Underwater robot hovering dynamic positioning control method, program, equipment and storage medium for subsea pipeline monitoring

Abstract

The invention belongs to the technical field of underwater robots, and particularly relates to an underwater robot hovering dynamic positioning control method for subsea pipeline monitoring, a program, equipment and a storage medium. On the basis of a finite time control theory, the uncertainty of an unmanned autonomous underwater robot model and the possibility that the unmanned autonomous underwater robot model is subjected to different types of time-varying disturbance in water areas with different depths are considered, and a finite time expansion state observer and a self-adaptive non-singular fast terminal sliding mode controller are designed. In the control process, the pose, the speed and the lumped disturbance value are adaptively updated through the pose estimation error and then substituted into the controller for compensation, the robustness of the system is improved, control force and torque are output according to the adaptive non-singular fast terminal sliding mode controller, the precision and the speed of pose error convergence are improved, and the robustness of the system is improved. The negative influence of buffeting is effectively suppressed, and the stability of the unmanned autonomous underwater robot in the subsea pipeline monitoring process is improved.

Description

Technical Field

[0001] This invention belongs to the field of underwater robot technology, specifically relating to a hovering dynamic positioning control method, program, equipment, and storage medium for underwater robots used in subsea pipeline monitoring. Background Technology

[0002] As land resources become increasingly depleted, the relatively underdeveloped ocean is receiving more and more attention. Covering 71% of the Earth's surface, the ocean's volume far exceeds that of land, holding immense energy potential. In this complex development environment, subsea pipelines, as critical infrastructure connecting wellheads to offshore platforms or onshore terminals, are crucial for ensuring operational safety and mitigating ecological risks due to their structural integrity.

[0003] Currently, in shallow water areas (depths less than 200 meters), pipeline inspection primarily relies on tethered remotely operated underwater vehicles (MAVs) deployed on multi-functional support vessels. This method is technologically mature, enabling real-time monitoring of pipeline conditions, and has become an industry standard. However, in deep-water environments (depths exceeding 200 meters), traditional underwater operations face significant challenges: the umbilical cable is prone to entanglement with underwater operating systems, wellheads, and other subsea facilities, posing a serious risk of cross-interference. Furthermore, deep-water operations are costly, heavily reliant on dedicated MSV support, leading to a substantial increase in manpower and logistical expenditures.

[0004] In contrast, autonomous underwater vehicles (AUVs), with their tetherless operation, long endurance, high degree of autonomy, and excellent maneuverability, are gradually becoming ideal tools for deep-water pipeline inspection. However, the laying process of subsea pipelines involves multiple complex procedures such as welding, visual inspection, and anti-corrosion coating, with an average daily laying speed of only 3 to 6 kilometers. For most of the time, the pipeline remains stationary, only shifting during ship movement and pipe laying. To ensure high-precision monitoring of subsea pipelines, AUVs need to maintain their position accurately at extremely low or even zero forward speeds, placing extremely high demands on the control system. Therefore, it is necessary to develop a hovering dynamic positioning control algorithm suitable for pipeline monitoring tasks, enabling autonomous underwater vehicles to effectively cope with environmental disturbances such as currents and waves in both deep and shallow water environments, achieving high-precision position-keeping capabilities. Summary of the Invention

[0005] The purpose of this invention is to solve the hovering dynamic positioning problem of an unmanned autonomous underwater robot used for subsea pipeline monitoring under random disturbances during the laying of subsea pipelines in different waters, and to provide a hovering dynamic positioning control method, program, device and storage medium for subsea pipeline monitoring.

[0006] A hovering dynamic positioning control method for an underwater robot used for subsea pipeline monitoring includes the following steps:

[0007] Obtain the pose and velocity information of the underwater robot at the current control moment;

[0008] Based on the pose estimate output by the finite-time extended state observer at the previous control moment, determine the pose estimation error;

[0009] The pose estimation error is input into the finite-time extended state observer to calculate the third-order observation state. The third-order observation state is integrated to obtain the perturbation observation value.

[0010] Obtain the desired pose of the underwater robot at the next control moment and determine the desired pose error;

[0011] The desired pose error and disturbance observations are input into the adaptive non-singular fast terminal sliding mode controller. The sliding surface is calculated based on the desired pose error and its derivative. The adaptive control gain is calculated based on the sliding surface, and then the control law is calculated.

