An adaptive control method for underwater robots considering actuator failures

Abstract

This invention relates to an adaptive control method for underwater robots considering actuator failures. The method includes establishing a dynamic model of the underwater robot with actuator failures; designing an adaptive extended state observer to simultaneously estimate unmeasurable velocity and unknown external environmental disturbances while adapting to model uncertainties; designing an integral sliding mode controller based on Lyapunov stability theory; and using an adaptive gain update algorithm to estimate the upper bound of model uncertainty and the upper bound of disturbance-related parameters online, thereby achieving adaptive control of the underwater robot. This invention accurately compensates for the uncertain hydrodynamic characteristics of the underwater robot and unknown external environmental disturbances such as ocean currents and waves, offsetting the effects of model uncertainties and disturbances, while suppressing chattering in sliding mode control. It effectively solves the problem of high-precision trajectory tracking control for underwater robots in complex marine environments caused by actuator failures, unmeasurable velocity, unknown external environmental disturbances, and model uncertainties.

Description

Technical Field

[0001] This invention relates to the field of underwater robot motion control technology, and in particular to an adaptive control method for underwater robots that takes into account actuator failures. Background Technology

[0002] With the accelerated global energy transition, offshore wind power has become a core development direction for green energy, experiencing explosive growth in its industry scale. Correspondingly, the scale and number of underwater foundation structures such as pile foundations and jacket structures are also expanding rapidly. These structures need to withstand the multiple erosions of complex marine environments such as ocean currents, waves, corrosion, and biofouling over long periods, easily leading to structural damage, coating peeling, and cable wear, among other hidden dangers. This is detrimental to the long-term stable operation of wind farms and threatens the safety and operational profitability of offshore wind farms throughout their entire life cycle. Traditional manual diving inspection and ship-assisted operation modes are limited by operating depth and sea conditions, resulting in high costs, high risks, low efficiency, and insufficient inspection accuracy. They are particularly difficult to meet the needs of refined operation and maintenance in deep-sea scenarios. Therefore, reducing long-term operating costs and personnel safety risks is the core support for building a future intelligent operation and maintenance system for offshore wind power.

[0003] Underwater robots (ROVs / AUVs), with their deep-water operation capabilities, high mobility, and multi-equipment carrying capacity, have become core equipment in the intelligent underwater operation and maintenance system for offshore wind power. They can achieve full-coverage inspection and partial maintenance of underwater structures, significantly improving operation and maintenance efficiency and reducing costs and safety risks. However, in practical applications, technical bottlenecks such as autonomous navigation and positioning accuracy in complex marine environments, adaptability to strong ocean currents, low-visibility detection capabilities, endurance and payload matching, and real-time data transmission and multi-robot collaborative operation still restrict their operational accuracy and efficiency. Therefore, breakthroughs in technologies such as nonlinear control, intelligent sensing, and collaborative decision-making are needed to provide more stable and efficient technical support for the underwater operation and maintenance of offshore wind power. Realizing this vision of intelligent operation and maintenance relies on a series of core enabling technologies; among them, highly robust and adaptive motion control is fundamental and crucial. The motion control performance of the underwater robot directly determines the accuracy of its inspection path, the stability of its operating arm, and its autonomy in responding to emergencies. Existing control methods mainly include PID control, fuzzy logic control, and sliding mode control. However, these methods face several bottlenecks in practical applications: increased tracking error under actuator failure and disturbances, long recovery time after disturbances, large overshoot, limited regulation capability, and insufficient robustness. Therefore, the tracking error and system robustness under actuator failure and external disturbances still require further investigation. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides an adaptive control method for underwater robots that takes into account actuator failures. This method solves the problem of high-precision trajectory tracking control for traditional underwater robots in complex marine environments, which is caused by the coupling effect of multiple factors such as the unpredictability of some system states, the possibility of actuator failures, the presence of unknown time-varying external disturbances, and the uncertainty of model parameters.

[0005] To achieve the above technical objectives, the present invention provides the following technical solution: an adaptive control method for an underwater robot considering actuator failure, comprising the following steps: S1. Based on the kinematic principle of underwater robots, establish the nonlinear dynamic equations of underwater robots in the body coordinate system, which include actuator faults and unknown external environmental disturbances. The established nonlinear dynamic equations have coefficient matrices that include the system inertia matrix, Coriolis force and centripetal force matrix, hydrodynamic damping matrix, and the resultant force matrix of gravity and buoyancy. S2. Rewrite the established nonlinear dynamic equations, divide each coefficient matrix into a nominal part and an uncertain perturbation part, construct a composite uncertainty term in the body coordinate system, and show the separation of the uncertainty; the composite uncertainty term in the body coordinate system includes the unknown external environmental disturbance component of the underwater robot in the body coordinate system, uncertain fluid dynamics, and uncertain disturbance caused by actuator failure; S3. Transform the rewritten nonlinear dynamic equations into the geodetic coordinate system to obtain a geodetic coordinate system model of the underwater robot that simultaneously includes actuator fault terms and unknown external environmental disturbance components. S4. Based on the geodetic coordinate system model of the underwater robot, an adaptive extended state observer is designed to perform online estimation, obtain the estimated pose, estimated velocity and estimated unknown external environmental disturbance components of the underwater robot in the geodetic coordinate system, and simultaneously estimate and adaptively update the boundary parameters of the composite uncertainty. S5. Based on the online estimation results of the adaptive extended state observer, a reference trajectory is set to construct an integral sliding surface, a sliding mode control arrival law is designed, an integral sliding mode controller is formed, the total control input of the underwater robot is calculated, and the uncertainty disturbance limit parameters are estimated and adaptively updated to realize the adaptive control of the underwater robot.

[0006] Optionally, in step S1, establishing the nonlinear dynamic equations of the underwater robot in its body coordinate system, which include actuator faults and unknown external environmental disturbances, based on the kinematic principles of the underwater robot, includes: With the center of gravity of the underwater robot as the origin of the body coordinate system, a body coordinate system is established, and the nonlinear dynamic equations of the underwater robot in the body coordinate system are constructed. These equations satisfy the following form: ; in, , , , These are the system inertia matrix, Coriolis force and centripetal force matrix, hydrodynamic damping matrix, and resultant force matrix of gravity and buoyancy of the underwater robot in its body coordinate system, respectively. This represents the velocity of the underwater robot in its body coordinate system, including the linear velocity vector and the angular velocity vector. for The first time derivative of represents the acceleration of the underwater robot in the body coordinate system, including the linear acceleration vector and the angular acceleration vector; The pose of the underwater robot is represented by its position vector and attitude vector. The thrust vector of an underwater robot's thruster with actuator malfunction. and allocation matrix The generalized driving force of the underwater robot, which includes actuator faults, is defined as follows: ,in , The fault offset vector, This is the fault impact matrix. This represents the total control input for the underwater robot; This represents the unknown external environmental disturbance component of the underwater robot in its body coordinate system.

