A fixed-time fault-tolerant trajectory tracking control method for underactuated AUV based on reduced-order extended observer

Abstract

The present application relates to the technical field of autonomous underwater vehicle control, and particularly relates to a fixed-time fault-tolerant trajectory tracking control method for underactuated AUV based on reduced-order extended observer, which comprises the following steps: firstly, establishing kinematics and dynamics model of AUV; designing reduced-order extended state observer, only using position error to estimate unmeasurable sway velocity and compensate collective disturbance online; designing adaptive fixed-time guidance law, generating surge velocity and heading angle command; designing fixed-time sliding mode dynamics controller, generating nominal control force and torque; designing actuator fault diagnosis and fault-tolerant compensation module, estimating loss factor of actuator efficiency in surge and rudder passage online and reconstructing control law, under the conditions of unmeasurable sway velocity, model uncertainty, external disturbance and partial actuator failure, the present application realizes high-precision fixed-time tracking of AUV to expected trajectory, and has the advantages of fast response, strong robustness, reduced dependence on lateral velocity sensor and active fault-tolerant capability.

Description

Technical Field

[0001] This invention relates to the field of autonomous underwater vehicle control technology, specifically to a fixed-time fault-tolerant trajectory tracking control method for underactuated AUVs based on a reduced-order extended observer. Background Technology

[0002] Autonomous underwater vehicles (AUVs) are widely used in marine resource exploration, environmental monitoring, and subsea pipeline inspection. Among them, underactuated AUVs, with control inputs less than system degrees of freedom, have attracted considerable attention due to their simple structure and low cost. However, their underactuated characteristics also present significant challenges to achieving high-precision trajectory tracking: First, the system exhibits highly nonlinear, multi-degree-of-freedom coupled dynamic characteristics, and the model parameters are uncertain and continuously affected by unknown marine environmental disturbances; second, the underactuated characteristics result in a lack of direct lateral control force; and third, accurate measurement of key state variables such as sway velocity typically relies on high-cost sensors, hindering their widespread application.

[0003] Existing techniques typically employ linearized models based on small-angle assumptions for sideslip angle compensation, which struggles to accurately characterize nonlinear dynamics under strong sway conditions. This results in insufficient tracking accuracy and robustness under model mismatch and external disturbances. Furthermore, during long-term operation, AUVs inevitably experience mechanical wear, electrical aging, or external impacts on their actuators (such as thrusters and control surfaces), leading to partial or complete efficiency loss or failure. Traditional control methods often assume ideal actuator operating conditions during design, lacking proactive compensation mechanisms for actuator failures. Once a failure occurs, system control performance deteriorates sharply, potentially leading to instability and severely impacting mission safety.

[0004] Therefore, there is an urgent need for a trajectory tracking control method that can achieve high precision, fast convergence, and active fault tolerance under conditions of unmeasurable sway velocity, model uncertainty, external disturbances, and partial actuator failure. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a fixed-time fault-tolerant trajectory tracking control method for underactuated AUVs based on a reduced-order extended observer.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a fixed-time fault-tolerant trajectory tracking control method for underactuated AUVs based on a reduced-order extended observer, comprising the following steps:

[0007] S1. Establish a horizontal three-degree-of-freedom kinematic and dynamic model of the underactuated autonomous underwater vehicle (AUV), and define the position tracking error based on the carrier coordinate system;

[0008] S2. Design a reduced-order extended state observer to estimate the unmeasurable sway velocity online in real time based on measurable position tracking error information, and estimate the composite disturbance that integrates model uncertainty and external environmental disturbance.

[0009] S3. Design an adaptive fixed-time guidance law. Using the sway velocity estimated by the reduced-order extended state observer, and by introducing a double power convergence term and adaptive parameters, generate the desired command for the sway velocity and heading angle.

[0010] S4. Design a fixed-time sliding mode dynamic controller. For the desired command generated by the guidance law, design fixed-time sliding surfaces for sway velocity and heading angle tracking error respectively, and derive the actuator nominal control law including disturbance compensation term.

[0011] S5. Design an actuator fault diagnosis and fault-tolerant compensation module to estimate the actuator efficiency loss factor of the sway and steering channels online, and reconstruct the control law to achieve fixed-time fault-tolerant trajectory tracking.

[0012] S6. Input the calculated control force and torque commands into the AUV's actuator to drive the AUV to track the desired trajectory.

[0013] In some embodiments, in step S1, the three-degree-of-freedom kinematic model of the horizontal plane is:

[0014] ,

[0015] in,( () represents the position in the inertial coordinate system. For heading angle, , , These are the sway velocity, roll velocity, and bow angular velocity in the carrier coordinate system, respectively. It is a rotation matrix;

[0016] The dynamic model, considering the uncertainties in hydrodynamic parameters and external disturbances, is expressed as follows:

[0017] ,

[0018] in, The inertia matrix includes the added mass. For the Coriolis and centripetal force matrices, Here is the damping matrix. , To control the input, For lumped disturbances;

[0019] The position tracking error and Defined in the carrier coordinate system as:

[0020] ,

[0021] in,( ) represents the position of the desired trajectory.