[0012] The control law is input to the finite-time extended state observer. The second-order observation state is calculated based on the disturbance observation, pose estimation error, and control law. The velocity observation is obtained by integrating the second-order observation state. The first-order observation state is calculated based on the velocity observation and pose estimation error. The pose estimation of the underwater robot at the next control moment is obtained by integrating the first-order observation state.

[0013] The underwater robot executes the control force and torque corresponding to the control rate until the next control moment.

[0014] Furthermore, the process of acquiring the pose information of the underwater robot at the current control moment... and speed information ;

[0015] Pose estimation based on the output of the finite-time extended state observer at the previous control time. Determine the pose estimation error:

[0016]

[0017] Obtain the desired pose of the underwater robot at the next control moment. Determine the desired pose error:

[0018]

[0019] Furthermore, the pose estimation error Input the data into the finite-time extended state observer to calculate the third-order observation state:

[0020]

[0021] in, This is the gain vector of the finite-time extended state observer; For the parameters of the finite-time extended state observer; for the vector , ;

[0022] For the third-order observation state Integrate to obtain the perturbation observation. .

[0023] Furthermore, the step based on the desired pose error and its derivative Calculate the sliding surface :

[0024]

[0025] in, and For the parameter vector of the adaptive nonsingular fast terminal sliding mode controller; , and All are positive odd numbers, and .

[0026] Furthermore, the method based on the sliding surface Calculate adaptive control gain :

[0027]

[0028] in, The parameters for controlling the adaptive gain law;

[0029] right Integrate to obtain the adaptive control gain. .

[0030] Furthermore, the control rate The calculation method is as follows:

[0031]

[0032] in, For continuous control rate, To switch control rates;

[0033]

[0034] in, This is the model parameter vector for the underwater robot; and For the parameter vector of the adaptive nonsingular fast terminal sliding mode controller; This is the rotation matrix of the underwater robot.

[0035] Furthermore, the observation based on the disturbance Pose estimation error and control rate Calculate the second-order observation state :

[0036]

[0037] For the second-order observation state Integrate to obtain the velocity observation value. ;

[0038] Based on velocity observations With pose estimation error Calculate the first-order observation state :

[0039]

[0040] For the first-order observation state Integrating, we obtain the pose estimate of the underwater robot at the next control moment. ;

[0041] in, and This is the gain vector of the finite-time extended state observer.

[0042] A computer device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described underwater robot hovering dynamic positioning control method for monitoring subsea pipelines.

[0043] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described underwater robot hovering dynamic positioning control method for monitoring subsea pipelines.

[0044] A computer program product includes computer instructions that, when executed by a processor, implement the steps of the above-described underwater robot hovering dynamic positioning control method for monitoring subsea pipelines.

[0045] The beneficial effects of this invention are as follows:

[0046] This invention addresses the uncertainties in the model of unmanned autonomous underwater vehicles (AUVs) and the potential for various time-varying disturbances at different depths. It establishes a kinematic and dynamic model of the AUV and rewrites it as a mathematical model considering model uncertainties and ocean current disturbances. Based on finite-time control theory, a finite-time extended state observer and an adaptive non-singular fast terminal sliding mode controller are designed. During the loop of the motion control algorithm, the pose, velocity, and lumped disturbance values ​​are adaptively updated based on the pose estimation error, and then fed into the controller for compensation, improving the system's robustness. Furthermore, the adaptive non-singular fast terminal sliding mode controller outputs control force and torque, improving the accuracy and speed of pose error convergence, effectively suppressing the negative impact of chattering, and enhancing the stability of the AUV during subsea pipeline monitoring.

[0047] This invention proves the stability of the finite-time extended state observer and the adaptive non-singular fast terminal sliding mode controller using Lyapunov theory. It also proves that both converge in finite time based on finite-time theory. Simulation comparison experiments under different types of perturbations demonstrate the superiority and effectiveness of the proposed method, which can support unmanned autonomous underwater robots to complete subsea pipeline monitoring tasks in different water environments. Attached Figure Description

[0048] Figure 1 This is the overall control flowchart of the present invention.

[0049] Figure 2 The diagram shows the structure of the finite-time extended state observer designed for this invention.

[0050] Figure 3 The diagram shows the structure of the adaptive non-singular fast terminal sliding mode controller designed for this invention.

