Gaussian process based method and system for flow disturbance resistance of a submarine cable laying underwater robot

Abstract

The application discloses a Gauss process-based anti-water-flow-disturbance method and system for a submarine cable laying underwater robot, and the anti-water-flow-disturbance method comprises the following steps: S1, establishing a water flow disturbance Gauss process probability model; S2, collecting state information and error information of the underwater robot at N D times before a current time k to construct a training set; training the water flow disturbance Gauss process probability model established in S1 to obtain a mean value μ D (x(k)) of the training set error information about the state information; S3, obtaining an actual state x * (k) of the underwater robot at the current time, and obtaining a mean value μ(x * (k)) of the water flow disturbance estimation value according to Gauss process regression; S4, calculating an optimal control input u * (k) of the underwater robot at the current time k according to the mean value of the water flow disturbance estimation value; and calculating a vector τ composed of thrust and torque inputs of the underwater robot at the current time k according to u * (k). According to the method, the control input is compensated according to the water flow disturbance, so that the errors of the posture and the moving speed of the underwater robot are reduced, and the cable laying quality is improved.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, specifically a method for controlling water flow disturbances when an underwater robot tracks the laying path during submarine cable laying. Background Technology

[0002] With scientific advancements, the development of underwater robots has laid the foundation for automated maintenance technologies in highly dangerous fields where personnel cannot perform tasks for extended periods. Submarine cables, also known as submarine cables, include cables laid on the seabed and wrapped with reinforced protective sheaths, optical cables, and fiber-optic composite cables. They possess irreplaceable advantages in power transmission, transoceanic communication, and marine engineering. However, the seabed environment may contain uncertain interferences such as constant currents and turbulent currents. These interferences can easily cause instability in the cable-laying posture of underwater robots and prevent them from achieving ideal movement speeds, all of which can reduce the quality of cable laying or even damage the cables. Currently, the mainstream anti-interference control algorithms include the following:

[0003] (1) Adaptive control

[0004] Adaptive control methods adjust the parameters of the underwater robot's controller in real time based on the feedback of the actual system's state error, enabling the controller to achieve optimal control performance in the current environment. This method has a strong adaptability to environmental changes. However, it has a low tolerance for uncertain disturbances in the environment. When uncertain disturbances exist, this method is easily affected by the disturbances, leading to incorrect optimization direction and causing the error between the underwater robot and the preset path to increase.

[0005] (2) Active disturbance rejection control

[0006] Active disturbance rejection control (ADRC) primarily estimates the total disturbance by designing a state observer for the underwater robot and incorporating a transient process into the existing PID algorithm. This method is characterized by strong anti-disturbance capability and independence from an accurate system model. However, when encountering complex systems, this method requires adjusting too many parameters, and since the working environment of an autonomous underwater vehicle (AUV) is primarily underwater, frequent parameter adjustments and experiments are not suitable.

[0007] (3) Machine Learning

[0008] Machine learning is currently the most common method for disturbance estimation. This method first establishes a neural network model of the disturbance, then gradually optimizes the network model parameters through a large amount of training data, and finally uses the robot's pose information as the input to the network at each control moment, with the network model's output used for controller compensation and optimization. However, due to the complex underwater environment where submarine cables are laid, the water flow contains a small portion of turbulence, which makes the direction of water thrust variable and the samples contain uncertain components, resulting in low learning efficiency and low accuracy of the above method.

[0009] To ensure the quality of cable laying, the underwater robot needs to maintain a stable posture within a certain range. While the methods described above can suppress interference from the external environment to some extent, the complex underwater environment and the presence of some random variations in the training samples lead to low learning efficiency of the algorithms and may even result in incorrect optimization directions, causing the error from the desired state to increase. Summary of the Invention

[0010] Purpose of the invention: To address the problems existing in the prior art, this invention provides a method for resisting water flow disturbances in underwater robots for laying submarine cables based on Gaussian processes. This method compensates for the control input based on water flow disturbances, thereby reducing errors in the underwater robot's attitude and movement speed, and improving the quality of cable laying.