[0007] Optionally, in step S2, rewriting the established nonlinear dynamic equations and dividing its coefficient matrices into nominal and uncertain perturbation parts includes: The system inertia matrix of the underwater robot in the body coordinate system Coriolis force and centripetal force matrix Hydrodynamic damping matrix The resultant force matrix of gravity and buoyancy The nominal and uncertain perturbation parts are separated, and the established nonlinear dynamic equations are rewritten. The rewritten nonlinear dynamic equations satisfy the following form: ; in, These represent the system inertia matrices in the body coordinate system, respectively. Coriolis force and centripetal force matrix Hydrodynamic damping matrix The resultant force matrix of gravity and buoyancy The nominal value; The composite uncertainty term of an underwater robot in its body coordinate system is defined as follows: , Uncertain fluid dynamics of an underwater robot in its body coordinate system is defined as follows: , , , , Let represent the system inertia matrices of the underwater robot in its body coordinate system. Coriolis force and centripetal force matrix Hydrodynamic damping matrix The resultant force matrix of gravity and buoyancy Perturbation values; Thruster allocation matrix for underwater robots with actuator faults. With fault offset vector product term Used to quantify uncertainty disturbances caused by actuator failure.

[0008] Optionally, in step S3, the transformation of the rewritten nonlinear dynamic equations to a geodetic coordinate system to obtain a geodetic coordinate system model of the underwater robot that simultaneously includes actuator fault terms and unknown external environmental disturbance components includes: A transformation equation is constructed between the geodetic coordinate system and the body coordinate system. Based on this transformation equation, the nonlinear dynamic equation rewritten in step S2 is transformed to the geodetic coordinate system, resulting in a geodetic coordinate system model of the underwater robot. This geodetic coordinate system model satisfies the following form: ; in, , , , These represent the Coriolis force and centripetal force matrices, hydrodynamic damping matrix, resultant force matrix of gravity and buoyancy, and system inertia matrix of the underwater robot in the geodetic coordinate system, respectively. , The poses of the underwater robot in the geodetic coordinate system are respectively The first and second time derivatives represent the velocity and acceleration of the underwater robot in the geodetic coordinate system, respectively. This represents the composite uncertainty of an underwater robot in the geodetic coordinate system, including the unknown external environmental disturbance components, uncertain fluid dynamics, and uncertain disturbances caused by actuator failures in the geodetic coordinate system.

[0009] Optionally, in step S4, the adaptive extended state observer designed based on the geodetic coordinate system model of the underwater robot is used for online estimation to obtain the estimated pose, estimated velocity, and estimated unknown external environmental disturbance components of the underwater robot in the geodetic coordinate system. Simultaneously, the boundary parameters of the composite uncertainty term are estimated and adaptively updated, including: S41. Position the underwater robot in the geodetic coordinate system. and speed Construct it as a state vector; S42. The unknown external environmental disturbance components of the underwater robot in the geodetic coordinate system. The extended state is defined as the state vector that is extended, and the extended state vector is defined as the true state. Mathematically, it is represented as: ;in, , , Representing pose respectively ,speed Unknown external environmental disturbance components In reality The corresponding sub-vector in This is a transpose operation; S43, in true state An adaptive extended state observer is designed based on the geodetic coordinate system model of the underwater robot. The adaptive extended state observer satisfies the following form: ; in, To estimate the state, including the underwater robot's estimated pose, estimated velocity, and estimated unknown external environmental disturbance components in the geodetic coordinate system; for The first time derivative of represents the dynamic update rate of the adaptive extended state observer itself; The external output is estimated for the adaptive extended state observer; This represents the total control input for the underwater robot; This is the state transition matrix; The control input matrix is ​​the system inertia matrix of the underwater robot in the geodetic coordinate system. Allocation matrix for thrusters of underwater robots with actuator malfunctions Decide; This is the external output matrix, used to control the estimated external output of the adaptive extended state observer. Only the pose item is retained; A nonlinear function is represented by the following block matrix form: ,in The estimation of a nonlinear function is defined as follows: , This represents the estimated velocity of the underwater robot in the geodetic coordinate system. , They represent , The estimated value; The number of degrees of freedom of an underwater robot; , , Let represent the Coriolis force and centripetal force matrices, hydrodynamic damping matrix, and resultant force matrix of gravity and buoyancy of the underwater robot in the geodetic coordinate system, respectively. Represents a zero matrix with dimension dof×1; Represents the observer gain matrix; The scaling transformation matrix is ​​defined in the following block matrix form: ; This represents an identity matrix of dimension dof × dof. Indicates the observer bandwidth; The perturbation estimation correction term for the adaptive extended state observer is defined as: ; in, The external output error of the adaptive extended state observer is defined as: , The true external output of the adaptive extended state observer; This represents the first-order time derivative of the unknown external environmental disturbance component of the underwater robot in the geodetic coordinate system. Uncertain fluid dynamics of underwater robots in the geodetic coordinate system The auxiliary perturbation term formed by the linear combination of The boundary parameter, The bounding parameters are estimated online by the adaptive extended state observer. The estimated value is used to quantify and adaptively update the bounding parameters of the composite uncertainty term; This indicates the correction term for the protection disturbance estimate. The constant for numerical stability, ; Describes a symmetric positive definite matrix. express The inverse matrix; Describing auxiliary functions The first-order time derivative satisfies Dynamic adjustment of disturbance estimation correction term The amplitude, auxiliary function Designed for ; Calculate the Euclidean norm; Indicates the time.

[0010] Optionally, the bounding parameters are estimated online by an adaptive extended state observer. The estimated value ,pass Adaptive update, where For the estimated value The first-order time derivative, representing The rate of change; This represents the adaptive adjustment coefficient associated with the composite uncertainty term. .