[0051] Figure 4 This is a three-dimensional trajectory diagram of an underwater robot under shallow water disturbance in an embodiment of the present invention.

[0052] Figure 5 This is a diagram showing the X-direction error of an underwater robot under shallow water disturbance in an embodiment of the present invention.

[0053] Figure 6 This is a diagram showing the Y-direction error of an underwater robot under shallow water disturbance in an embodiment of the present invention.

[0054] Figure 7 This is a diagram showing the Z-direction error of an underwater robot under shallow water disturbance in an embodiment of the present invention.

[0055] Figure 8 An underwater robot under shallow water disturbance in an embodiment of the present invention Orientation error diagram.

[0056] Figure 9 This is a three-dimensional trajectory diagram of an underwater robot under deep-water disturbance in an embodiment of the present invention.

[0057] Figure 10 This is a diagram showing the X-direction error of an underwater robot under deep-water disturbance in an embodiment of the present invention.

[0058] Figure 11 This is a diagram showing the Y-direction error of an underwater robot under deep-water disturbance in an embodiment of the present invention.

[0059] Figure 12 This is a diagram showing the Z-direction error of an underwater robot under deep-water disturbance in an embodiment of the present invention.

[0060] Figure 13 An underwater robot under deep-water disturbance in an embodiment of the present invention Orientation error diagram. Detailed Implementation

[0061] The present invention will now be further described with reference to the accompanying drawings.

[0062] The basic working process of this invention is as follows: The unmanned autonomous underwater vehicle (AUV) dives to the vicinity of the subsea pipeline, calculates the pose of the subsea pipeline relative to the AUV using a camera and a graphics processing computer, and calculates the desired position for dynamic positioning of the AUV based on prior information. The subsea pipeline monitoring hovering dynamic positioning program is then initiated. The position error is obtained based on the desired position and the current position. The error is input to the dynamic positioning motion control algorithm, which calculates the desired rotational speed of the thruster and sends it to the thruster. This process continues until the monitoring task ends.

[0063] This invention utilizes a finite-time extended state observer to monitor the lumped disturbances comprised of model uncertainties and time-varying ocean current disturbances, and incorporates these observations into the controller for online compensation. Simultaneously, an adaptive non-singular fast terminal sliding mode controller is designed, achieving rapid and high-precision convergence of control errors, and the closed-loop stability of the system is proven using Lyapunov theory. Finally, simulation experiments verify the effectiveness and superiority of the proposed control algorithm. This invention solves the problem of hovering and positioning control for unmanned autonomous underwater vehicles observing subsea pipelines under different water depth conditions.

[0064] The fully driven, unmanned, autonomous underwater robot model used in this invention is described as follows:

[0065]

[0066] in, This indicates the position and attitude of the unmanned autonomous underwater robot. for The first derivative with respect to time, For velocity and angular velocity, satisfy Represents the rotation matrix. The Coriolis force matrix, Represents the damping matrix. For the quality matrix, For restoring force and torque, It is a time-varying perturbation.

[0067] Introducing model uncertainty, the model can be rewritten as:

[0068]

[0069] Furthermore, the following definition exists:

[0070]

[0071]

[0072]

[0073] in, , , Defined as the uncertainty of model parameters, This is a lumped disturbance.

[0074] Therefore, the fully driven unmanned autonomous underwater robot model adopted can be rewritten in the following form:

[0075]

[0076] For a finite-time extended state observer, the observation error is defined as:

[0077]

[0078] The errors of the three observations in the observer can be expressed as:

[0079]

[0080] Design Lyapunov functions :

[0081]

[0082] in, Its derivative is:

[0083]

[0084] make Therefore, there is ,as well as:

[0085]

[0086] right Differentiation yields:

[0087]

[0088] If Let be the Herwitz matrix, then we have:

[0089]

[0090] therefore, have:

[0091]

[0092] in, , .

[0093] If there is and Then we have:

[0094]

[0095] According to finite-time control theory, the error of the finite-time extended state observer will converge to:

[0096]

[0097] The convergence time is:

[0098]

[0099] For an adaptive nonsingular fast terminal sliding mode controller, the derivative with respect to the sliding surface is:

[0100]

[0101] We can obtain:

[0102]

[0103] in, For adaptive control of the gain, it is expressed as follows:

[0104]

[0105] Design Lyapunov functions And differentiate it:

[0106]

[0107] Considering the convergence performance of the finite-time extended state observer, It has been proven to be bounded, therefore there exists a Make Therefore, it is established that:

[0108]

[0109] in, .

