Robust Motion Control Method and System Based on State-Dependent Riccati Equation

Abstract

The present invention belongs to the technical field of unmanned underwater vehicles, and particularly relates to a robust motion control method and system based on a state-dependent Riccati equation. The robust motion control method based on the state-dependent Riccati equation is applied to an unmanned underwater vehicle with a manipulator arm. The unmanned underwater vehicle with a manipulator arm includes a hull and an underwater manipulator arm arranged on the hull. The method includes establishing a dynamic model of the unmanned underwater vehicle with a manipulator arm based on the Lagrangian energy method; designing a fuzzy disturbance observer based on the dynamic model, and using a fuzzy logic system to compensate for the external disturbance forces received by the hull and the underwater manipulator arm of the unmanned underwater vehicle with a manipulator arm during the motion process; designing a robust controller based on the state-dependent Riccati equation based on the fuzzy disturbance estimator, and compensating for errors by adjusting the ranges of the state weight matrix and the input weight matrix and restricting the upper bounds of parameter uncertainties. The present invention realizes the robust control of the unmanned underwater vehicle with a manipulator arm.

Description

Technical Field

[0001] The present invention belongs to the technical field of boom-carrying unmanned underwater vehicles, and in particular relates to a robust motion control method and system based on a state-dependent Riccati equation. Background Art

[0002] The complexity and uncertainty of the underwater environment bring many challenges to the research of boom-carrying unmanned underwater vehicles.

[0003] Unlike the land environment, the uncertainty and influence of hydrodynamics underwater make it a difficult task to achieve the autonomy and intelligence of the boom-carrying unmanned submersible.

[0004] Although there are motion control solutions for underwater robots in the prior art, these methods usually require a lot of calculations to estimate disturbances and then optimize the controller, which increases the corresponding computational burden. In addition, in the prior art, there will also be local optimal problems when combining observers and control technologies. For example, the update law of the disturbance observer is inconsistent with the parameter adjustment direction of the controller. The system will be limited to exploring the local optimal situation, making it impossible for the adaptive update of the system to promote the convergence of the two.

[0005] Therefore, the problem of the difficulty in achieving robust control of the boom-carrying unmanned submersible in a water disturbance environment and under the conditions of internal parameter uncertainty needs to be solved urgently. Summary of the invention

[0006] In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a robust motion control method and system based on the state-dependent Riccati equation, so as to realize robust control of the boom-carrying unmanned underwater vehicle.

[0007] To achieve the above purpose, the present invention adopts the following technical solution.

[0008] A first aspect of the present invention provides a robust motion control method based on a state-dependent Riccati equation, which is applied to an arm-carrying unmanned submersible, wherein the arm-carrying unmanned submersible includes a hull and an underwater mechanical arm disposed on the hull, including:

[0009] A dynamic model of the arm-carrying unmanned underwater vehicle is established based on the Lagrangian energy method;

[0010] A fuzzy disturbance observer is designed based on the dynamic model, and a fuzzy logic system is used to compensate for the external disturbance force on the hull and the underwater mechanical arm of the arm-carrying unmanned underwater vehicle during movement;

[0011] A robust controller based on the state-dependent Riccati equation is designed based on the fuzzy disturbance estimator, and the error caused by parameter uncertainty is effectively compensated by adjusting the state weight matrix, the range of the input weight matrix and limiting the upper bound of parameter uncertainty.

[0012] As an alternative implementation, the dynamic model of the carrier arm unmanned submersible established based on the Lagrangian energy method is expressed by the following formula:

[0013] ;

[0014] where, , is the position vector and Euler angle vector of the hull; x , y , z are the position components of the carrier arm unmanned submersible in the longitudinal, lateral, and vertical directions respectively; are the attitude components of the carrier arm unmanned submersible in the roll, pitch, and yaw directions respectively; is the angle vector of the two-degree-of-freedom articulated robotic arm, and are the corresponding speed and acceleration of the carrier arm unmanned submersible respectively, is the inertia matrix; is the Coriolis force and centripetal force matrix; is the water resistance matrix; is the restoring force matrix; is the hull-hand coupling matrix; is the environmental disturbance force matrix; u is the driving force matrix.