[0011] Technical solution: This invention discloses a method for resisting water flow disturbance by an underwater robot for laying submarine cables based on Gaussian processes, including the following steps:

[0012] S1. Establish a probabilistic model for the Gaussian process of water flow disturbance:

[0013]

[0014] Where x(k) is the state variable of the underwater robot laying the submarine cable at time k under the interference of water flow, n is the dimension of x(k), e(x(k)) is the interference error between the actual state and the expected state of the underwater robot laying the submarine cable at time k under the interference of water flow, e(x(k))=f(x(k))+ε, f(x(k)) is the constant current component in the water flow interference, and its Gaussian process probability function is: ε represents the random component in the water flow disturbance, and the model is: σ n Let be the variance of ε; μ(x(k)) be the mean function of e(x(k)) with respect to the state variable x(k), and k(x(k),x(k)) be the mean of ε. T Let covariance function be the function of water flow disturbance. Let μ represent a Gaussian process. m (x(k)) is the m-th component of μ(x(k)), k m (x(k),x(k) T) is k(x(k),x(k) T The m-th component, where m is an integer in the interval [1,n];

[0015] S2, Collect N data points k before the current time. D The underwater robot's state information X and error information Y at each moment are used to construct a training set;

[0016]

[0017] x(ki) represents the state of the underwater robot at time k before the current time, and e(x(ki)) represents the interference error between the actual state and the expected state of the underwater robot at time k before the current time; i = 1, 2, ..., N D ;

[0018] The probabilistic model of the Gaussian process of water flow disturbance established in S1 is trained using the training set, and the mean μ of the training set error information Y with respect to the state information X is obtained. D (x(k));

[0019] S3. Obtain the current state x of the underwater robot. * (k), the mean value μ(x) of the estimated water flow disturbance is obtained by Gaussian process regression. * (k));

[0020] S4. Calculate the optimal control input u of the underwater robot at the current time k based on the mean of the estimated water flow disturbance values. * (k); according to u * (k) Calculate the vector τ consisting of the thrust and torque inputs of the underwater robot at the current time k.

[0021] Furthermore, the state variable x(k) of the underwater robot laying the submarine cable at time k under the interference of water flow is an n-dimensional vector composed of the underwater robot's pose η(k) and movement velocity v(k) at time k, x(k) = [η(k) v(k)] T ;

[0022] in px, py, and pz represent the longitudinal, lateral, and vertical displacements of the underwater robot, respectively. These are the roll angle, pitch angle, and yaw angle, respectively; v(k) = [u,v,w,p,q,r], where u,v,w are the longitudinal speed, lateral speed, and vertical speed, respectively, and p,q,r are the roll speed, pitch speed, and yaw speed, respectively.

[0023] Furthermore, the mean value μ(x) of the estimated water flow disturbance in step S3. * The calculation steps for (k) are as follows:

[0024] S31. Calculate the estimated value of water flow disturbance e(x) * The mean of each component of (k) and the mean μ of the m-th component. m (x * (k) is:

[0025] Where K m (x * (k),X) represents the current actual state of the underwater robot at the current moment. * (k) is the m-th component of the covariance matrix of the state information X in the training set, K m (X,X) is the m-th component of the covariance matrix of the state information X in the training set. For N D ×N D The identity matrix; For the m-th column of the training set error information Y, The mean μ of the training set error information Y with respect to the state information X D The m-th column of (x(k));

[0026] S32, Mean value of estimated water flow disturbance μ(x) * (k) is:

[0027]

[0028] Furthermore, in step S4, the optimal control input u of the underwater robot at the current time k * (k) is:

[0029]

[0030] Where u d (k) is the control input before compensation, u d (k) = v(k+1) - v(k), where v(k) is the current speed of the underwater robot at time k;

[0031] The vector τ formed by the thrust and torque inputs of the underwater robot at the current time k is:

[0032] τ=u * (k)+M -1 C(v(k))v(k)+M -1 D(v(k))v(k)+M -1 g(η(k))

[0033] Where M is the inertia matrix caused by the rigid body and the added mass; C(v(k)) is the Coriolis force matrix; D(v(k)) is the fluid damping matrix; and g(η(k)) is the restoring force vector generated by gravity and buoyancy.