[0110] If it makes and Rewrite the above formula as:

[0111]

[0112] According to the finite-time control theory, the sliding surface will converge to... Within this domain, the convergence time is:

[0113]

[0114] Thus, the design of the hovering dynamic positioning control method for unmanned autonomous underwater robots monitoring subsea pipelines under various water depth conditions has been completed.

[0115] Based on the above derivation, the present invention provides a hovering dynamic positioning control method for an underwater robot used for subsea pipeline monitoring, comprising the following steps:

[0116] Step 1: During the underwater robot's mission, the current control moment is obtained, i.e. pose information of underwater robots in real time and speed information ;

[0117]

[0118]

[0119] for The three-dimensional position of the underwater robot at all times; for The three-dimensional attitude angles of the underwater robot at all times; for The three-dimensional velocity of the underwater robot at any given time; for The three-dimensional angular velocity of the underwater robot at any given time;

[0120] Then determine the current Rotation matrix of underwater robot ;

[0121]

[0122] Step 2: Based on the previous control time, i.e. Pose estimation from the output of a time-finite-time extended state observer Determine the pose estimation error ;

[0123] Step 3: Convert pose estimation error Input to the finite-time extended state observer to calculate the third-order observation state. ;

[0124]

[0125] in, Let be the gain vector of the finite-time extended state observer, which is a 6-dimensional column vector with all elements greater than 0;

[0126] ,satisfy

[0127] in, For vectors All elements in; For the parameters of the finite-time extended state observer;

[0128] For the third-order observation state Integrate to obtain the perturbation observation. ;

[0129]

[0130] Step 4: Obtain the underwater robot's next control moment, i.e. Expected pose at time Determine the desired pose error ;

[0131] Step 5: Calculate the desired pose error With disturbance observations The input is fed into an adaptive non-singular fast terminal sliding mode controller to calculate the control law. ;

[0132] Step 5.1: Based on the desired pose error and its derivative Calculate the sliding surface ;

[0133]

[0134] in, and The parameter vectors for the adaptive nonsingular fast terminal sliding mode controller are all 6-dimensional column vectors, with all elements greater than 0. , and All are positive odd numbers, and ; for The first derivative, i.e. ;

[0135] Step 5.2: Based on the sliding surface Calculate adaptive control gain ;

[0136]

[0137] in, The parameters for controlling the adaptive gain law;

[0138] right Integrate to obtain the adaptive control gain. ;

[0139]

[0140] Step 5.3: Calculate the control rate ;

[0141]

[0142] in, For continuous control rate, To switch control rates;

[0143]

[0144] in, This is the model parameter vector for the underwater robot, which is a 6-dimensional column vector. and The parameter vectors for the adaptive nonsingular fast terminal sliding mode controller are all 6-dimensional column vectors, with all elements greater than 0. for The first derivative, i.e. ; for The second derivative, i.e. , ;

[0145] The obtained control rate That is, to obtain the three-dimensional control force of the underwater robot. With torque ;

[0146] Step 6: Control rate Input the values ​​into the finite-time extended state observer to calculate the pose estimate of the underwater robot at the next control time step. ;

[0147] Step 6.1: Based on the disturbance observations Pose estimation error and control rate Calculate the second-order observation state :

[0148]

[0149] For the second-order observation state Integrate to obtain the velocity observation value. ;

[0150]

[0151] Step 6.2: Based on the velocity observations With pose estimation error Calculate the first-order observation state :

[0152]

[0153] Integral over the first-order observed state This yields the pose estimate of the underwater robot at the next control moment. ;

[0154]

[0155] in, and , where is the gain vector of the finite-time extended state observer, which is a 6-dimensional column vector and all elements are greater than 0;

[0156] Step 7: The underwater robot starts from the current position. Execution control rate at all times To the next control moment If the task is not completed, return to step 1.

[0157] After the mission is completed, the unmanned autonomous underwater robot returns to port or floats to the surface to await recovery.