[0015] As an alternative implementation, the fuzzy disturbance observer designed based on the dynamic model is expressed by the following formula:

[0016] ;

[0017] where, L >0, L is the observer gain matrix selected by the designer, and are the estimated values of the observer parameters, is the estimated value of the external disturbance;

[0018] Define as the observation error of the fuzzy disturbance observer, and define and as the parameter error of the fuzzy disturbance observer;

[0019] According to the approximate discrete-time linear model, it is expressed by the following formula:

[0020] ;

[0021] where, and Prepare the parameter matrix under the carrier arm unmanned submersible for suboptimal control, N is the weighted vector matrix corresponding to the disturbance, is the set disturbance value of the fuzzy disturbance observer;

[0022] Therefore, the dynamic equation of the fuzzy disturbance observer error is expressed as follows:

[0023] .

[0024] As an alternative implementation, the use of the fuzzy logic system to compensate for the external disturbance forces on the hull and the underwater manipulator of the carrier arm unmanned submersible during movement includes:

[0025] Adjust the observer parameters through the adaptive law, and the adaptive law is expressed as follows:

[0026] ;

[0027] where the adjustment parameters and are positive constant matrices, and .

[0028] As an alternative implementation, the equivalent state-dependent coefficient form of the system compensated by the fuzzy disturbance observer is expressed as follows:

[0029] ;

[0030] where, u r is the nominal controller that does not consider external disturbances and parameter uncertainties, that is, the control input, u s is the compensation input for dealing with external disturbances.

[0031] As an alternative implementation, the robust controller based on the state-dependent Riccati equation designed based on the fuzzy disturbance estimator is expressed as follows:

[0032] ;

[0033] where, Q is the symmetric positive definite semi-definite weighted matrix of the state, R is the symmetric positive definite weighted matrix of the input;

[0034] Set the control input of the reference system to:

[0035] ;

[0036] where, p (x ) is a symmetric positive definite matrix, and its solution system is defined as:

[0037] .

[0038] As an alternative implementation, the reference form of the established uncertainty system is expressed by the following formula:

[0039] ;

[0040] where, x r is the state vector, is the nominal input;

[0041] According to the actual system and the reference form, the form of the closed-loop error can be obtained and expressed by the following formula:

[0042] ;

[0043] where, is defined as: .

[0044] As an alternative implementation, the control input of the reference system is set as:

[0045] ;

[0046] where, p ( x ) is a symmetric positive definite matrix, and its solution system is defined as:

[0047] .

[0048] The second aspect of the present invention provides a robust motion control system based on the state-dependent Riccati equation, which is applied to an underwater vehicle with a manipulator arm. The underwater vehicle with a manipulator arm includes a hull and an underwater manipulator arm arranged on the hull. This system is applied to the robust motion control method based on the state-dependent Riccati equation described in the first aspect of the present invention.

[0049] The third aspect of the present invention provides a robust motion control system based on the state-dependent Riccati equation, which is applied to an underwater vehicle with a manipulator arm. The underwater vehicle with a manipulator arm includes a hull and an underwater manipulator arm arranged on the hull, and includes:

[0050] The first unit is at least used to establish the dynamic model of the underwater vehicle with a manipulator arm based on the Lagrangian energy method;

[0051] The second unit is at least used to design a fuzzy disturbance estimator based on the dynamic model, and use a fuzzy logic system to compensate for the external disturbance forces on the hull and the underwater manipulator of the vehicle-mounted arm unmanned submersible during the movement process;

[0052] The third unit is at least used to design a robust controller based on the state-dependent Riccati equation based on the fuzzy disturbance estimator, and effectively compensate for the errors caused by parameter uncertainty by adjusting the ranges of the state weight matrix, the input weight matrix, and the upper bound of restricting parameter uncertainty.

[0053] In summary, compared with the prior art, the present invention can achieve robust control of the vehicle-mounted arm unmanned submersible considering system model uncertainty and water flow disturbance, and can also be widely applied to the system design of the vehicle-mounted arm unmanned submersible, providing new ideas and methods for the design and application of underwater manipulators and robot systems, and promoting the further development of underwater operation technology. Description of the Drawings

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present application. For those skilled in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0055] Figure 1 It is a schematic flowchart of a robust motion control method based on the state-dependent Riccati equation according to an embodiment of the present invention.

[0056] Figure 2 It is a control block diagram of a robust motion control method based on the state-dependent Riccati equation according to an embodiment of the present invention.