[0011] Optionally, in step S5, the online estimation results based on the adaptive extended state observer are used to construct an integral sliding surface by setting a reference trajectory, designing a sliding mode control arrival law, forming an integral sliding mode controller, solving for the total control input of the underwater robot, and simultaneously estimating and adaptively updating the uncertainty disturbance limit parameters, including: S51, Set reference trajectory and calculate time. Tracking error and the first time derivative of its estimate Mathematically, it is represented as: ; in , , , These represent the estimated pose, pose reference trajectory, estimated velocity, and velocity reference trajectory of the underwater robot in the geodetic coordinate system, respectively. S52. Combining the tracking error and its estimated first-order time derivative, construct an integral sliding surface containing an error proportional term, an error integral term, and an error differential term. The constructed integral sliding surface satisfies the following form: ; in, Indicates time Integral sliding surface; These are the proportional gain matrix, integral gain matrix, and differential gain matrix, all designed as diagonal matrices. express From 0 For a certain moment within the interval Integral; S53. Based on the constructed integral sliding surface, design a sliding mode control arrival law, wherein the sliding mode control arrival law satisfies the following form: ; in, For integral sliding surface The first time derivative; , These represent the linear feedback gain matrix and the switching gain matrix, respectively, both designed as positive definite diagonal matrices; For the smooth switching vector, where Represents the hyperbolic tangent function; S54. Calculate the total control input of the underwater robot, including the equivalent control input. and switching control input ; S541, Solve for equivalent control input : ; in, , , , These represent the Coriolis force and centripetal force matrices, hydrodynamic damping matrix, resultant force matrix of gravity and buoyancy, and system inertia matrix of the underwater robot in the geodetic coordinate system, respectively. Assignment matrix for thrusters of underwater robots with actuator malfunctions; express The inverse matrix; This represents the acceleration reference trajectory of the underwater robot in the geodetic coordinate system; This represents the estimated unknown external environmental disturbance component of the underwater robot in the geodetic coordinate system; This represents the estimated velocity of the underwater robot in the geodetic coordinate system. S542, Solving Switching Control Input : ; in, express The largest eigenvalue; Uncertainty disturbance limit parameter The estimated values ​​are used to quantify and adaptively update the perturbation bound parameters. ; S55, Input the equivalent control input With the switching control input Adding them together gives the total control input for the underwater robot. .

[0012] Optional uncertainty perturbation bound parameters The estimated value ,satisfy Its update formula is: ; in This represents the adaptive gain coefficient for uncertainty perturbations, and ; Indicates time Uncertain fluid dynamics of underwater robots in a geodetic coordinate system; Represents the calculation of the Euclidean norm; For the estimated value The first-order time derivative, representing The rate of change.

[0013] The present invention also provides an electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the underwater robot adaptive control method considering actuator failure.

[0014] The present invention also provides a computer-readable storage medium storing computer instructions for causing a processor to execute the aforementioned adaptive control method for an underwater robot that takes into account actuator failures.

[0015] By employing the above technical solution, the present invention provides an adaptive control method for underwater robots that considers actuator failure, which has at least the following beneficial effects: (1) The adaptive extended state observer designed in this invention can simultaneously estimate the unmeasurable motion state (linear velocity, angular velocity) and unknown external environmental disturbances without the need for a velocity sensor, and adaptively compensate for the influence of model parameters and actuator failures. The controller provides accurate and real-time state and disturbance feedback. (2) This invention constructs an integral sliding mode controller based on Lyapunov stability theory, which overcomes the problems of large steady-state error and obvious chattering in traditional sliding mode control, while effectively improving the ability to suppress model uncertainty and unknown environmental disturbances during the control process; (3) The present invention further verified through simulation, simulating various complex working conditions (including unknown environmental disturbances, actuator failures of different degrees, model uncertainty and unmeasurable state), and verified that the proposed method has high precision and strong robust tracking performance. This shows that the present invention has not only achieved important breakthroughs in theory, but also demonstrated wide applicability in practical applications, thus making a significant contribution to promoting the development of underwater robot motion control technology and providing beneficial effects for related technical fields. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of an adaptive control method for an underwater robot that takes into account actuator failure, according to the present invention. Figure 2This is a schematic diagram showing the comparison of the external disturbance estimation over time in the simulation experiment of this invention embodiment; Figure 3 This is a schematic diagram showing the change of thrust of the underwater robot's thruster over time in a simulation experiment according to an embodiment of the present invention. Figure 4 This is a schematic diagram comparing the change of tracking error over time in a simulation experiment of an embodiment of the present invention; Figure 5 This is a schematic diagram showing the comparison of tracking error over time under three different actuator failure conditions in the simulation experiment of this invention. Detailed Implementation

[0017] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0018] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0019] Please refer to Figures 1-5 This embodiment illustrates a specific implementation of the present invention. This embodiment establishes a dynamic model of an underwater robot with actuator faults; designs an adaptive extended state observer to simultaneously estimate unmeasurable speeds and unknown external environmental disturbances while adapting to model uncertainties; designs an integral sliding mode controller to solve for the total control input; and uses an adaptive gain update algorithm to estimate the upper bound of model uncertainty and the upper bound of disturbance-related parameters online, thereby achieving adaptive control of the underwater robot. Furthermore, this embodiment also provides an observer estimation error convergence analysis and controller stability proof, and designs simulation experiments for verification.

[0020] Please refer to Figure 1 This embodiment proposes an adaptive control method for an underwater robot that considers actuator failure. The method includes the following steps: S1. Based on the kinematic principles of underwater robots, establish the nonlinear dynamic equations of the underwater robot in the body coordinate system, which include actuator faults and unknown external environmental disturbances.