[0158] Example 1:

[0159] To demonstrate the effectiveness of this invention, two sets of simulation experiments were conducted on the hovering dynamic positioning control method for unmanned autonomous underwater robots, verifying the method under shallow water disturbance and deep water disturbance respectively. In each set of simulations, the method was compared with multiple other methods to verify the superior performance of this invention.

[0160] In this simulation experiment, the present invention, referred to as the ESOFTSMC (Non-Singular Fast Ending Sliding Mode Controller Based on Finite-Time Extended State Observer) controller, will be compared and verified with the NFTSMC (Non-Singular Fast Ending Sliding Mode Controller), SMC (Sliding Mode Controller), and PID (Proportional Integral Derivative) controller to determine the initial position of the unmanned autonomous underwater robot. Initial heading angle Expected position The geodetic coordinate system adopts the northeast-northeast geodetic coordinate system, and the body coordinate system takes the front, right, and bottom sides of the unmanned autonomous underwater robot as positive directions.

[0161] (1) Shallow water disturbance scenario

[0162] The expression for shallow water current disturbance is as follows:

[0163]

[0164] in, For Pierson-Moskowitz (PM) spectrum, , It is the acceleration due to gravity. , For the discretized range of the frequency spectrum, The meeting angular frequency, For the initial random phase, The number of waves.

[0165] The results of the simulation experiment are as follows Figure 4 - Figure 8 As shown in Table 1, all the methods in the simulation can bring the unmanned autonomous underwater vehicle (UUV) closer to the desired position, but the proposed method converges significantly faster, reaching the vicinity of the desired position around 40 seconds. Furthermore, Table 1 shows that during the convergence phase of the control error (after 200 seconds), the proposed method exhibits smaller control error and higher convergence accuracy. The average horizontal positioning error is only 61.5% of NFTSMC, 15.3% of SMC, and 13.3% of PID. The average depth positioning error is 55.8% of NFTSMC, 21.1% of SMC, and 11.9% of PID, demonstrating the superior steady-state performance of this invention.

[0166] Table 1. Positioning error analysis after 200s in shallow water environment

[0167]

[0168] (2) Deep water disturbance scenario

[0169] The expression for deep-water current disturbance is as follows:

[0170]

[0171] in, , In geodetic coordinate system , The amplitude of the directional disturbance.

[0172] As can be seen from the expression for the disturbance, deep-water disturbances have a much smaller impact on unmanned autonomous underwater vehicles compared to shallow-water disturbances. Simulation results are as follows... Figure 9 - Figure 13 As shown. By Figure 10 - Figure 13 As can be seen, even under deep-water disturbance, the proposed method still achieves the highest accuracy and convergence speed. After 200 s, the average horizontal tracking error is only 0.006 m, far lower than NFTSMC (0.016 m), SMC (0.035 m), and PID (0.077 m). In the depth direction, the average tracking error of the proposed method is only 0.004 m, which is only 33.3% of NFTSMC, 10.3% of SMC, and 6.1% of PID, further demonstrating the effectiveness of the proposed method.

[0173] Table 2. Positioning error analysis after 200s in deep water environment

[0174]

[0175] In summary, this invention, based on finite-time control theory, considers the uncertainties of the unmanned autonomous underwater robot model and the different types of time-varying disturbances that may occur at different depths of water, and designs a finite-time extended state observer and an adaptive non-singular fast terminal sliding mode controller.

[0176] First, a six-dimensional, third-order finite-time extended state observer was designed to observe model uncertainties and time-varying disturbances. This observer constructs a third-order extended system model including position, velocity, and disturbance terms, and introduces a nonlinear high-gain feedback mechanism. It can synchronously reconstruct the lumped disturbance of the system by relying solely on the system output error. The third-order observed state directly represents the time derivative of the total disturbance. By integrating or directly compensating for this state, high-precision and robust online estimation of lumped disturbances (wave force, ocean current load, and model uncertainty) can be achieved, significantly improving the anti-interference capability and control accuracy of unmanned autonomous underwater vehicles in subsea pipeline monitoring tasks.

[0177] Subsequently, the observed terms are fed into the controller. The controller in this invention first designs a non-singular fast terminal sliding surface based on the position variables and their derivatives of the unmanned autonomous underwater robot, and then designs an adaptive control gain term based on the sliding surface, thereby obtaining an adaptive non-singular fast terminal sliding controller.