[0057] Figure 3 It is a simulation effect diagram of the hull path tracking applying a robust controller according to an embodiment of the present invention, where: Figure 3 in the a is a simulation effect diagram of the position tracking of the hull path in the x direction applying a robust controller according to an embodiment of the present invention; Figure 3 in the b is a simulation effect diagram of the position tracking of the hull path in the roll direction applying a robust controller according to an embodiment of the present invention; Figure 3 in the c is a simulation effect diagram of the position tracking of the hull path in the y direction applying a robust controller according to an embodiment of the present invention; Figure 3 in the dis the simulation effect diagram of the position tracking in the pitch direction of the hull path applying the robust controller according to the embodiment of the present invention; Figure 3 in e is the simulation effect diagram of the position tracking in the hull path z in the pitch direction applying the robust controller according to the embodiment of the present invention; Figure 3 in f is the simulation effect diagram of the position tracking in the yaw direction of the hull path applying the robust controller according to the embodiment of the present invention.

[0058] Figure 4 is the pose result diagram of the end effector applying the robust controller according to the embodiment of the present invention, wherein: Figure 4 in a is the simulation effect diagram of the position tracking in the end effector x in the direction applying the robust controller according to the embodiment of the present invention; Figure 4 in b is the simulation effect diagram of the position tracking in the roll direction of the end effector applying the robust controller according to the embodiment of the present invention; Figure 4 in c is the simulation effect diagram of the position tracking in the end effector y in the direction applying the robust controller according to the embodiment of the present invention; Figure 4 in d is the simulation result diagram of the position tracking in the pitch direction of the end effector applying the robust controller according to the embodiment of the present invention; Figure 4 in e is the simulation effect diagram of the position tracking in the end effector z in the direction applying the robust controller according to the embodiment of the present invention; Figure 4 in f is the simulation effect diagram of the position tracking in the yaw direction of the end effector applying the robust controller according to the embodiment of the present invention.

[0059] Figure 5 is the block diagram of the robust motion control system based on the state-dependent Riccati equation according to the embodiment of the present invention. Detailed implementation manners

[0060] Next, the technical solutions in the embodiments of the present application will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without making creative efforts belong to the scope protected by the present application. In addition, it should be understood that the specific implementation manners described herein are only used to illustrate and explain the present application, and are not used to limit the present application.

[0061] It should be noted that the description order of the following embodiments does not limit the preferred order of the embodiments of the present application. And in the following embodiments, the descriptions of each embodiment have their own emphases. For parts not detailed in a certain embodiment, reference may be made to the relevant descriptions of other embodiments.

[0062] As Figure 1 and Figure 2 shown, in the first aspect of the present invention, a robust motion control method based on a state-dependent Riccati equation is provided, which is applied to an articulated underwater vehicle (hereinafter referred to as the underwater vehicle). The underwater vehicle includes a hull and an underwater manipulator provided on the hull, and the method includes the following steps.

[0063] Step S100: Establish a dynamic model of the articulated underwater vehicle based on the Lagrangian energy method.

[0064] Specifically, in step S100, considering the dynamic effects of external disturbances and internal parameter uncertainties on the articulated underwater vehicle, the dynamic model of the articulated underwater vehicle established based on the Lagrangian energy method is represented by the following formula:

[0065] ;

[0066] where represents the position vector of the underwater vehicle, is the position vector and Euler angle vector of the hull, x , y , z are respectively the position components of the hull in the longitudinal, lateral, and vertical directions; are respectively the attitude components of the hull in the roll, pitch, and yaw directions, is the angle vector of the two-degree-of-freedom joint manipulator; and are respectively the corresponding speed and acceleration of the underwater vehicle, is the inertia matrix, is the Coriolis force and centripetal force matrix; is the water resistance matrix; is the restoring force matrix; is the hull-manipulator coupling matrix; is the environmental disturbance force matrix, where includes model uncertainty and external disturbance ; u is the driving force matrix.

[0067] In an embodiment of the present invention, in order to define the model uncertainty of the system and facilitate control design, the dynamic model uncertainty can be represented by the following formula:

[0068] ;

[0069] wherein, is the true value, is the estimated value of the established dynamic model, is the dynamic error caused by model uncertainty; Specifically, it is the true value of the established Coriolis force and centripetal force matrix, is the estimated value of the established Coriolis force and centripetal force matrix, is the dynamic error of the established Coriolis force and centripetal force matrix; Specifically, it is the true value of the water resistance matrix, is the estimated value of the water resistance matrix, is the dynamic error of the water resistance matrix, and so on.

[0070] Furthermore, the dynamic model considering external disturbances and model uncertainty is represented by the following formula:

[0071] ;

[0072] wherein, the model uncertainty of the system .