[0034] On the other hand, the present invention also discloses a system for implementing the above-mentioned method for resisting water flow disturbance of underwater robots for submarine cable laying based on Gaussian processes, comprising:

[0035] Module 1 for establishing a probabilistic model of a Gaussian process with water flow disturbance is used to establish a probabilistic model of a Gaussian process with water flow disturbance.

[0036]

[0037] Where x(k) is the state variable of the underwater robot laying the submarine cable at time k under the interference of water flow, n is the dimension of x(k), e(x(k)) is the interference error between the actual state and the expected state of the underwater robot laying the submarine cable at time k under the interference of water flow, e(x(k))=f(x(k))+ε, f(x(k)) is the constant current component in the water flow interference, and its Gaussian process probability function is: ε represents the random component in the water flow disturbance, and the model is: σ n Let be the variance of ε; μ(x(k)) be the mean function of e(x(k)) with respect to the state variable x(k), and k(x(k),x(k)) be the mean of ε. T Let covariance function be the function of water flow disturbance. Let μ represent a Gaussian process. m (x(k)) is the m-th component of μ(x(k)), k m (x(k),x(k) T ) is k(x(k),x(k) T The m-th component, where m is an integer in the interval [1,n];

[0038] Training set construction module 2 is used to collect N data from the previous k time steps. D The underwater robot's state information X and error information Y at each moment are used to construct a training set;

[0039]

[0040] x(ki) represents the state of the underwater robot at time k before the current time, and e(x(ki)) represents the interference error between the actual state and the expected state of the underwater robot at time k before the current time; i = 1, 2, ..., N D ;

[0041] The probabilistic model of the Gaussian process of water flow disturbance established in S1 is trained using the training set, and the mean μ of the training set error information Y with respect to the state information X is obtained. D (x(k));

[0042] The water flow disturbance estimation module 3 is used to obtain the actual state x of the underwater robot at the current moment. *(k), the mean value μ(x) of the estimated water flow disturbance is obtained by Gaussian process regression. * (k));

[0043] The water flow disturbance compensation module 4 is used to calculate the optimal control input u of the underwater robot at the current time k based on the mean of the water flow disturbance estimates. * (k); according to u * (k) Calculate the vector τ consisting of the thrust and torque inputs of the underwater robot at the current time k.

[0044] On the other hand, the present invention also discloses a computer storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for resisting water flow disturbance by an underwater robot for laying submarine cables.

[0045] On the other hand, the present invention also discloses an anti-current disturbance device for an underwater robot for laying submarine cables, which includes:

[0046] A memory on which computer programs are stored;

[0047] A processor is used to execute the computer program in the memory to implement the steps of the above-described method for underwater robots to resist water flow disturbance during submarine cable laying.

[0048] Beneficial Effects: The method and system for resisting water flow disturbances in underwater robots used for submarine cable laying disclosed in this invention employs a Gaussian process to represent the relationship between water flow disturbances and the underwater robot, and establishes a water flow disturbance model in a probabilistic manner, effectively reducing the impact of random components in the samples on prediction accuracy. It expresses the nonlinear and complex relationship between water flow disturbances and the underwater robot using a Gaussian process-based water flow disturbance modeling approach. This method and system can accurately estimate water flow disturbances and then compensate for control inputs based on these disturbances, thereby reducing errors in the underwater robot's attitude and movement speed, and improving the quality of cable laying. Attached Figure Description

[0049] Figure 1 A flowchart of the method for resisting water flow disturbance by an underwater robot for laying submarine cables disclosed in this invention;