[0022] In some embodiments, in step S2, the equation of the reduced-order extended state observer is:

[0023] ,

[0024] in, For sway speed The estimated value, is the observer gain, and p is an intermediate variable. Let be the reference velocity constructed from the differential of the desired trajectory, and > 0.

[0025] In some embodiments, in step S3, the desired oscillation velocity generated by the adaptive fixed-time guidance law... and expected heading angle for:

[0026] ,

[0027] ,

[0028] in, For reference heading angle, , > 0, β1> 0, q1 > 1 is a design parameter. , , > 1 is a constant;

[0029] The intermediate variable Θ is defined as follows:

[0030] ,

[0031] Where ω is the adaptive compensation term, and its adaptive law is: , > 0 represents adaptive gain;

[0032] Ξ is a variable representing the dynamic gain adjustment parameter. .

[0033] In some embodiments, in step S3, the guidance law is improved by introducing a smoothing parameter. Ensure that |Θ| ≤ 1, the Defined as:

[0034] ,

[0035] in, , , It is a positive number.

[0036] In some embodiments, in step S4, the tracking error of the sway velocity is addressed. and heading angle tracking error The designed fixed-time sliding surfaces are as follows:

[0037] ,

[0038] ,

[0039] in, .

[0040] In some embodiments, in step S4, the derived actuator nominal control law is... and for:

[0041] ,

[0042]

[0043] in, and This is the nominal nonlinear term in the dynamic model. For control parameters, and These are the upper limits of the disturbances in the oscillation and turning channels, respectively. It is the hyperbolic tangent function. It is a small positive number.

[0044] In some embodiments, in step S5, the actuator failure model is:

[0045] The actual control input is represented as:

[0046]

[0047] Where ρ u , ρ r ∈(0, 1] represents the unknown actuator efficiency factor. An actuator efficiency factor of 1 indicates a healthy state, while a factor of less than 1 indicates a partial failure.

[0048] In some embodiments, in step S4, based on the output of the reduced-order extended state observer (step S2), an adaptive law for fault diagnosis is designed to estimate the efficiency loss factor online.

[0049]

[0050] Wherein: γ u , γ r > 0 represents adaptive gain; s u , s ψ The fixed-time sliding surface as described in claim 6; Ψ u Ψ r As an intermediate variable, it is defined as:

[0051] .

[0052] In some embodiments, in step S5, the reconstructed fault-tolerant control law is:

[0053]

[0054] Where δ > 0 is a small constant to prevent division by zero;

[0055] This refers to the nominal control law.

[0056] In some embodiments, the method constructs a cascaded fault-tolerant control architecture through the reduced-order extended state observer, the adaptive fixed-time guidance law, the fixed-time sliding mode controller, and the actuator fault diagnosis and fault-tolerant compensation module, so that the entire closed-loop system still has fixed-time stability under actuator partial failure, that is, the upper bound of the convergence time of the system state is independent of the initial state and the degree of failure.

[0057] To achieve the above objectives, the present invention also provides the following technical solution: an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method.

[0058] To achieve the above objectives, the present invention also provides the following technical solution: a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the steps of the method.

[0059] Compared with the prior art, the beneficial effects of the present invention are:

[0060] 1. Achieved high-precision and robust tracking control: By estimating and compensating for unmeasurable sway velocity and lumped disturbances online through a reduced-order extended observer, combined with fixed-time sliding mode control, the effects of model uncertainty, parameter perturbation and unknown marine environmental disturbances are effectively overcome, significantly improving the system's tracking accuracy and anti-interference capability under complex operating conditions.

[0061] 2. Superior convergence performance: The designed adaptive fixed-time guidance law and fixed-time sliding mode controller ensure the fixed-time stability of the entire cascaded closed-loop system. The system state can quickly converge to the neighborhood of the equilibrium point within a predetermined time bound that is independent of the initial state, exhibiting fast response speed and good dynamic performance.

[0062] 3. Possesses proactive fault tolerance capabilities, ensuring long-term operational safety: By designing an actuator fault diagnosis and fault-tolerant compensation module, the efficiency loss factors of the actuators in the sway and steering channels are estimated online, and the control law is reconstructed, enabling the system to maintain stable trajectory tracking performance even when partial actuator failures occur. The fault-tolerant compensation component does not affect the fixed-time convergence characteristics of the original system, and the upper bound of the convergence time is independent of the fault severity, significantly improving the reliability and safety of the AUV during long-term autonomous operation.