[0021] The dynamic model is the foundation for designing an intelligent controller for underwater robots. As a preferred implementation of step S1, it specifically includes the following steps: First, based on the kinematic principles of underwater robots, a geodetic coordinate system and a body coordinate system are established, with the origin of the body coordinate system set as the center of gravity of the underwater robot. The nonlinear dynamics of the underwater robot in the body coordinate system are described as follows: ; This equation is the nonlinear dynamic equation of the underwater robot in its body coordinate system, which includes actuator failures and unknown external environmental disturbances. , , , These are the system inertia matrix, Coriolis force and centripetal force matrix, hydrodynamic damping matrix, and resultant force matrix of gravity and buoyancy of the underwater robot in its body coordinate system, respectively. The velocity of an underwater robot is represented by its linear velocity vector and angular velocity vector. angular velocity vector , , , These represent the sway velocity, transverse velocity, and heave velocity, respectively. These represent the roll rate, pitch rate, and yaw rate, respectively. Indicates the transpose operation; For speed The first time derivative of represents the acceleration of the underwater robot in the body coordinate system, including the linear acceleration vector and the angular acceleration vector; The pose of an underwater robot is represented by a position vector and an attitude vector. Attitude vector , , , These are respectively longitudinal sway, transverse sway, and helical displacement. , , These are roll angle, pitch angle, and yaw angle, respectively. The thrust vector of an underwater robot's thruster with actuator malfunction. and allocation matrix The generalized driving force of the underwater robot, which includes actuator faults, is defined as follows: ,in , The fault offset vector, This is the fault impact matrix. Represents the total control input of the underwater robot; allocation matrix Used to map thruster thrust to a 6-DOF generalized force; The unknown external environmental disturbance component is defined as the underwater robot's position in its body coordinate system. This disturbance is one of the components of the system's uncertainty.

[0022] S2. Rewrite the established nonlinear dynamic equations, divide each coefficient matrix into a nominal part and an uncertain perturbation part, construct a composite uncertainty term in the body coordinate system, and show the separation of the uncertainty.

[0023] The system inertia matrix can typically be represented by two parts: a nominal part and an uncertain perturbation part, i.e.: Similarly, the Coriolis force and centripetal force matrices can also be expressed as... The hydrodynamic damping matrix is ​​expressed as The resultant force matrix of gravity and buoyancy is expressed as: In the above disassembly These represent the system inertia matrices in the body coordinate system, respectively. Coriolis force and centripetal force matrix Hydrodynamic damping matrix The resultant force matrix of gravity and buoyancy The nominal part, , , , Let represent the system inertia matrices of the underwater robot in its body coordinate system. Coriolis force and centripetal force matrix Hydrodynamic damping matrix The resultant force matrix of gravity and buoyancy The perturbation part.

[0024] The nominal parameters are obtained through numerical calculations and system identification methods, which significantly reduces system uncertainty. The physical parameters used in the numerical calculations are exported using 3D software, such as the underwater robot's total mass, moment of inertia, physical distance, and thruster layout parameters. Some parameters that cannot be directly measured, such as the damping coefficient, are obtained through experimental data combined with parameter identification methods. The parameter identification process solves the optimization problem of matching the dynamic model with experimental data, using the least squares method to obtain a set of optimal parameters that minimize the error function between the predicted and measured outputs. Finally, the nominal parameters are calculated based on the above parameters and physical theorems. .

[0025] As a preferred embodiment of step S2, it specifically includes the following steps: The system inertia matrix of the underwater robot in the body coordinate system Coriolis force and centripetal force matrix Hydrodynamic damping matrix The resultant force matrix of gravity and buoyancy The nominal and uncertain perturbation components are separated, and the established nonlinear dynamic equations are rewritten to show the separation of uncertainties. The rewritten nonlinear dynamic equations satisfy the following form: ; in, This represents the total control input of the underwater robot. , The fault offset vector, This is the fault impact matrix; The composite uncertainty term of an underwater robot in its body coordinate system is defined as follows: , Uncertain fluid dynamics of an underwater robot in its body coordinate system is defined as follows: ; Thruster allocation matrix for underwater robots with actuator malfunctions With fault offset vector product term Used to quantify uncertainty disturbances caused by actuator failure.

[0026] S3. Transform the rewritten nonlinear dynamic equations into the geodetic coordinate system to obtain a geodetic coordinate system model of the underwater robot that simultaneously includes actuator fault terms and unknown external environmental disturbance components.

[0027] As a preferred embodiment of step S3, it specifically includes the following steps: Construct the transformation equations between the geodetic coordinate system and the body coordinate system: ; in, pose of the underwater robot in the geodetic coordinate system The first time derivative of represents the velocity of the underwater robot in the geodetic coordinate system; Let represent the transformation matrix between the geodetic coordinate system and the body coordinate system, and assume that during the underwater robot's movement, ( (representing the pitch angle), i.e. It is reversible, therefore the nonlinear dynamics of the underwater robot relative to the Earth coordinate system can be described as follows: ; This equation represents the geodetic coordinate system model of an underwater robot that incorporates actuator malfunctions and unknown external environmental disturbances. , , , These represent the Coriolis force and centripetal force matrices, hydrodynamic damping matrix, resultant force matrix of gravity and buoyancy, and system inertia matrix of the underwater robot in the geodetic coordinate system, respectively. , The poses of the underwater robot in the geodetic coordinate system are respectively The first and second time derivatives represent the velocity and acceleration of the underwater robot in the geodetic coordinate system, respectively. The term represents the composite uncertainty of an underwater robot in the geodetic coordinate system, including the unknown external environmental disturbance components, uncertain fluid dynamics, and uncertain disturbances caused by actuator failures. Its mathematical expression is: ;in, , Represent the unknown external environmental disturbance components and uncertain fluid dynamics of the underwater robot in the geodetic coordinate system, respectively, and are respectively composed of , Combination Obtained through conversion; It is an identity matrix.

[0028] Will Abbreviated as The coefficient matrices of the geodetic coordinate system model are represented as follows: ; ; ; ; in, express The inverse matrix; express The first-order time derivative is used to represent The rate of change.

[0029] Steps S1-S3 involve problem modeling, establishing a dynamic model of the underwater robot with actuator failure.

[0030] S4. Based on the geodetic coordinate system model of the underwater robot, an adaptive extended state observer is designed to perform online estimation and obtain the estimated pose of the underwater robot in the geodetic coordinate system. Estimate speed With estimation of unknown external environmental disturbance components Simultaneously, the bounding parameters of the composite uncertainty term are estimated and adaptively updated.