[0050] Figure 2 This is a schematic diagram of the composition of the underwater robot anti-water flow disturbance system for laying submarine cables disclosed in this invention;

[0051] Figure 3 This is a schematic diagram of the composition of the underwater robot anti-water flow disturbance device for laying submarine cables disclosed in this invention. Detailed Implementation

[0052] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0053] To enable underwater robots to perform cable-laying operations in complex seabed environments, a predictive control model for underwater robot seabed cable laying operations is needed. This invention uses the state variable x(k) = [η(k) v(k)]. T ,in Let be the pose of the underwater robot at time k, and let px, py, and pz be the longitudinal, lateral, and vertical displacements of the underwater robot, respectively. Let be the roll angle, pitch angle, and yaw angle, respectively; v(k) = [u,v,w,p,q,r] be the moving speed, where u,v,w are the longitudinal, lateral, and vertical moving speeds, respectively, and p,q,r are the roll speed, pitch speed, and yaw speed, respectively. Assuming the sampling time is t, the discretized control state equation of the underwater robot can be expressed as:

[0054]

[0055] In equation (1), x(k) is the state variable of the underwater robot laying the submarine cable under the interference of water flow at time k. In this embodiment, x(k) is a 12-dimensional vector; u(k) is the control input vector of the underwater robot at time k. respectively The identity matrix and zero matrix; J(η(k)) is the coordinate transformation matrix of the underwater robot; assuming the control input of the underwater robot at time k is u d (k)), the desired state of the underwater robot at time k+1 is x d (k+1), due to the interference of water flow, the underwater robot cannot reach the ideal state. The actual state equation can be expressed as:

[0056]

[0057] In equation (2), e(x(k)) is the interference error between the actual operating state and the desired state of the underwater robot. In a non-turbulent underwater environment, this interference can be decomposed into a relatively regular constant current component and a random component.

[0058] 1. Modeling of constant flow components in water flow disturbances

[0059] The constant-current component of water flow disturbance in the seabed environment mainly refers to the regular, continuous convection formed by regional undercurrents, monsoons, and persistent submarine volcanoes. This constant-current component can be considered as a constant thrust component of the water flow on the underwater robot. The impact of this thrust on the underwater robot is related to its state variables such as attitude and speed. Therefore, the constant disturbance can be modeled using a multidimensional Gaussian process nonlinear function, which can be expressed as:

[0060]

[0061] In equation (3), P(f(x(k))) is the Gaussian process probability function of the error between the underwater robot and the ideal state, where f(x(k)) is the constant current component in the water flow disturbance, and its value is related to the underwater robot's speed, position, and attitude at time k; μ(x(k)) is the mean function of e(x(k)) with respect to the state variable x(k), k(x(k), x(k)) T Let covariance function be the function of water flow disturbance. This represents a Gaussian process.

[0062] 2. Modeling of random components in water flow disturbance

[0063] Random water flow disturbances in the seabed environment mainly refer to irregular convection such as turbulence and rough currents. Since random water flow disturbances account for a relatively small proportion in underwater robot cable laying operations, this invention uses random white noise to model them.

[0064]

[0065] In equation (4), ε represents disordered white noise, used to describe the interference of a small proportion of turbulence in the water flow on the underwater robot, i.e., the random component in the water flow interference; σ n Let V be the variance of the noise.

[0066] 3. Water flow interference modeling

[0067] Considering the impact of constant current component and random current component interference on AUV path tracking in the seabed environment, according to equations (3) and (4), the water flow interference model for laying submarine cables can be expressed as e(x(k))=f(x(k))+ε.