[0063] 4. Effectively reduces system hardware costs and complexity: It eliminates the need to rely on expensive or difficult-to-maintain lateral velocity measurement sensors (such as Doppler logs). Equivalent lateral velocity can be estimated by an observer using only conventional pose sensor information, reducing dependence on dedicated hardware and improving the economy and feasibility of engineering applications.

[0064] 5. Enhanced engineering practicality of the system: The dynamic gain adjustment mechanism introduced in the guidance law can suppress the amplitude of the control command under large tracking errors, effectively avoiding actuator saturation; the controller uses a continuous smooth function (such as tanh) instead of the sign function, which reduces control chatter and makes the method easier to implement and apply in practical engineering.

[0065] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. The embodiments of this application will provide a detailed description and understanding of the application. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the overall cascaded control architecture of the underactuated AUV fixed-time fault-tolerant trajectory tracking control method based on a reduced-order extended observer proposed in this invention;

[0067] Figure 2 This is a comparison diagram of the actual tracking trajectory of the AUV and the desired trajectory under a circular desired trajectory when using the method of the present invention;

[0068] Figure 3 When using the method of the present invention, the position tracking error x in the carrier coordinate system e With y e Convergence process curve over time;

[0069] Figure 4The figure shows the time-domain response curves of the AUV's sway velocity u versus heading angle ψ when using the method of the present invention.

[0070] Figure 5 The graph shows a comparison of the estimation performance of the reduced-order extended observer on the actual sway velocity v and its estimated value v̂ when using the method of the present invention. Detailed Implementation

[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] This invention provides a fixed-time fault-tolerant trajectory tracking control method for an underactuated autonomous underwater vehicle (AUV) based on a reduced-order extended state observer. The core of this method lies in constructing a cascaded anti-interference fault-tolerant control framework, which consists of four key modules working collaboratively: a reduced-order extended state observer (RESO), an adaptive fixed-time guidance law (AFTGL), a fixed-time sliding mode controller (FTSMC), and an actuator fault diagnosis and fault-tolerant compensation module (EFTCM). The overall architecture is as follows: Figure 1 As shown. This invention aims to solve the problem of high-precision, fast-convergence trajectory tracking control of underactuated AUVs under conditions of unmeasurable sway velocity, model uncertainty, and unknown marine environmental disturbances. It also provides online diagnosis and active compensation for actuator failures, and the upper bound of the system convergence time is independent of the initial state and the degree of fault.

[0073] The steps of the method of the present invention will be described in detail below with reference to several embodiments.

[0074] Example 1: Basic Methodology and Core Design

[0075] This embodiment elaborates on the defined basic method and process, as well as the defined fault-tolerant control design, covering the entire process of system modeling, observer design, guidance law design, controller design, fault-tolerant compensation design, and stability analysis.

[0076] S1: System Modeling and Problem Description

[0077] First, a three-degree-of-freedom (3-DOF) kinematic and dynamic model of the underactuated AUV in the horizontal plane is established. The motion of the AUV in the horizontal plane is considered, including its position in the inertial coordinate system (…). ), heading angle and the oscillation velocity in the carrier coordinate system sway speed and bow angular velocity .

[0078] Kinematic model:

[0079]

[0080] in, The rotation matrix from the vehicle coordinate system to the inertial coordinate system:

[0081]

[0082] The system is underactuated, and the control input is... That is, a lack of direct lateral control. .

[0083] Dynamic model:

[0084] Considering uncertainties in hydrodynamic parameters (such as added mass and damping coefficient perturbations) and external environmental disturbances (such as ocean currents and waves), the dynamic equations are expressed as follows:

[0085]

[0086] in, . The inertia matrix includes the added mass. For the Coriolis and centripetal force matrices, It is a linear damping matrix. To incorporate the composite disturbance vector of model uncertainty and external disturbance, it is assumed that the vector and its first derivative are bounded.

[0087] To simplify the subsequent controller design, the dynamic equations can be written in component form:

[0088]

[0089] in, , , This is the nominal nonlinear dynamic term of the system.

[0090] Tracking error definition:

[0091] Set the desired trajectory as Its derivatives are smooth and bounded. The position tracking error in the carrier coordinate system is defined as:

[0092]

[0093] This definition maps the position error in the inertial coordinate system to the carrier coordinate system, making it easier to perceive and control based on the AUV itself.

[0094] S2: Design a reduced-order extended state observer (RESO)

[0095] Regarding sway speed Unmeasurable and subject to complex interference To address this problem, a simplified reduced-order extended state observer is designed. This observer utilizes only measurable position tracking errors. It is constructed using known expected trajectory information.