[0031] The designed adaptive extended state observer distinguishes and processes uncertainties from different sources based on the dynamic deviation relationship between the system's external output and control input. As a preferred embodiment of step S4, it specifically includes the following steps: S41. Position the underwater robot in the geodetic coordinate system. and speed Construct it as a state vector; S42. The unknown external environmental disturbance components of the underwater robot in the geodetic coordinate system. The extended state is defined as the state vector that is extended, and the extended state vector is defined as the true state. Mathematically, it is represented as: ;in, , , Representing pose respectively ,speed Unknown external environmental disturbance components In reality The corresponding sub-vector in This is a transpose operation; Represent the space of real numbers; The number of degrees of freedom of an underwater robot; S43, in true state An adaptive extended state observer is designed based on the geodetic coordinate system model of the underwater robot. The adaptive extended state observer satisfies the following form: ; in, To estimate the state, including the underwater robot's estimated pose, estimated velocity, and estimated unknown external environmental disturbance components in the geodetic coordinate system; for The first time derivative of represents the dynamic update rate of the adaptive extended state observer itself; The external output is estimated for the adaptive extended state observer; This represents the total control input for the underwater robot; The state transition matrix is ​​defined in the following block matrix form: ,in , Let these represent the zero matrix and the identity matrix, respectively, of a 6×6 matrix. matrix The structural pattern is universal. If the underwater robot only has 3 degrees of freedom, then 6 can be changed to 3 (and the subsequent related matrices will also change accordingly). Here, the matrix... The dimensions and partitioning are specific to this invention. The advantage of this design is that the structure is clear and facilitates the design of subsequent observers.

[0032] To control the input matrix, it is defined in the following block matrix form: ,in, This represents the system inertia matrix of the underwater robot in the geodetic coordinate system. Assignment matrix for thrusters of underwater robots with actuator malfunctions; The external output matrix is ​​defined as follows: Used to control the estimated external output of the adaptive extended state observer Only the pose item is retained; The nonlinear function representing the dynamic characteristics of the system is used to describe the combined influence of different uncertainty components on the state evolution, and is defined in the following block matrix form: ,in The estimation of a nonlinear function is defined as follows: , This represents the estimated velocity of the underwater robot in the geodetic coordinate system. , They represent , The estimated value; The observer gain matrix is ​​defined in the following block matrix form: ; in, Indicates the observer bandwidth; The scaling transformation matrix is ​​defined in the following block matrix form: ; The dimension is The identity matrix; The perturbation estimation correction term for the adaptive extended state observer is defined as: ; in, The external output error of the adaptive extended state observer is defined as: , The true external output of the adaptive extended state observer; This represents the first-order time derivative of the unknown external environmental disturbance component of the underwater robot in the geodetic coordinate system. Uncertain fluid dynamics of underwater robots in the geodetic coordinate system The auxiliary perturbation term formed by the linear combination of Boundary parameters, auxiliary disturbance terms The linear expression is defined as: ; in, , The auxiliary selection matrix is ​​defined as follows: , , The bounding parameters are estimated online by the adaptive extended state observer. The estimated value, through Adaptive update, where Calculate the Euclidean norm. for The first-order time derivative, representing The rate of change is used to quantify and adaptively update the limit parameters of the composite uncertainty term; This represents the adaptive adjustment coefficient associated with the composite uncertainty term. ; This indicates the correction term for the protection disturbance estimate. The constant for numerical stability, ; Describing auxiliary functions The first-order time derivative satisfies Dynamic adjustment of disturbance estimation correction term The amplitude, auxiliary function Designed for ; Indicates the time; in the initial stage of the adaptive extended state observer's operation, The larger the value, the stronger the correction term, enabling the adaptive extended state observer's output estimation error to converge to near zero more quickly. Based on this, the estimation accuracy of the adaptive extended state observer for unmeasured velocities and external environmental disturbances also improves. As time increases, Gradually decrease, the disturbance estimation correction term The effect is weakened to avoid estimation jitter caused by over-correction, among which Calculations are performed using absolute values; This represents a symmetric positive definite matrix used to assist in perturbation estimation correction terms. This provides a mathematical basis for proving the convergence of the estimation error, and is defined in the following block matrix form: , express The inverse matrix.

[0033] The following is a proof of the convergence performance of the estimation error of the adaptive extended state observer: Depend on The estimation error of the adaptive extended state observer can be described as follows: ; in For the estimation error of the adaptive extended state observer, , , These are respectively the pose estimation error, velocity estimation error, and unknown external environment disturbance estimation error; the scaling estimation error of the adaptive extended state observer is defined. , , , pose respectively ,speed Unknown external environmental disturbances The corresponding scaling estimation error is then: , , , Indicates correspondence , , Three-item error category index, auxiliary selection matrix Auxiliary selection matrix , First time derivative It is bounded. for The first time derivative; ; in , , These represent the error dynamic matrix, nonlinear function, and nonlinear term estimation bias of the adaptive extended state observer, respectively.

[0034] The Lyapunov function is chosen when proving the convergence performance of the estimation error of the adaptive extended state observer. as follows: ; The first-order time derivative is (for ease of description, the auxiliary perturbation term will be used below). Represented as ): ; because If it is a symmetric positive definite matrix, then we have: ; Rewritten as: ; and satisfy Substitute and rewrite get: ,in , Both represent the Lipschitz coefficients of the nonlinear term; make , It is a positive constant and satisfies , The convergence rate parameter is further obtained. for: ; Therefore, it is proven Compare It has a faster convergence speed or a slower divergence speed.

[0035] Step S4 involves the design of the observer, specifically the Adaptive Extended State Observer (AESO). This observer incorporates an adaptive mechanism for adaptively updating the upper bound of the auxiliary disturbance term. Convergence analysis is performed on the estimation error of the Adaptive Extended State Observer to demonstrate its effectiveness. The Adaptive Extended State Observer designed in this invention can simultaneously estimate unmeasurable motion states (linear velocity, angular velocity) and unknown external environmental disturbances without the need for velocity sensors. It also adaptively compensates for the influence of model parameters and actuator faults, and the controller provides accurate and real-time state and disturbance feedback.

[0036] S5. Based on the online estimation results of the adaptive extended state observer, a reference trajectory is set to construct an integral sliding surface, a sliding mode control arrival law is designed, an integral sliding mode controller is formed, the total control input of the underwater robot is calculated, and the uncertainty disturbance limit parameters are estimated and adaptively updated to realize the adaptive control of the underwater robot.