[0068] Based on the above analysis, this invention discloses a method for resisting water flow disturbances in underwater robots used for submarine cable laying based on Gaussian processes, such as... Figure 1 As shown, the steps include:

[0069] S1. Based on the ship's control equation (1), define n independent Gaussian processes to establish a probabilistic model of the water flow disturbance e(x(k)), that is, establish a probabilistic model of the water flow disturbance Gaussian process:

[0070]

[0071] Where x(k) is the state variable of the underwater robot laying the submarine cable at time k under the interference of water flow, n is the dimension of x(k), e(x(k)) is the interference error between the actual state and the expected state of the underwater robot laying the submarine cable at time k under the interference of water flow, e(x(k))=f(x(k))+ε, f(x(k)) is the constant current component in the water flow interference, and its Gaussian process probability function is: ε represents the random component in the water flow disturbance, and the model is: σn Let be the variance of ε; μ(x(k)) be the mean function of e(x(k)) with respect to the state variable x(k), and k(x(k),x(k)) be the mean of ε. T Let covariance function be the function of water flow disturbance. Let μ represent a Gaussian process. m (x(k)) is the m-th component of μ(x(k)), which is the mean function of the m-th component of e(x(k)) with respect to the state variable x(k); k m (x(k),x(k)T) is k(x(k),x(k) T The m-th component is the covariance function of the water flow disturbance on the m-th component of e(x(k)), where m is an integer in the interval [1,n].

[0072] S2, Collect N data points k before the current time. D Given the state information X and error information Y of the underwater robot at each moment, a training set D is constructed: D = {X, Y} = {(x(ki), ...,} Where x(ki) represents the state of the underwater robot at the current time k, i times ago, and e(x(ki)) = x(ki) - x d (ki), x d (ki) represents the desired state variable of the underwater robot at time ki, where i = 1, 2, ..., N. D ;

[0073]

[0074] The probabilistic model of the Gaussian process of water flow disturbance established in S1 is trained using the training set, and the mean μ of the training set error information Y with respect to the state information X is obtained. D (x(k));

[0075] S3. Use sensors to obtain the current real-time state x of the underwater robot. * (k), the mean value μ(x) of the estimated water flow disturbance is obtained by Gaussian process regression. * (k)), the specific steps are as follows:

[0076] S31. Calculate the estimated value of water flow disturbance e(x) * The mean of each component of (k) and the mean μ of the m-th component. m (x * (k) is:

[0077] Where K m (x * (k),X) represents the current actual state of the underwater robot at the current moment. * (k) is the m-th component of the covariance matrix of the state information X in the training set, Km (X,X) is the m-th component of the covariance matrix of the state information X in the training set. For N D ×N D The identity matrix; For the m-th column of the training set error information Y, The mean μ of the training set error information Y with respect to the state information X D The m-th column of (x(k));

[0078] S32, Mean value of estimated water flow disturbance μ(x) * (k) is:

[0079]

[0080] S4. Calculate the optimal control input u of the underwater robot at the current time k based on the mean of the estimated water flow disturbance values. * (k); according to u * (k) Calculate the vector τ consisting of the thrust and torque inputs of the underwater robot at the current time k. The specific steps are as follows:

[0081] The optimal control input u of the underwater robot at the current time k * (k) is:

[0082]

[0083] Where u d (k) is the control input before compensation, u d (k) = v(k+1) - v(k), where v(k) is the current speed of the underwater robot at time k;

[0084] The vector τ formed by the thrust and torque inputs of the underwater robot at the current time k is:

[0085] τ=u * (k)+M -1 C(v(k))v(k)+M -1 D(v(k))v(k)+M -1 g(η(k))

[0086] Where M is the inertia matrix caused by the rigid body and the added mass; C(v(k)) is the Coriolis force matrix; D(v(k)) is the fluid damping matrix; and g(η(k)) is the restoring force vector generated by gravity and buoyancy.