[0096] Observer equations:

[0097] In the kinematic model The dynamics are analyzed and combined with the dynamic model. The equations are used to design the following observer:

[0098]

[0099] in, It is the sway speed The estimated value, >0 represents the observer gain, and p represents an intermediate variable. The reference velocity is constructed from the differential of the desired trajectory and is a known time-varying signal.

[0100] Working principle and advantages:

[0101] Analysis of error dynamics can prove that the estimation error It converges exponentially, and the convergence rate is determined by the gain. The decision. Its core advantage lies in:

[0102] Structural order reduction: No need for composite interference Additional observation channels were designed, simplifying the structure.

[0103] No speed sensor required: Relying only on position / attitude sensors (such as GPS, DVL, INS) and desired trajectory information, significantly reducing hardware costs and system complexity.

[0104] Implicit disturbance estimation: Observer output It actually contains Dynamics and right The equivalent information of the channel influence provides crucial "equivalent lateral velocity" feedback for the upper-level guidance law.

[0105] S3: Design an Adaptive Fixed-Time Guidance Law (AFTGL)

[0106] The guidance layer's task is based on position error. and the observer provided Generate the desired oscillation speed command and heading angle command This drives the position error to converge.

[0107] Expected oscillation speed design:

[0108]

[0109] in, For heading error, . For gain, and This forms a double power term. When When it is large, The dominant factor provides a large gain to accelerate convergence; when When smaller, This process is primarily driven by the principle of ensuring sufficient convergence momentum near the equilibrium point. This is crucial for achieving fixed-time convergence.

[0110] Desired heading angle design:

[0111]

[0112] Among them, intermediate variables The design is the core of the guidance law, used to handle the coupling caused by underactuated characteristics (no lateral force):

[0113]

[0114] : Use the lateral velocity estimated by the observer for feedforward compensation to counteract the lateral drift it causes.

[0115] The adaptive compensation term has the following update law: , >0. This integral term can estimate and compensate for the equivalent lateral bias caused by model uncertainty and observation error online, further enhancing robustness.

[0116] Double power feedback term drives lateral error Convergence occurs within a fixed time. It is a dynamic gain adjustment variable:

[0117]

[0118] Smoothing process:

[0119] Smoothing parameter Δ g Under the guarantee While satisfying the constraint |Θ| ≤ 1, the lateral error y is achieved. e A smooth transition. Smoothing parameter Δ g The specific form is:

[0120]

[0121] Where μ1 and μ2 are the parameters to be designed, and Δ0 is the initial look-ahead distance. The parameter selection must strictly satisfy the critical state constraint |Ξ| ≤ 1, and the global stability of the system is ensured by a composite control law.

[0122] S4: Design a fixed-time sliding mode dynamics controller (FTSMC)

[0123] The task of the dynamic control layer is to ensure the actual sway speed of the AUV. and heading angle Capable of quickly and accurately tracking commands generated by the guidance layer. and And suppress disturbances at the dynamic level.

[0124] Define tracking error:

[0125]

[0126]

[0127] Design a fixed-time sliding surface:

[0128] For each error channel, a sliding surface containing double-power terms is designed to ensure that once the system state reaches the sliding surface, it will converge to zero within a fixed time.

[0129]

[0130]

[0131] Among them, the design parameters satisfy , .

[0132] Derivation of the fixed-time control law:

[0133] Based on Lyapunov's stability theory, the sliding surface s u and s ψ Differentiate and substitute into the dynamic model. To counteract the combined disturbance d u and d r The design incorporates a nominal control law that includes a double power-law approach and upper bound compensation for perturbations:

[0134]

[0135]

[0136] in:

[0137] , , This is the controller gain.

[0138] These are the estimated upper bounds of the combined interference of the oscillation and turning channels, respectively.

[0139] Functions are used to replace traditional symbolic functions To mitigate and control flutter, It is a small constant used to adjust the smoothness.

[0140] S5: Design of an actuator fault diagnosis and fault tolerance compensation module (EFTCM)

[0141] In actual long-term operation, the actuators of an AUV (such as propellers and control surfaces) inevitably experience mechanical wear, electrical aging, or external collisions, leading to partial or even complete loss of actuator efficiency. Traditional control methods typically assume that the actuators are in ideal operating conditions during design and lack proactive compensation mechanisms for actuator failures. Once a failure occurs, the system control performance will drop sharply, or even become unstable. To address this, this embodiment designs an actuator fault diagnosis and fault-tolerant compensation module to estimate the actuator efficiency loss factors in the sway and yaw channels online, and reconstruct the control law to achieve fixed-time fault-tolerant trajectory tracking.