[0178] During each loop of the controller, the adaptive variables from the previous time step are first inherited, including position estimation, velocity estimation, disturbance estimation, and adaptive control gain. Then, the current position of the unmanned autonomous underwater vehicle (UUV) is obtained through sensors and fed into the disturbance observer to obtain the disturbance estimate for the current time step. Next, the desired pose is output from the planning layer and the difference between it and the current position of the UUV is calculated to obtain the pose error. The pose error and the disturbance observation are substituted into the adaptive non-singular fast terminal sliding mode controller to obtain the control forces and torques for each degree of freedom. Finally, the forces and torques are converted into the corresponding thruster rotation speeds and sent to the thruster control program. The above process is repeated until the subsea pipeline monitoring task ends.

[0179] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An underwater robot hover dynamic positioning control method for submarine pipeline monitoring, characterized in that: obtaining the pose and velocity information of the underwater robot at the current control time; determining the pose estimation error according to the pose estimation output by the finite-time extended state observer at the last control time; inputting the pose estimation error into the finite-time extended state observer, calculating the third-order observation state, integrating the third-order observation state to obtain the disturbance observation value; obtaining the expected pose of the underwater robot at the next control time, and determining the expected pose error; inputting the expected pose error and the disturbance observation value into the adaptive nonsingular fast terminal sliding mode controller, calculating the sliding mode surface according to the expected pose error and its derivative, calculating the adaptive control gain according to the sliding mode surface, and then calculating the control rate; inputting the control rate into the finite-time extended state observer, calculating the second-order observation state according to the disturbance observation value, the pose estimation error and the control rate, integrating the second-order observation state to obtain the velocity observation value; calculating the first-order observation state according to the velocity observation value and the pose estimation error, and integrating the first-order observation state to obtain the pose estimation of the underwater robot at the next control time; the underwater robot executes the control force and moment corresponding to the control rate until the next control time.

2. The method of hover DP control for an underwater vehicle for monitoring a subsea pipeline according to claim 1, wherein: The pose information of the underwater robot at the current control time is acquired and speed information ; a pose estimate output by a finite-time extended state observer at a previous control time determining a pose estimate error: acquiring a desired pose of the underwater robot at a next control time determining a desired pose error: 。 3. The method of hover DP control for an ROV used for monitoring a marine pipeline according to claim 2, characterized in that: the pose estimation error input to the finite-time extended state observer, a third-order observed state is calculated: wherein, is a gain vector of the finite-time extended state observer; is a parameter of the finite-time extended state observer; for the vector , ; for the third order observation state integrating, to obtain a disturbance observation .

4. The method of hover DP control for an ROV used for monitoring a marine pipeline according to claim 3, characterized in that: The desired pose error and its derivative Computing the sliding surface : wherein with is a parameter vector of the adaptive non-singular fast terminal sliding mode controller; , with are both positive odd integers, and .

5. The method of hover DP control for an ROV used for monitoring a marine pipeline according to claim 4, characterized in that: The control gain is calculated according to the sliding surface Computing adaptive control gain : wherein, are parameters for controlling the gain adaptive law; To Integrate, resulting in adaptive control gain .

6. The method of hover DP control for an underwater vehicle for monitoring a subsea pipeline of claim 5, wherein: The control rate The calculation method is: wherein is a continuous control rate, is a switching control rate; wherein, is a model parameter vector of the underwater robot; with is a parameter vector of the adaptive non-singular fast terminal sliding mode controller; is a rotation matrix of the underwater robot.

7. The method of hover DP control for an underwater vehicle for monitoring a marine pipeline according to claim 6, wherein: The disturbance observation value , pose estimation error , and control rate Calculate the second order observation state : for the second order observation state integrating to obtain a velocity observation ; According to the speed observation value With the pose estimation error Calculate the first-order observation state : for the first order observation state integrating to obtain a pose estimate of the underwater vehicle at the next control time ; wherein with is the gain vector of the finite-time extended state observer.

8. A computer device comprising a memory, a processor, and a computer program stored on the memory, wherein: The processor executes the computer program to realize the steps of the method of any one of claims 1 to 7.

9. A computer readable storage medium having stored thereon a computer program, characterized in that: The computer program is executed by the processor to realize the steps of the method of any one of claims 1 to 7.

10. A computer program product comprising computer instructions, characterized in that: The computer instructions are executed by the processor to realize the steps of the method of any one of claims 1 to 7.

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