[0037] Step S5 introduces a compensation mechanism for complex uncertainties to correct for the impact of unknown external environmental disturbances. A preferred implementation of step S5 specifically includes the following steps: S51, Set reference trajectory and calculate time. Tracking error and the first time derivative of its estimate Mathematically, it is represented as: ; in , , , These represent the estimated pose, pose reference trajectory, estimated velocity, and velocity reference trajectory of the underwater robot in the geodetic coordinate system, respectively. S52. Combining the tracking error and its estimated first-order time derivative, construct an integral sliding surface containing an error proportional term, an error integral term, and an error differential term. The constructed integral sliding surface satisfies the following form: ; in, Indicates time Integral sliding surface; These are the proportional gain matrix, integral gain matrix, and differential gain matrix, all designed as diagonal matrices. express From 0 For a certain moment within the interval Integral; S53. Based on the constructed integral sliding surface, design a sliding mode control arrival law, wherein the sliding mode control arrival law satisfies the following form: ; in, For integral sliding surface The first time derivative of represents the arrival law of sliding mode control; , These represent the linear feedback gain matrix and the switching gain matrix, respectively, both designed as positive definite diagonal matrices; To smoothly switch vectors, ensure that the underwater robot's trajectory tracking error converges quickly to and remains on the sliding surface, and simultaneously suppress the effects of unknown disturbances and model uncertainties, the following measures are taken: This represents the hyperbolic tangent function. The traditional method uses... Function hard switching and discontinuity offer strong robustness but are prone to chattering. In contrast, The function's continuous and smooth switching can suppress chattering, although robustness is slightly compromised, but this can be mitigated by adjusting its built-in smoothing coefficient. Balancing smoothness and anti-interference ability.

[0038] S54. Calculate the total control input of the underwater robot, including the equivalent control input. and switching control input ; S541, Solve for equivalent control input : ; in, express The inverse matrix; This represents the acceleration reference trajectory of the underwater robot in the geodetic coordinate system; This represents the estimated unknown external environmental disturbance component of the underwater robot in the geodetic coordinate system; This represents the estimated velocity of the underwater robot in the geodetic coordinate system. S542, Solving Switching Control Input : ; in, Representation matrix The largest eigenvalue; Uncertainty disturbance limit parameter The estimated values ​​are used to quantify and adaptively update the perturbation bound parameters. ,satisfy Its update formula is: ; in This represents the adaptive gain coefficient for uncertainty perturbations, and ; Indicates time Uncertain fluid dynamics of underwater robots in a geodetic coordinate system; Represents the space of positive real numbers. Represents the calculation of the Euclidean norm; for The first-order time derivative, representing The rate of change.

[0039] S55, Input the equivalent control input With the switching control input Adding them together gives the total control input for the underwater robot. The format is as follows: .

[0040] The stability of the integral sliding mode controller is then demonstrated: Constructing Lyapunov functions as follows: ; , They are respectively , The estimation error.

[0041] The first time derivative is: ; Substitution and And simplifying, we get: ; in ,in This represents the estimation error of unknown external environmental disturbances; therefore, we can summarize as follows: ; Depend on , Simplifying, we get: ;in: , , This represents the positive definite weight matrix. , , They represent The three block diagonal submatrices, This represents the system's integrated state vector, which consists of the scaling estimation error vector and the sliding surface vector. Representation matrix The smallest eigenvalue.

[0042] Therefore, the derivative can be seen. The fact that the system energy is negatively definite, meaning that the system energy continuously decays over time, indicates that the observer error, sliding surface error, and adaptive gain error of the underwater robot system are all bounded, providing a basis for the final convergence of the trajectory tracking error.

[0043] Define auxiliary vector And there are: ; ; , This represents the channel index for degrees of freedom. In the 6-DOF scenario of this invention, ; After Laplace transformation, we get: ; According to the final value theorem of the Laplace transform, we have: ; The Laplace transform operator , The imaginary unit, It means "infinity"; , express The real part, , express The imaginary part, , The Laplace transform satisfies: ; This indicates the absolute value operation; Calculate the cosine; express The upper bound; Further, we can conclude that:

[0044] because Therefore, the final result is: ; This proves that the trajectory tracking error of the underwater robot asymptotically converges to zero.

[0045] Step S5 involves controller design, specifically the integral sliding mode controller (ISMC), which includes designing the integral sliding surface and calculating the total control input to achieve adaptive gain updates. This step also verifies the stability of the ISMC, ensuring that all signals are bounded and the tracking error asymptotically converges to zero. This invention, by constructing an integral sliding mode controller based on Lyapunov stability theory, overcomes the problems of large steady-state error and significant chattering in traditional sliding mode control, while effectively improving the suppression of model uncertainties and unknown disturbances during the control process.

[0046] This embodiment also provides an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to execute the underwater robot adaptive control method considering actuator failure.

[0047] This embodiment also provides a computer-readable storage medium storing computer instructions, which are used to cause a processor to execute the aforementioned adaptive control method for underwater robots that takes into account actuator failures.

[0048] To enable researchers in the field to better understand the implementation of this invention, this embodiment also provides simulation experiments (based on Matlab software) for verification.

[0049] The specific information about the simulation software is as follows: Software Name: MATLAB; Version: R2024b The parameters for the simulation experiment are set as follows: ; in This indicates the construction of a diagonal matrix; ; ; The reference trajectory for the underwater robot's position is as follows: , , ,in , Calculate for sine and cosine respectively. , , Reference trajectories representing longitudinal, transverse, and helical displacements; For other parameter settings, please refer to Table 1.

[0050] Table 1. Some parameter settings for the simulation experiment

[0051] The simulation results can be referenced. Figures 2-4 .in Figure 2 This is a schematic diagram showing the variation of external disturbance estimation over time in a simulation experiment. Figure 2 In These represent estimates of unknown external environmental disturbances. The first to sixth components in a 6-DOF scene; Figure 3 The thrust of the underwater robot's thruster in the simulation experiment ( - That is, thrust vector A comparative diagram showing the changes of the first to sixth components (in a 6-DOF scenario) over time. Figure 4 This is a schematic diagram comparing the tracking error over time in the simulation experiment (the sway error, roll error, pitch error, and yaw error of the integral sliding mode controller AISMC designed in this invention are compared with those of the traditional sliding mode control SMC method; the zero line is marked in the figure).

[0052] This invention also compares three different actuator failure scenarios (case 1, case 2, and case 3) to highlight the strong robustness of the invention, wherein: Case 1 is: , Case 2 is: , Case 3 is: .

[0053] Figure 5 This is a comparative diagram showing the changes in tracking errors (including sway error, roll error, pitch error, and yaw error) over time under the three different actuator failure conditions mentioned above.