[0073] Step S200: Design a fuzzy disturbance observer based on the dynamic model, and use a fuzzy logic system to compensate for the external disturbance forces acting on the hull and the underwater manipulator of the vehicle-mounted unmanned submersible during movement.

[0074] Specifically, in step S200, the fuzzy disturbance observer designed based on the dynamic model is represented by the following formula:

[0075] ;

[0076] wherein, L >0, L is the observer gain matrix selected by the designer, and are the estimated values of the observer parameters, is the estimated value of the external disturbance, is the basis function of the fuzzy logic system.

[0077] Furthermore, is defined as the observation error of the fuzzy disturbance observer, and and are defined as the parameter errors of the fuzzy disturbance observer;

[0078] According to the approximate discrete-time linear model, it is represented by the following formula:

[0079] ;

[0080] Among them, and are respectively the parameter matrices of the vehicle-mounted unmanned submersible system prepared for implementing suboptimal control, N is the weighted vector matrix corresponding to the disturbance, is the set disturbance estimation value of the fuzzy disturbance observer.

[0081] Therefore, the dynamic equation of the fuzzy disturbance observer error is expressed by the following formula:

[0082] .

[0083] In an embodiment of the present invention, the compensation for the external disturbance forces received by the hull and the underwater manipulator of the vehicle-mounted unmanned submersible during the movement by using the fuzzy logic system includes:

[0084] Adjust the observer parameters through the adaptation law, and the adaptation law is expressed by the following formula:

[0085] ;

[0086] Among them, the adjustment parameters γ (learning rate) and β (damping coefficient) are both positive constant matrices, is the basis function of the fuzzy logic system.

[0087] Furthermore, the adaptation law must satisfy and to ensure the optimality of the observer in the ideal state.

[0088] In addition, for a specific deterministic nonlinear function, the optimal parameter is uniquely determined by the designed fuzzy logic system and satisfies = 0.

[0089] Step S300: Design a robust controller based on the state-dependent Riccati equation based on the fuzzy disturbance estimator, and effectively compensate for the error caused by parameter uncertainty by adjusting the ranges of the state weight matrix, the input weight matrix, and the upper bound of the restricted parameter uncertainty.

[0090] Specifically, in step S300, the robust controller designed based on the fuzzy disturbance estimator based on the state-dependent Riccati equation is expressed by the following formula:

[0091] ;

[0092] Among them, Q is a symmetric positive definite semi-definite weighted matrix of the state, Ris the input symmetric positive definite weighted matrix.

[0093] Furthermore, the control input of the reference system is set as:

[0094] ;

[0095] where, P(x) is a symmetric positive definite matrix, and its solution system is defined as:

[0096] .

[0097] In an embodiment of the present invention, the reference form of the established uncertain system is represented by the following formula:

[0098] ;

[0099] where, x r is the state vector, is the nominal input;

[0100] According to the actual system and the reference form, the form of the closed-loop error can be obtained and represented by the following formula:

[0101] ;

[0102] where, in order to converge the tracking error to zero, the corrective input is adopted under the approximation given by the equation. Therefore, is defined as: .

[0103] In an embodiment of the present invention, considering a nonlinear control system, a robust state-dependent Riccati controller is designed, and the external disturbance satisfies the assumption. In this case, appropriate parameters need to be selected to converge the tracking error within the desired threshold, and the parameters are defined as:

[0104] .

[0105] To better express the content to be protected by the present invention, the present invention conducts relevant simulation experiments based on MATLAB / SIMULINK, verifies the effectiveness of the proposed coordinated control method for the submersible vehicle, and the simulation duration is 40 seconds. The simulation results are as shown in Figure 3 and Figure 4 . Among them, the roll angle is the angle of the object rotating around the Z-axis, which is manifested as a "rolling" action; the pitch angle is the angle of the object rotating around the X-axis, which is manifested as a "nodding" action; the yaw angle is the angle of the object rotating around the Y-axis, which is manifested as a "shaking head" action; the red curve represents the desired trajectory, and the blue curve represents the actual trajectory.

[0106] Please continue to refer to Figure 3 , in the simulation, the robust control method of the submersible system is verified from the perspective of hull path tracking. Among them, Figure 3 in a () represents the tracking effect of the hull path x direction position, Figure 3 in b () represents the tracking effect of the hull path roll direction position, Figure 3 in c () represents the tracking effect of the hull path y direction position, Figure 3 in d () represents the tracking effect of the hull path pitch direction position, Figure 3 in e () represents the tracking effect of the hull path z direction position, Figure 3 in f () represents the tracking effect of the hull path yaw direction position.