[0087] This invention also discloses a system for implementing the above-mentioned method for resisting water flow disturbance in underwater robots used for submarine cable laying based on Gaussian processes, such as... Figure 2 As shown, it includes:

[0088] Module 1 for establishing the probabilistic model of the Gaussian process of water flow disturbance is used to establish the probabilistic model of the Gaussian process of water flow disturbance based on step S1:

[0089]

[0090] Where x(k) is the state variable of the underwater robot laying the submarine cable at time k under the interference of water flow, n is the dimension of x(k), e(x(k)) is the interference error between the actual state and the expected state of the underwater robot laying the submarine cable at time k under the interference of water flow, e(x(k))=f(x(k))+ε, f(x(k)) is the constant current component in the water flow interference, and its Gaussian process probability function is: ε represents the random component in the water flow disturbance, and the model is: σ n Let be the variance of ε; μ(x(k)) be the mean function of e(x(k)) with respect to the state variable x(k), and k(x(k),x(k)) be the mean of ε. T Let covariance function be the function of water flow disturbance. Let μ represent a Gaussian process. m (x(k)) is the m-th component of μ(x(k)), k m (x(k),x(k) T ) is k(x(k),x(k) T The m-th component, where m is an integer in the interval [1,n];

[0091] Training set building module 2 is used to collect N samples from the previous k time step according to step S2. D The underwater robot's state information X and error information Y at each moment are used to construct a training set;

[0092]

[0093] x(ki) represents the state of the underwater robot at time k before the current time, and e(x(ki)) represents the interference error between the actual state and the expected state of the underwater robot at time k before the current time; i = 1, 2, ..., N D ;

[0094] The probabilistic model of the Gaussian process of water flow disturbance established in S1 is trained using the training set, and the mean μ of the training set error information Y with respect to the state information X is obtained. D (x(k));

[0095] The water flow disturbance estimation module 3 is used to obtain the actual state x*(k) of the underwater robot at the current moment according to step S3, and to obtain the mean value μ(x) of the water flow disturbance estimate by Gaussian process regression. * (k));

[0096] The water flow disturbance compensation module 4 is used to calculate the optimal control input u of the underwater robot at the current time k based on the mean of the water flow disturbance estimates in step S4. * (k); according to u * (k) Calculate the vector τ consisting of the thrust and torque inputs of the underwater robot at the current time k.

[0097] The present invention also discloses a computer storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for resisting water flow disturbance by an underwater robot for laying submarine cables.

[0098] This invention also discloses an underwater robot anti-current disturbance device for laying submarine cables, such as... Figure 3 As shown, it includes:

[0099] A memory on which computer programs are stored;

[0100] A processor is used to execute the computer program in the memory to implement the steps of the above-described method for underwater robots to resist water flow disturbance during submarine cable laying.

Claims

1. A method for resisting water flow disturbance using an underwater robot for submarine cable laying based on Gaussian processes, characterized in that, Including the following steps: S1. Establish a probabilistic model for the Gaussian process of water flow disturbance: Where x(k) is the state variable of the underwater robot laying the submarine cable at time k under the interference of water flow, n is the dimension of x(k), e(x(k)) is the interference error between the actual state and the expected state of the underwater robot laying the submarine cable at time k under the interference of water flow, e(x(k))=f(x(k))+ε, f(x(k)) is the constant current component in the water flow interference, and its Gaussian process probability function is: ε represents the random component in the water flow disturbance, and the model is: σ n Let be the variance of ε; μ(x(k)) be the mean function of e(x(k)) with respect to the state variable x(k), and k(x(k),x(k)) be the mean of ε. T Let covariance function be the function of water flow disturbance. Let μ represent a Gaussian process. m (x(k)) is the m-th component of μ(x(k)), k m (x(k),x(k) T ) is k(x(k),x(k) T The m-th component, where m is an integer in the interval [1,n]; S2, Collect N data points k before the current time. D The underwater robot's state information X and error information Y at each moment are used to construct a training set; x(ki) represents the state of the underwater robot at time k before the current time, and e(x(ki)) represents the interference error between the actual state and the expected state of the underwater robot at time k before the current time; i = 1, 2, ..., N D ; The probabilistic model of the Gaussian process of water flow disturbance established in S1 is trained using the training set, and the mean μ of the training set error information Y with respect to the state information X is obtained. D (x(k)); S3. Obtain the current state x of the underwater robot. * (k), the mean value μ(x) of the estimated water flow disturbance is obtained by Gaussian process regression. * (k)); S4. Calculate the optimal control input u of the underwater robot at the current time k based on the mean of the estimated water flow disturbance values. * (k); according to u * (k) Calculate the vector τ consisting of the thrust and torque inputs of the underwater robot at the current time k.