[0142] S5.1 Actuator Failure Model:

[0143] Considering partial actuator failure, the following fault model is established: the actual control input is represented as the product of the nominal control input and the efficiency factor, i.e.:

[0144]

[0145] in, , ∈(0,1] represents the unknown actuator efficiency factor. An actuator efficiency factor of 1 indicates a healthy state; a factor less than 1 indicates a partial failure. When an actuator fails, the actual control input... and The value calculated by the control law is less than the nominal control law. and This leads to a decrease in tracking performance. The core task of this module is online estimation. and Based on this, the control law is reconstructed to offset the impact of efficiency loss.

[0146] S5.2 Fault Diagnosis Adaptive Law Design:

[0147] Based on the output of the reduced-order extended state observer (S2), an adaptive law for fault diagnosis is designed to estimate the efficiency loss factor online. This utilizes a sliding mode surface. and Based on the dynamic information, the following adaptive update law is constructed:

[0148]

[0149] in: , >0 represents adaptive gain; , The fixed-time sliding surface described in S4; , As an intermediate variable, it is defined as:

[0150]

[0151] The design principle of this adaptive law is that when the actuator experiences efficiency loss, the sliding surface... (or The convergence process of the sliding surface will be affected, and its dynamic changes contain information about efficiency loss. This is achieved by dynamically adjusting the sliding surface and the nominal control input. (or In association, the adaptive law can extract equivalent information of the efficiency loss factor online and drive the estimate. and It converges to the true value. Since this adaptive law is based on the output of RESO and the known dynamics of the sliding surface, no additional fault detection sensors are required, achieving a deep integration of fault diagnosis and control.

[0152] S5.3 Reconstructing the Fault-Tolerant Control Law Design:

[0153] To obtain an online estimate of the actuator efficiency factor and Then, the nominal control law derived from S4 is reconstructed to compensate for efficiency losses and restore the system's tracking performance. The reconstructed fault-tolerant control law is:

[0154]

[0155]

[0156] Where δ > 0 is a small constant to prevent division by zero; The nominal control law described in S4. When the actuator is healthy ( ≈1), ≈ The reconfiguration law degenerates into the nominal control law; when the actuator experiences partial failure ( <1), The input will automatically increase to compensate for efficiency losses, ensuring that the actual control input can still maintain the required control effect. This reconfiguration strategy has a clear physical meaning, is computationally simple, and is easy to implement in engineering.

[0157] S5.4 Fault-Tolerant Control Implementation Process:

[0158] Within each control cycle, the fault tolerance compensation module executes the following steps:

[0159] (1) Collect the current system status and RESO output ;

[0160] (2) Calculate the nominal control law and (S4);

[0161] (3) Calculate the sliding surface and Update the adaptive law to obtain and ;

[0162] (4) Calculate fault-tolerant control instructions using the reconstruction law. and ;

[0163] (5) and The output is sent to the actuator. This process integrates seamlessly with the existing RESO-guidance-control cascade architecture without compromising the fixed-time convergence characteristics of the original system.

[0164] S6: Stability Analysis of Closed-Loop Systems

[0165] It can be proven that the cascaded fault-tolerant closed-loop system consisting of RESO, AFTGL, FTSMC, and EFTCM is practically fixed-time stable.

[0166] Observer Subsystem: Estimation Error It is exponentially convergent and asymptotically stable; its convergence performance can be included in subsequent analysis.

[0167] Guidance-Kinematic Subsystem: Constructing Lyapunov Functions Through the analysis of Find the derivative and substitute it into the guidance and control laws, and then reasonably select the parameters (such as satisfying the following conditions). Under the condition that its derivative satisfies the inequality:

[0168]

[0169] in >0, Let be a normal constant related to the upper bound of the perturbation. According to the fixed-time stability theory, this subsystem is practically fixed-time stable, i.e., its state is stable. In a limited time Converging inward to a compact set associated with the upper bound of the perturbation Inside, and The upper bound is independent of the initial state.

[0170] Steady-state error compact set D g satisfy:

[0171]

[0172] The proof process establishes the fixed-time convergence characteristics of the cascaded system by constructing a double-power Lyapunov function and combining it with the boundedness condition of the error estimator.

[0173] Dynamics control subsystem: for sliding surfaces and Construct Lyapunov functions respectively and Substitute into the control law and Then it can be proven that:

[0174]

[0175]

[0176] in , This is a small constant related to the error in estimating the upper bound of the disturbance. Therefore, even if the actuator partially fails ( , In the case of <1), through compensation by the reconstruction law, the sliding surface and It still converges within a fixed time. Furthermore, according to the definition of a sliding surface, the tracking error... and It also converges to a small neighborhood of zero within a fixed time. Furthermore, the upper bound of the convergence time is related to the degree of fault. , It is irrelevant; it depends only on the controller parameters and the upper bound of the disturbance.