[0107] First, input the desired trajectory of the hull system state into the simulation environment. This trajectory represents the motion path that the submersible should follow under ideal conditions. Then, through the designed robust controller, calculate the corresponding control input according to the current system state and apply it to the dynamic model of the submersible. During the simulation, the system adjusts the feedback according to the control input, and finally obtains the actual state trajectory of the submersible. By comparing with the preset desired trajectory, it is observed that the actual state trajectory of the submersible is highly consistent with the desired trajectory, and the tracking error always remains within the set allowable range. This shows that the robust controller can effectively maintain the system performance in the face of system uncertainties, external disturbances, and possible modeling errors, ensuring that the system state runs stably along the expected trajectory.

[0108] Please continue to refer to Figure 4 , in the simulation, the robust control method of the submersible system is verified from the perspective of the pose information of the end effector. Among them, Figure 4 in a () represents the end effector x direction position tracking effect, Figure 4 in b () represents the end effector roll direction position tracking effect, Figure 4 in c () represents the end effector y direction position tracking effect, Figure 4 in d () represents the end effector pitch direction position tracking effect, Figure 4 in e () represents the end effectorz Directional position tracking effect Figure 4 in f ), which represents the yaw-direction position tracking effect of the end effector.

[0109] To evaluate the trajectory tracking effectiveness of the proposed controller in the task space, in the simulation, the attitude data of the hull and the manipulator joints are converted into the position information of the end effector using the Newton-Euler equations. By comparing with the preset trajectory, it is observed that the error between the trajectory of the end effector and the desired trajectory always remains within the allowable error range, meeting the requirements of robust control.

[0110] The present invention realizes the robust control of the submersible under system parameter uncertainties and water flow disturbances by integrating a fuzzy disturbance observer and a state-dependent Riccati equation.

[0111] The second aspect of the present invention provides a robust motion control system based on a state-dependent Riccati equation, which is applied to an unmanned submersible with a manipulator arm. The unmanned submersible with a manipulator arm includes a hull and an underwater manipulator arm disposed on the hull. This system applies the robust motion control method based on the state-dependent Riccati equation described in any one of the above embodiments.

[0112] As Figure 5 shown, the third aspect of the present invention provides a robust motion control system based on a state-dependent Riccati equation, which is applied to an unmanned submersible with a manipulator arm. The unmanned submersible with a manipulator arm includes a hull and an underwater manipulator arm disposed on the hull, and includes:

[0113] A first unit, at least for establishing a dynamic model of the unmanned submersible with a manipulator arm based on the Lagrangian energy method;

[0114] A second unit, at least for designing a fuzzy disturbance estimator based on the dynamic model and compensating for the external disturbance forces acting on the hull and the underwater manipulator arm of the unmanned submersible with a manipulator arm during the motion process using a fuzzy logic system;

[0115] A third unit, at least for designing a robust controller based on a state-dependent Riccati equation based on the fuzzy disturbance estimator, and effectively compensating for the error caused by parameter uncertainties by adjusting the ranges of the state weight matrix, the input weight matrix, and the upper bound of the restricted parameter uncertainties.

[0116] Any process or method description represented in a flowchart or otherwise described herein may be understood to represent a module, segment, or portion of code including one or more executable instructions for implementing a specific logical function or process. The scope of the preferred embodiments of the present invention includes additional implementations, where functions may be performed in a substantially simultaneous manner or in a reverse order according to the functions involved, rather than in the order shown or discussed. This should be understood by those skilled in the art to which the embodiments of the present invention pertain.

[0117] The logic and / or steps represented in a flowchart or otherwise described herein, for example, may be considered a sequenced list of executable instructions for implementing a logical function, and may be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, a system including a processing module, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device.