2. The method for resisting water flow disturbance of underwater robots for submarine cable laying based on Gaussian processes according to claim 1, characterized in that, The state variable x(k) of the underwater robot laying submarine cable at time k under the interference of water flow is an n-dimensional vector composed of the underwater robot's pose η(k) and movement velocity v(k) at time k, x(k) = [η(k) v(k)] T ; in px, py, and pz represent the longitudinal, lateral, and vertical displacements of the underwater robot, respectively. θ and ψ represent the roll angle, pitch angle, and yaw angle, respectively; v(k) = [u,v,w,p,q,r], where u,v,w represent the longitudinal movement speed, lateral movement speed, and vertical movement speed, respectively, and p,q,r represent the roll rotation speed, pitch rotation speed, and yaw rotation speed, respectively.

3. The method for resisting water flow disturbance of underwater robots for submarine cable laying based on Gaussian processes according to claim 1, characterized in that, The mean value of the estimated water flow disturbance in step S3 is μ(x) * The calculation steps for (k) are as follows: S31. Calculate the estimated value of water flow disturbance e(x) * The mean of each component of (k) and the mean μ of the m-th component. m (x * (k) is: Where K m (x * (k),X) represents the current actual state of the underwater robot at the current moment. * (k) is the m-th component of the covariance matrix of the state information X in the training set, K m (X,X) is the m-th component of the covariance matrix of the state information X in the training set. For N D ×N D The identity matrix; For the m-th column of the training set error information Y, The mean μ of the training set error information Y with respect to the state information X D The m-th column of (x(k)); S32, Mean value of estimated water flow disturbance μ(x) * (k) is:

4. The method for resisting water flow disturbance of underwater robots for submarine cable laying based on Gaussian processes according to claim 1, characterized in that, In step S4, the optimal control input u of the underwater robot at the current time k is... * (k) is: Where u d (k) is the control input before compensation, u d (k) = v(k+1) - v(k), where v(k) is the current speed of the underwater robot at time k; The vector τ formed by the thrust and torque inputs of the underwater robot at the current time k is: τ=u * (k)+M -1 C(v(k))v(k)+M -1 D(v(k))v(k)+M -1 g(η(k)) Where M is the inertia matrix caused by the rigid body and the added mass; C(v(k)) is the Coriolis force matrix; D(v(k)) is the fluid damping matrix; and g(η(k)) is the restoring force vector generated by gravity and buoyancy.