[0177] Cascaded Fault-Tolerant Control Architecture: Since the guidance subsystem (outer loop), dynamics control subsystem (inner loop), and fault-tolerant compensation module are all fixed-time stable, and the convergence time of the inner loop can usually be designed to be shorter than that of the outer loop, the entire cascaded fault-tolerant system satisfies the fixed-time stability condition. The upper bound of the system's total convergence time is... ,in This is the upper bound of the inner loop convergence time, and This characteristic is independent of the system's initial state and the degree of actuator failure. It significantly improves the reliability and safety of AUVs during long-term autonomous operation.

[0178] In summary, the method constructs a cascaded fault-tolerant control architecture through a reduced-order extended state observer, an adaptive fixed-time guidance law, a fixed-time sliding mode controller, and an actuator fault diagnosis and fault-tolerant compensation module. This enables the entire closed-loop system to maintain fixed-time stability even under partial actuator failure, meaning that the upper bound of the system state convergence time is independent of the initial state and the degree of fault.

[0179] S7: Execution and Control Process

[0180] The reconstructed fault-tolerant control force calculated in step S5 and torque Commands are input to the AUV's thrusters (such as propellers) and servo mechanisms, thereby driving the AUV's actual position and attitude. and speed To achieve the desired trajectory The tracking is performed. The entire control algorithm runs online in real time on the AUV's onboard computer.

[0181] Example 2: Parameter Selection and Adjustment Strategy

[0182] This embodiment provides the selection principles and adjustment strategies for key parameters in Embodiment 1 to guide engineering practice.

[0183] Reduced-order extended observer gain k:

[0184] Principle: k determines the observer bandwidth and convergence speed. The larger k is, the higher the estimated value. The faster the tracking of the true value v, the more sensitive it is to measurement noise.

[0185] Strategy: Initially, k can be set to 2-5. Adjust according to the estimation results in simulation or experiment: if the estimated response is slow, increase k; if the estimated signal has high noise and significant jitter, decrease k. Stability conditions must be met simultaneously. .

[0186] Guidance law double power parameters With gain :

[0187] This determines the shape of the convergence curve. A fixed choice is usually made. =0.5, =1.5 or =0.7, =2 and other combinations are used as the benchmark.

[0188] This directly affects the convergence speed of the position error. Initial values ​​can be determined using empirical formulas. = =1.0 setting.

[0189] Adjustment strategy: Observe x in the simulation e , y e The convergence process. If the convergence is too slow, the ratio can be increased proportionally. If overshoot or oscillation occurs, the speed can be appropriately reduced. (Because it plays a dominant role when the error is large) or fine-tuning .

[0190] Adaptive gain γ and smoothing parameter :

[0191] γ: Determines the adjustment speed of the adaptive term ω. Too large a value will cause oscillations, while too small a value will result in slow compensation. It is recommended to start with a smaller value, such as γ = 0.1, based on y e The steady-state error is increased.

[0192] b g Used to prevent guidance command saturation when there is a large initial error. It is usually set to a constant slightly greater than 1, such as b. g =1.1.

[0193] Used for smooth transitions. (Can be set) =1.0, =0.1, =0.1, the specific value of which is not sensitive to the performance impact, mainly to ensure the numerical stability of the algorithm.

[0194] Sliding surface parameters :

[0195] Power parameter The guidance law can be used as a reference for selection, for example, p2 = 0.5, q2 = 1.5.

[0196] Gain : Affects the convergence behavior of speed / heading tracking error. Initially, it can be set to be equivalent to or slightly larger than the guidance law gain, such as... .

[0197] Controller reaching law parameters and the upper boundary of disturbance :

[0198] Usually, p is chosen. s =0.5, g s =1.5.

[0199] These determine the speed at which the system tends towards the sliding surface. Increasing these values ​​can accelerate convergence, but may lead to excessive control inputs or chattering. Recommended initial values... .

[0200] This is an estimate of the upper bound of the disturbance. The approximate range of the disturbance can be obtained through offline simulation analysis or system identification, with a certain margin. For example, if the disturbance amplitude is estimated to be within 5N, then E can be set as... u = 8.

[0201] Flutter suppression parameters :

[0202] :control The linear region range. The smaller, The closer a function is to a sign function, the stronger its robustness, but the increased potential risk of flutter. The larger the value, the smoother the control, but the resistance to interference decreases slightly. Typical values ​​are between 0.01 and 0.5. =0.1.

[0203] Fault tolerance compensation module parameters , and :

[0204] , : Determines the adjustment speed of the actuator efficiency factor estimate. It is recommended to set the initial value to . = =0.5. If the fault estimation response is slow, it can be increased appropriately; if the estimated value fluctuates, it can be decreased appropriately.

[0205] Small constants to prevent division by zero are usually taken as... =0.01~0.05. Too small Numerical risks still exist when the value is close to zero; An excessively large value will lead to insufficient compensation in the reconfigured control law. Recommendation: =0.01.