[0054] Based on the simulation results above, this invention verifies that under conditions of unknown external environmental disturbances, actuator failures, model uncertainties, and unmeasurable speed, the underwater robot's trajectory tracking error can asymptotically converge to zero using the adaptive extended state observer (AESO) and integral sliding mode controller (AISMC) approach. A comparison of AISMC and Sliding Mode Control (SMC) methods for tracking error demonstrates that the system of this invention exhibits more stable and higher-precision trajectory tracking performance. Furthermore, comparing the tracking errors under three different actuator failure conditions highlights the strong robustness of this invention. Simulation verification of various complex working conditions (including unknown disturbances, actuator failures of varying degrees, model uncertainties, and unmeasurable state) verifies the high-precision and robust tracking performance of the proposed method. This demonstrates that this invention not only represents a significant theoretical breakthrough but also exhibits broad applicability in practical applications, thus making a significant contribution to the development of underwater robot motion control technology and providing beneficial effects to related technical fields.

[0055] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0056] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0057] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. An adaptive control method for an underwater robot considering actuator failure, characterized in that, include: S1. Based on the kinematic principle of underwater robots, establish the nonlinear dynamic equations of underwater robots in the body coordinate system, which contain actuator faults and unknown external environmental disturbances. The established nonlinear dynamic equations have coefficient matrices that include the system inertia matrix, Coriolis force and centripetal force matrix, hydrodynamic damping matrix, and the resultant force matrix of gravity and buoyancy. S2. Rewrite the established nonlinear dynamic equations, divide each coefficient matrix into a nominal part and an uncertain perturbation part, construct a composite uncertainty term in the body coordinate system, and show the separation of the uncertainty. The composite uncertainty in the body coordinate system includes unknown external environmental disturbance components, uncertain fluid dynamics, and uncertain disturbances caused by actuator failures in the body coordinate system of the underwater robot. S3. Transform the rewritten nonlinear dynamic equations into the geodetic coordinate system to obtain a geodetic coordinate system model of the underwater robot that simultaneously includes actuator fault terms and unknown external environmental disturbance components. S4. Based on the geodetic coordinate system model of the underwater robot, an adaptive extended state observer is designed to perform online estimation, obtain the estimated pose, estimated velocity and estimated unknown external environmental disturbance components of the underwater robot in the geodetic coordinate system, and simultaneously estimate and adaptively update the boundary parameters of the composite uncertainty. S5. Based on the online estimation results of the adaptive extended state observer, a reference trajectory is set to construct an integral sliding surface, a sliding mode control arrival law is designed, an integral sliding mode controller is formed, the total control input of the underwater robot is calculated, and the uncertainty disturbance limit parameters are estimated and adaptively updated to realize the adaptive control of the underwater robot.

2. The adaptive control method for an underwater robot considering actuator failure according to claim 1, characterized in that: In step S1, establishing the nonlinear dynamic equations of the underwater robot in its body coordinate system, which include actuator faults and unknown external environmental disturbances, based on the kinematic principles of underwater robots, includes: With the center of gravity of the underwater robot as the origin of the body coordinate system, a body coordinate system is established, and the nonlinear dynamic equations of the underwater robot in the body coordinate system are constructed. These equations satisfy the following form: ； in, , , , These are the system inertia matrix, Coriolis force and centripetal force matrix, hydrodynamic damping matrix, and resultant force matrix of gravity and buoyancy of the underwater robot in its body coordinate system, respectively. This represents the velocity of the underwater robot in its body coordinate system, including the linear velocity vector and the angular velocity vector. for The first time derivative of represents the acceleration of the underwater robot in the body coordinate system, including the linear acceleration vector and the angular acceleration vector; The pose of the underwater robot is represented by its position vector and attitude vector. The thrust vector of an underwater robot's thruster with actuator malfunction. and allocation matrix The generalized driving force of the underwater robot, which includes actuator faults, is defined as follows: ,in , The fault offset vector, This is the fault impact matrix. This represents the total control input for the underwater robot; This represents the unknown external environmental disturbance component of the underwater robot in its body coordinate system.

3. The adaptive control method for an underwater robot considering actuator failure according to claim 2, characterized in that: In step S2, the rewriting of the established nonlinear dynamic equations, dividing each coefficient matrix into a nominal part and an uncertain perturbation part, includes: The system inertia matrix of the underwater robot in the body coordinate system Coriolis force and centripetal force matrix Hydrodynamic damping matrix The resultant force matrix of gravity and buoyancy The nominal and uncertain perturbation parts are separated, and the established nonlinear dynamic equations are rewritten. The rewritten nonlinear dynamic equations satisfy the following form: ； in, These represent the system inertia matrices in the body coordinate system, respectively. Coriolis force and centripetal force matrix Hydrodynamic damping matrix The resultant force matrix of gravity and buoyancy The nominal value; The composite uncertainty term of an underwater robot in its body coordinate system is defined as follows: , Uncertain fluid dynamics of an underwater robot in its body coordinate system is defined as follows: , , , , Let represent the system inertia matrices of the underwater robot in its body coordinate system. Coriolis force and centripetal force matrix Hydrodynamic damping matrix The resultant force matrix of gravity and buoyancy Perturbation values; Thruster allocation matrix for underwater robots with actuator faults. With fault offset vector product term Used to quantify uncertainty disturbances caused by actuator failure.

4. The adaptive control method for an underwater robot considering actuator failure according to claim 3, characterized in that: In step S3, the process of transforming the rewritten nonlinear dynamic equations to a geodetic coordinate system to obtain a geodetic coordinate system model of the underwater robot that simultaneously includes actuator fault terms and unknown external environmental disturbance components includes: A transformation equation is constructed between the geodetic coordinate system and the body coordinate system. Based on this transformation equation, the nonlinear dynamic equation rewritten in step S2 is transformed to the geodetic coordinate system, resulting in a geodetic coordinate system model of the underwater robot. This geodetic coordinate system model satisfies the following form: ； in, , , , These represent the Coriolis force and centripetal force matrices, hydrodynamic damping matrix, resultant force matrix of gravity and buoyancy, and system inertia matrix of the underwater robot in the geodetic coordinate system, respectively. , The poses of the underwater robot in the geodetic coordinate system are respectively The first and second time derivatives represent the velocity and acceleration of the underwater robot in the geodetic coordinate system, respectively. This represents the composite uncertainty of an underwater robot in the geodetic coordinate system, including the unknown external environmental disturbance components, uncertain fluid dynamics, and uncertain disturbances caused by actuator failures in the geodetic coordinate system.