5. A system for resisting water flow disturbance in an underwater robot for submarine cable laying based on a Gaussian process, characterized in that, include: The module for establishing a probabilistic model of a Gaussian process with water flow disturbance (1) is used to establish a probabilistic model of a Gaussian process with water flow disturbance. Where x(k) is the state variable of the underwater robot laying the submarine cable at time k under the interference of water flow, n is the dimension of x(k), e(x(k)) is the interference error between the actual state and the expected state of the underwater robot laying the submarine cable at time k under the interference of water flow, e(x(k))=f(x(k))+ε, f(x(k)) is the constant current component in the water flow interference, and its Gaussian process probability function is: ε represents the random component in the water flow disturbance, and the model is: σ n Let be the variance of ε; μ(x(k)) be the mean function of e(x(k)) with respect to the state variable x(k), and k(x(k),x(k)) be the mean of ε. T Let covariance function be the function of water flow disturbance. Let μ represent a Gaussian process. m (x(k)) is the m-th component of μ(x(k)), k m (x(k),x(k) T ) is k(x(k),x(k) T The m-th component, where m is an integer in the interval [1,n]; Training set building module (2) is used to collect N data from the previous k time step. D The underwater robot's state information X and error information Y at each moment are used to construct a training set; x(ki) represents the state of the underwater robot at time k before the current time, and e(x(ki)) represents the interference error between the actual state and the expected state of the underwater robot at time k before the current time; i = 1, 2, ..., N D ; The probabilistic model of the Gaussian process of water flow disturbance established in S1 is trained using the training set, and the mean μ of the training set error information Y with respect to the state information X is obtained. D (x(k)); The water flow disturbance estimation module (3) is used to obtain the actual state x of the underwater robot at the current moment. * (k), the mean value μ(x) of the estimated water flow disturbance is obtained by Gaussian process regression. * (k)); The water flow disturbance compensation module (4) is used to calculate the optimal control input u of the underwater robot at the current time k based on the mean of the water flow disturbance estimate. * (k); according to u * (k) Calculate the vector τ consisting of the thrust and torque inputs of the underwater robot at the current time k.

6. The underwater robot anti-current disturbance system for submarine cable laying based on Gaussian process according to claim 5, characterized in that, The state variable x(k) of the underwater robot laying submarine cable at time k under the interference of water flow is an n-dimensional vector composed of the underwater robot's pose η(k) and movement velocity v(k) at time k, x(k) = [η(k) v(k)] T ; in px, py, and pz represent the longitudinal, lateral, and vertical displacements of the underwater robot, respectively. θ and ψ represent the roll angle, pitch angle, and yaw angle, respectively; v(k) = [u,v,w,p,q,r], where u,v,w represent the longitudinal movement speed, lateral movement speed, and vertical movement speed, respectively, and p,q,r represent the roll rotation speed, pitch rotation speed, and yaw rotation speed, respectively.

7. The anti-current disturbance system for underwater robot cable laying based on Gaussian process as described in claim 5, wherein the mean value of the current disturbance estimate in the current disturbance estimation module (3) is μ(x * The calculation steps for (k) are as follows: S31. Calculate the estimated value of water flow disturbance e(x) * The mean of each component of (k) and the mean μ of the m-th component. m (x * (k) is: Where K m (x * (k),X) represents the current actual state of the underwater robot at the current moment. * (k) is the m-th component of the covariance matrix of the state information X in the training set, K m (X,X) is the m-th component of the covariance matrix of the state information X in the training set. For N D ×N D The identity matrix; For the m-th column of the training set error information Y, The mean μ of the training set error information Y with respect to the state information X D The m-th column of (x(k)); S32, Mean value of estimated water flow disturbance μ(x) * (k) is:

8. The anti-current disturbance system for underwater robot laying submarine cables based on Gaussian process as described in claim 5, wherein the optimal control input u of the underwater robot at the current time k in the current current disturbance compensation module (4) is... * (k) is: Where u d (k) is the control input before compensation, u d (k) = v(k+1) - v(k), where v(k) is the current speed of the underwater robot at time k; The vector τ formed by the thrust and torque inputs of the underwater robot at the current time k is: τ=u * (k)+M -1 C(v(k))v(k)+M -1 D(v(k))v(k)+M -1 g(η(k)) Where M is the inertia matrix caused by the rigid body and the added mass; C(v(k)) is the Coriolis force matrix; D(v(k)) is the fluid damping matrix; and g(η(k)) is the restoring force vector generated by gravity and buoyancy.

9. A computer storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the underwater robot anti-water flow disturbance method for laying submarine cables according to any one of claims 1 to 4.

10. A device for resisting water flow disturbance in an underwater robot for laying submarine cables, characterized in that, include: A memory on which computer programs are stored; A processor is configured to execute the computer program in the memory to implement the steps of the method for resisting water flow disturbance of an underwater robot for laying submarine cables according to any one of claims 1 to 4.

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