[0206] Initial values ​​for fault estimation: usually set as follows This indicates that the initial assumption is that the executor is healthy.

[0207] Example 3: Simulation Verification and Performance Analysis

[0208] This embodiment uses the MATLAB / Simulink simulation platform to numerically verify the method of the present invention and compare it with traditional methods to highlight its superiority.

[0209] Simulation settings:

[0210] AUV Model: Using parameters of a certain type of underactuated AUV, m 11 =12kg, m 22 =18kg, m 33 =8kg⋅m 2 , d 11 =7⋅kg / s, d 22 =10kg / s, d 33 =5kg⋅m 2 / s.

[0211] Disturbance: Incorporating time-varying marine environmental disturbances:

[0212] .

[0213] Expected trajectory:

[0214] Circular trajectory: , , .

[0215] Straight-curve combined trajectory: used to verify more complex tracking scenarios.

[0216] Initial state: The AUV is initially located at (x0, y0, ψ0)=(−5,−5,0) with zero velocity.

[0217] Controller parameters: Set according to the principles of Example 2.

[0218] Fault scenario: To verify the fault-tolerant control performance, the following actuator fault scenario was set in the simulation: at t = 40s, the efficiency of the oscillating thruster suddenly drops to =0.7 (i.e., a 30% efficiency loss); at t = 80s, the efficiency of the steering servo suddenly drops to 0.7. =0.8 (i.e., a 20% efficiency loss)

[0219] Simulation results and analysis:

[0220] Tracking effect:

[0221] Figure 2 The tracking performance under a circular desired trajectory is demonstrated. The actual trajectory of the method of this invention (solid red line) closely matches the desired trajectory (dashed blue line), with minimal tracking deviation even in regions of varying curvature. In contrast, a traditional backstepping method based on linearized sideslip angle compensation (dashed green line) is introduced. It can be seen that the traditional method exhibits significant tracking lag and deviation in the initial stage and on curved segments. This visually demonstrates the high-precision tracking capability of the method of this invention.

[0222] Position tracking error convergence:

[0223] Figure 3 Displays the position tracking error in the carrier coordinate system. and The time-domain response of both values ​​is shown. It can be seen that both rapidly decay from their initial values ​​and converge to a very small neighborhood close to zero (<0.1m) within 20 seconds, remaining stable throughout the simulation without divergence or continuous oscillation. This verifies that the fixed-time guidance law proposed in this invention can ensure rapid and accurate convergence of position errors.

[0224] Internal state response:

[0225] Figure 4 Demonstrates oscillation speed and heading angle The oscillation velocity u can smoothly track the time-varying commands generated by the guidance law. Heading angle It exhibits approximately linear growth (due to the need for continuous turning on a circular trajectory) and closely tracks the desired course. Both curves are smooth and free of high-frequency chatter, proving that the fixed-time sliding mode controller effectively suppresses disturbances while significantly reducing control chatter through the tanh function, thus ensuring the smoothness of actuator movements.

[0226] Observer performance:

[0227] Figure 5 This is a key innovation verification. Although the sway velocity v (blue dashed line) is not directly measured, the estimated value output by the reduced-order extended observer is... (The solid red line) accurately and smoothly reproduces the true dynamic change trend. The estimation error is small, and there is no large hysteresis or distortion due to the lack of direct measurement. This fully demonstrates the effectiveness of RESO, successfully replacing expensive lateral velocity sensors and providing reliable information for upper-level guidance.

[0228] Robustness testing:

[0229] During the simulation (e.g., t=50s), artificially increase the amplitude of the disturbance or introduce AUV model parameters (e.g.) The simulation results show that the tracking error under the method of this invention exhibits only small and brief fluctuations, which then quickly recover to the convergent state. In contrast, the comparative method shows a larger and more persistent deviation. This demonstrates that the method of this invention has strong robustness to model uncertainties and external disturbances.

[0230] Convergence time independence verification:

[0231] Change the initial position of the AUV (e.g., set it to...) The simulation was then repeated. The results show that, although the initial errors are different, the convergence time of the system state (the time it takes for the error to enter the steady-state small neighborhood) is basically consistent with the results in the previous example, both within the preset time upper bound. This preliminarily verifies the fixed-time convergence characteristic, that is, the convergence speed does not depend on the initial conditions.

[0232] Example 4: Hardware-in-the-Loop (HIL) Simulation and Engineering Implementation Considerations

[0233] This embodiment explores the issues that need to be considered when applying the method of the present invention to engineering practice and conducts preliminary verification.

[0234] Discretization implementation:

[0235] The control law described above is in continuous-time form. In practical digital controllers, it needs to be discretized. The first-order Euler method or Tustin transform is recommended. Taking the observer as an example, its discretized form is:

[0236]

[0237] in For the control cycle. The differential terms in the guidance law and controller (e.g.) The results must be obtained using differential or observer methods, and care should be taken to avoid noise amplification.