5. The adaptive control method for an underwater robot considering actuator failure according to claim 1, characterized in that: In step S4, the adaptive extended state observer based on the geodetic coordinate system model of the underwater robot is designed to perform online estimation, obtaining the estimated pose, estimated velocity, and estimated unknown external environmental disturbance components of the underwater robot in the geodetic coordinate system. Simultaneously, the boundary parameters of the composite uncertainty term are estimated and adaptively updated, including: S41. Position the underwater robot in the geodetic coordinate system. and speed Construct it as a state vector; S42. The unknown external environmental disturbance components of the underwater robot in the geodetic coordinate system. The extended state is defined as the state vector that is extended, and the extended state vector is defined as the true state. Mathematically, this is expressed as: ;in, , , Representing pose respectively ,speed Unknown external environmental disturbance components In reality The corresponding sub-vector in This is a transpose operation; S43, in true state An adaptive extended state observer is designed based on the geodetic coordinate system model of the underwater robot. The adaptive extended state observer satisfies the following form: ； in, To estimate the state, including the underwater robot's estimated pose, estimated velocity, and estimated unknown external environmental disturbance components in the geodetic coordinate system; for The first time derivative of represents the dynamic update rate of the adaptive extended state observer itself; The external output is estimated for the adaptive extended state observer; This represents the total control input for the underwater robot; This is the state transition matrix; The control input matrix is ​​the system inertia matrix of the underwater robot in the geodetic coordinate system. Allocation matrix for thrusters of underwater robots with actuator malfunctions Decide; This is the external output matrix, used to control the estimated external output of the adaptive extended state observer. Only the pose item is retained; A nonlinear function is represented by the following block matrix form: ,in The estimation of a nonlinear function is defined as follows: , This represents the estimated velocity of the underwater robot in the geodetic coordinate system. , They represent , The estimated value; The number of degrees of freedom of an underwater robot; , , Let represent the Coriolis force and centripetal force matrices, hydrodynamic damping matrix, and resultant force matrix of gravity and buoyancy of the underwater robot in the geodetic coordinate system, respectively. Represents a zero matrix with dimension dof×1; Represents the observer gain matrix; The scaling transformation matrix is ​​defined in the following block matrix form: ; This represents an identity matrix of dimension dof × dof. Indicates the observer bandwidth; The perturbation estimation correction term for the adaptive extended state observer is defined as: ； in, The external output error of the adaptive extended state observer is defined as: , The true external output of the adaptive extended state observer; This represents the first-order time derivative of the unknown external environmental disturbance component of the underwater robot in the geodetic coordinate system. Uncertain fluid dynamics of underwater robots in the geodetic coordinate system The auxiliary perturbation term formed by the linear combination of The boundary parameter, The bounding parameters are estimated online by the adaptive extended state observer. The estimated value is used to quantify and adaptively update the bounding parameters of the composite uncertainty term; This indicates the correction term for the protection disturbance estimate. The constant for numerical stability, ; Describes a symmetric positive definite matrix. express The inverse matrix; Describing auxiliary functions The first-order time derivative satisfies Dynamic adjustment of disturbance estimation correction term The amplitude, auxiliary function Designed for ; Calculate the Euclidean norm; Indicates the time.

6. The adaptive control method for an underwater robot considering actuator failure according to claim 5, characterized in that: Boundary parameters obtained by online estimation using an adaptive extended state observer The estimated value ,pass Adaptive update, where For estimated value The first-order time derivative characterizes The rate of change; This represents the adaptive adjustment coefficient associated with the composite uncertainty term. .

7. The adaptive control method for an underwater robot considering actuator failure according to claim 1, characterized in that: In step S5, the online estimation results based on the adaptive extended state observer are used to construct an integral sliding mode surface by setting a reference trajectory, designing a sliding mode control arrival law, forming an integral sliding mode controller, solving for the total control input of the underwater robot, and simultaneously estimating and adaptively updating the uncertainty disturbance limit parameters, including: S51, Set reference trajectory and calculate time. Tracking error and the first time derivative of its estimate Mathematically, this is expressed as: ； in , , , These represent the estimated pose, pose reference trajectory, estimated velocity, and velocity reference trajectory of the underwater robot in the geodetic coordinate system, respectively. S52. Combining the tracking error and its estimated first-order time derivative, construct an integral sliding surface containing an error proportional term, an error integral term, and an error differential term. The constructed integral sliding surface satisfies the following form: ； in, Indicates time Integral sliding surface; These are the proportional gain matrix, integral gain matrix, and differential gain matrix, all designed as diagonal matrices. express From 0 For a certain moment within the interval Integral; S53. Based on the constructed integral sliding surface, design a sliding mode control arrival law, wherein the sliding mode control arrival law satisfies the following form: ； in, For integral sliding surface The first time derivative; , These represent the linear feedback gain matrix and the switching gain matrix, respectively, both designed as positive definite diagonal matrices; For the smooth switching vector, where Represents the hyperbolic tangent function; S54. Calculate the total control input of the underwater robot, including the equivalent control input. and switching control input ; S541, Solve for equivalent control input : ； in, , , , These represent the Coriolis force and centripetal force matrices, hydrodynamic damping matrix, resultant force matrix of gravity and buoyancy, and system inertia matrix of the underwater robot in the geodetic coordinate system, respectively. Assignment matrix for thrusters of underwater robots with actuator malfunctions; express The inverse matrix; This represents the acceleration reference trajectory of the underwater robot in the geodetic coordinate system; This represents the estimated unknown external environmental disturbance component of the underwater robot in the geodetic coordinate system; This represents the estimated velocity of the underwater robot in the geodetic coordinate system. S542, Solving Switching Control Input : ； in, express The largest eigenvalue; Uncertainty disturbance limit parameter The estimated values ​​are used to quantify and adaptively update the perturbation bound parameters. ; S55, Input the equivalent control input With the switching control input Adding them together gives the total control input for the underwater robot. .

8. The adaptive control method for an underwater robot considering actuator failure according to claim 7, characterized in that: Uncertainty perturbation limit parameter The estimated value ,satisfy Its update formula is: ； in This represents the adaptive gain coefficient for uncertainty perturbations, and ; Indicates time Uncertain fluid dynamics of underwater robots in a geodetic coordinate system; Represents the calculation of the Euclidean norm; For estimated value The first-order time derivative characterizes The rate of change.

9. An electronic device, characterized in that, The electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the underwater robot adaptive control method considering actuator failure as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when executed by a processor, implement the underwater robot adaptive control method considering actuator failure as described in any one of claims 1-8.

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