[0118] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A robust motion control method based on the state-dependent Riccati equation, applied to an underwater vehicle with an articulated arm, the underwater vehicle with an articulated arm comprising a hull and an underwater robotic arm disposed on the hull, characterized in that, Including: Establishing a dynamic model of the carrier-arm unmanned underwater vehicle (UUV) based on the Lagrangian energy method; Designing a fuzzy disturbance observer based on the dynamic model, and compensating for the external disturbance forces acting on the hull and the underwater manipulator of the carrier-arm UUV during motion using a fuzzy logic system; Designing a robust controller based on the state-dependent Riccati equation based on the fuzzy disturbance estimator, and effectively compensating for the errors caused by parameter uncertainties by adjusting the ranges of the state weight matrix, the input weight matrix, and the upper bound of the restricted parameter uncertainties, where: The fuzzy disturbance observer designed based on the dynamic model is represented by the following formula: ； wherein, L > 0, L is the observer gain matrix selected by the designer, and are the estimated values of the observer parameters, is the estimated value of the external disturbance, is the basis function of the fuzzy logic system; Define as the observation error of the fuzzy disturbance observer, and define and as the parameter errors of the fuzzy disturbance observer; According to the approximate discrete-time linear model, it is represented by the following formula: ； Among them, and prepare the parameter matrix under the carrier arm unmanned submersible for implementing sub-optimal control, N is the weighted vector matrix corresponding to the disturbance, is the set disturbance estimation value of the fuzzy disturbance observer; Therefore, the dynamic equation of the fuzzy disturbance observer error is represented by the following formula: ； The robust controller based on the state-dependent Riccati equation designed based on the fuzzy disturbance estimator is represented by the following formula: ； Among them, Q is a symmetric positive definite semi-definite weighted matrix of the state, R is a symmetric positive definite weighted matrix of the input; Setting the control input of the reference system as: ； Among them, p ( x ) is a symmetric positive definite matrix, and its solution system is defined as: ； The reference form of the established uncertain system is represented by the following formula: ； wherein, x r is the state vector, is the nominal input; Based on the actual system and the reference form, the form of the closed-loop error can be obtained as represented by the following formula: ； Among them, is defined as: .

2. The robust motion control method based on the state-dependent Riccati equation according to claim 1, wherein The dynamic model of the carrier-arm UUV established based on the Lagrangian energy method is represented by the following formula: ； Among them, represents the position vector of the carrier arm unmanned submersible, is the position vector and Euler angle vector of the hull; x , y , z are the position components of the hull in the longitudinal, lateral, and vertical directions respectively; are the attitude components of the hull in the roll, pitch, and yaw directions respectively; is the angle vector of the two-degree-of-freedom articulated robotic arm, and are the corresponding speed and acceleration of the carrier arm unmanned submersible respectively, is the inertia matrix; is the Coriolis force and centripetal force matrix; is the water resistance matrix; is the restoring force matrix; is the hull-hand coupling matrix; is the environmental disturbance force matrix; u is the driving force matrix.

3. The robust motion control method based on the state-dependent Riccati equation according to claim 1, characterized in that The compensating for the external disturbance forces acting on the hull and the underwater manipulator of the carrier-arm UUV during motion using the fuzzy logic system includes: Adjusting the observer parameters through an adaptive law, and the adaptive law is represented by the following formula: ； Among them, the adjustment parameters and are positive definite matrices, and .

4. The robust motion control method based on the state-dependent Riccati equation according to claim 1, characterized in that The equivalent state-dependent coefficient form of the system compensated by the fuzzy disturbance observer is represented by the following formula: ； Among them, u r is the nominal controller that does not consider external disturbances and parameter uncertainties, u s is the input for handling external disturbances.

5. The robust motion control method based on the state-dependent Riccati equation according to claim 1, characterized in that Setting the control input of the reference system as: ； Among them, p ( x ) is a symmetric positive definite matrix, and its solution system is defined as: 。 6. A robust motion control system based on the state-dependent Riccati equation, applied to an underwater vehicle with a manipulator arm. The underwater vehicle with a manipulator arm includes a hull and an underwater manipulator arm disposed on the hull, and is characterized in that, This system is applied to the robust motion control method based on the state-dependent Riccati equation according to any one of claims 1-5.

7. A robust motion control system based on the state-dependent Riccati equation for the robust motion control method based on the state-dependent Riccati equation according to claim 1, applied to an articulated-arm unmanned underwater vehicle, the articulated-arm unmanned underwater vehicle comprising a hull and an underwater robotic arm provided on the hull, characterized in that, Including: A first unit, at least for establishing a dynamic model of the carrier-arm UUV based on the Lagrangian energy method; A second unit, at least for designing a fuzzy disturbance estimator based on the dynamic model, and compensating for the external disturbance forces acting on the hull and the underwater manipulator of the carrier-arm UUV during motion using a fuzzy logic system; A third unit, at least for designing a robust controller based on the state-dependent Riccati equation based on the fuzzy disturbance estimator, and effectively compensating for the errors caused by parameter uncertainties by adjusting the ranges of the state weight matrix, the input weight matrix, and the upper bound of the restricted parameter uncertainties.

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