above embodiments are only exemplary embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art may make various modifications or equivalent substitutions to the present invention within the essence and protection scope of the present invention, and such modifications or equivalent substitutions shall also be deemed to fall within the protection scope of the present invention.

Claims

1. A safe motion control method for a deformable unmanned boat, characterized in that: The steps include: Step 1: Train a Gaussian process regression prediction model based on the speed and heading data collected by the unmanned ship in real time to predict the speed of the unmanned ship at future times. ; Step 2: Cluster the speed data predicted by the Gaussian process regression prediction model using the improved k-means++ algorithm. There are three navigation state categories: displacement, semi-planing and planing. The speed is less than 3m / s for displacement, between 3-9m / s for semi-planing, and greater than 9m / s for planing. Step 3: Model and predict the heading of the unmanned ship through the nonlinear reserve pool calculation algorithm to predict the heading of the unmanned ship at future times. ; Step 4: The controller completes the deformation of the object ship according to the changes of its own state, surrounding environment, and execution task at the present and future time. Step 4.1: When the unmanned ship is performing an operation in a narrow channel, if the predicted speed Higher than the speed range in displacement state , adjust the side wings and tail fins of the ship close to the hull, and only the main propeller provides power to help it slow down; if the predicted course and measuring heading Changes Above the narrow channel heading change threshold , then retract the rudder: ; ; ; Step 4.2: When the unmanned vessel approaches the narrow channel operation site, if the predicted speed Above the semi-planing speed range , adjust the side wings and tail fins of the ship close to the hull, and only the main propeller provides power to help it slow down. If the predicted course and measuring heading Changes Above heading change threshold , then retract the rudder: ; ; ; Step 4.3, when the unmanned ship is away from the narrow channel operation site, if the predicted speed Below the semi-planing speed range , adjust the electric push rod to push out the wing, the wing driver rotates to drive the propeller, the main propeller and wing propeller provide power to the hull at the same time to help increase the speed of the ship; if the predicted course and measuring heading Changes Above heading change threshold , then retract the rudder: ; ; ; Step 4.4: When the unmanned ship is performing an operation in a wide and unobstructed sea area, if the predicted speed Below the taxiing speed range , adjust the electric push rod to push out the side wing of the boat, and the electric telescopic rod to push out the tail wing. The tail wing driver rotates to drive the tail wing propeller to rotate. The main propeller, the side wing propeller, and the tail wing propeller provide power to the hull at the same time to help increase the speed of the ship. There is no special steering requirement: 。 2. The safe motion control method of a deformable unmanned boat according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1.1, Gaussian process It can be completely determined by the mean function and covariance function To describe: ; Step 1.2, collect speed and heading information as the training set of Gaussian process regression prediction model: ; in, is the i-th input data, is the i-th output data; Step 1.3, the mapping relationship between input and output in Gaussian process regression is: ; in, is subject to mean 0 and covariance is Independent Gaussian distributed noise; The joint probability distribution of multidimensional Gaussian distribution is: ; Among them, the mean function of the training sample The a priori is given as 0, represents the output of the test sample, N represents Gaussian distribution, represents the mixed kernel function between the test sample and the training sample, represents the mixed kernel function between training samples, represents the mixed kernel function between test samples, represents the covariance of the noise, represents the identity matrix; Step 1.4, derive from the Schulb formula: ; in, Represents the mean function of the test sample output, that is, the predicted speed vector and heading of the unmanned ship, represents the covariance function, that is, the uncertainty of the predicted speed vector and speed of the unmanned ship, and y represents the output of the training sample; Step 1.5, output the speed forecast information to the improved k-means++ algorithm module to cluster the speed.

3. The safe motion control method of a deformable unmanned boat according to claim 2, characterized in that: The mixed kernel function in step 1.3 adopts a mixed kernel function of a square exponential kernel function and a polynomial kernel function, and the specific formula is: ; in, is a constant, and is the weight of the square exponential function and the polynomial kernel function, and the weight is adaptively adjusted according to the ocean sampling environment. , is the hyperparameter of the kernel function. The selection of hyperparameters is optimized through the maximum likelihood boundary function. The mathematical formula is: ; in, represents Gaussian noise with zero mean, is the hyperparameter vector; In order to calculate the maximum likelihood boundary function, the partial derivative of the formula in step 1.4 is: ; in, represents a vector; Output the forecast information of speed vector and heading.

4. The safe motion control method of a deformable unmanned boat according to claim 1, characterized in that: The step 2 specifically includes: Step 2.1, the input is the speed data set predicted by the mixed kernel function Gaussian process regression: , ,in yes Axis sway speed, yes Axis sway speed, Axis speed is ignored and output data is divided into clusters ; Step 2.2, from the dataset Select 3 as the initial centroid vectors: , The centroids are randomly initialized as: ; ; ; in, , is the length Froude number, is the waterline length of the ship, g is the acceleration due to gravity, Refers to the speed range under displacement state. Refers to the speed range in semi-planing state. Refers to the speed range in the planing state; Step 2.3, at the maximum number of iterations , calculate the distance between each sample point and the randomly initialized centroid: ; in, is the number of centroids; the sample points with larger distance have a higher probability of becoming cluster centers, and the probability is calculated as follows: ; The larger it is, the greater the probability of being selected as the centroid. The sample point with the highest probability is set as the next centroid until three centroids are found. The initial k-means algorithm is used to assign each sample point to the nearest cluster, and finally the cluster classification is output.

5. The safe motion control method of a deformable unmanned boat according to claim 1, characterized in that: The step 3 is specifically as follows: Step 3.1: Take the measured heading at the historical moment as input , The output at time is recorded as , reserve pool The state at the moment is recorded as , in At this moment, the relationship between the internal state of the reserve pool and the input of the reserve pool at the historical moment is: ; for , is the sparsity of the integrating neuron, is the activation function , is the strong nonlinear coefficient in the marine environment, is a hyperparameter, is the connection weight matrix from the input layer to the reserve pool, is the connection weight matrix from the reservoir state to the next reservoir state, is the connection weight matrix from the reserve pool to the output layer; Step 3.2, in At this moment, the state equation of the output layer is: ; Represents vector connection; Step 3.3: Use the ridge regression method to train and solve : ; is the state matrix of the reserve pool, is the regularization coefficient, For one dimensional identity matrix, is the target output matrix; Step 3.4: Output the unmanned ship’s heading information at the future moment .

Citation Information

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