[0238] Discretization of the fault-tolerant control module:

[0239] For the discrete implementation of the adaptive law for fault diagnosis, the forward Euler method is recommended. To prevent the estimated value from exceeding the physical range (i.e. >1 or If ≤0), a limiting logic needs to be added to the code: if >1, then let =1; if < Then let = Similarly, handle it. The division operation in the reconstruction law must ensure that the denominator ( The value is not zero, and the above limiting logic has already guaranteed this condition.

[0240] Calculation of load analysis:

[0241] The calculations involved in the method of this invention mainly include: matrix operations ( ), exponentiation ( It can perform trigonometric functions (arctan, cos) and simple algebraic operations. On modern AUVs, using commonly used embedded processors (such as ARM Cortex-A series and DSP), the computational load is well within acceptable limits when operating at a control frequency of 100Hz.

[0242] Sensor requirements:

[0243] The method of this invention only requires:

[0244] Positioning sensors: GPS (surface), USBL / LBL (underwater), or a combination of inertial navigation system (INS) and Doppler log (DVL) for obtaining... .

[0245] Attitude and angular velocity sensor: IMU, used to acquire (Some IMUs may also provide this service) However, this invention does not depend on it. (measurement).

[0246] Expected trajectory : Preloaded by the task planning system or generated online.

[0247] The elimination of the need for dedicated lateral velocity sensors (such as the lateral channel of DVL) reduces hardware costs and system complexity. Simultaneously, the fault diagnosis module requires no additional actuator status sensors, utilizing only existing control commands and sliding surface information to achieve fault estimation, further reducing hardware dependence.

[0248] Actuator saturation handling:

[0249] Although smoothness is considered in the guidance law through dynamic gain E, and the fault-tolerant reconfiguration law can compensate for efficiency loss, reconfiguration control instructions still need to be added to the actual code. , The amplitude is limited to conform to the physical constraints of the thruster. When the efficiency loss is too large (e.g. When <0.5), even Even if the saturation limit is reached, it may still be impossible to fully compensate for the fault. In this case, a higher-level safety strategy such as task refactoring or emergency ascent should be triggered.

[0250] Hardware-in-the-loop (HIL) simulation:

[0251] To further verify the feasibility of the project, a HIL simulation platform can be built. The control algorithm of this invention can be deployed on a real AUV onboard computer (such as a ROS-based industrial computer), and the control algorithm output... , Given a real-time running AUV dynamics model (running on another high-performance computer or real-time simulator), the model calculates the state. Feedback is transmitted to the onboard computer via a simulated sensor interface. In HIL simulations, actuator fault injection can be simulated (e.g., by injecting faults into the model via software). The value was changed from 1 to 0.7 to verify the real-time performance and effectiveness of the fault-tolerant control module in a real computing environment. The HIL simulation results are expected to be largely consistent with the pure digital simulation results, further confirming the engineering practical value of this invention.

[0252] In summary, this invention, through the cascaded design of a reduced-order extended observer, an adaptive fixed-time guidance law, and a fixed-time sliding mode controller, forms a complete, efficient, and robust underactuated AUV trajectory tracking control solution. Multiple embodiments comprehensively and thoroughly illustrate the specific implementation of this invention, from theoretical design and parameter tuning to performance simulation and engineering implementation, fully demonstrating its significant advantages in improving tracking accuracy, enhancing robustness, ensuring fast convergence, and reducing hardware dependence.

[0253] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0254] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A fixed-time fault-tolerant trajectory tracking control method for underactuated AUVs based on a reduced-order extended observer, characterized in that, Includes the following steps: S1. Establish a horizontal three-degree-of-freedom kinematic and dynamic model of the underactuated autonomous underwater vehicle (AUV), and define the position tracking error based on the carrier coordinate system; S2. Design a reduced-order extended state observer to estimate the unmeasurable sway velocity online in real time based on measurable position tracking error information, and estimate the composite disturbance that integrates model uncertainty and external environmental disturbance. S3. Design an adaptive fixed-time guidance law. Using the sway velocity estimated by the reduced-order extended state observer, and by introducing a double power convergence term and adaptive parameters, generate the desired command for the sway velocity and heading angle. S4. Design a fixed-time sliding mode dynamic controller. For the desired command generated by the guidance law, design fixed-time sliding surfaces for sway velocity and heading angle tracking error respectively, and derive the actuator nominal control law including disturbance compensation term. S5. Design an actuator fault diagnosis and fault-tolerant compensation module to estimate the actuator efficiency loss factor of the sway and steering channels online, and reconstruct the control law to achieve fixed-time fault-tolerant trajectory tracking. S6. Input the calculated control force and torque commands into the AUV's actuator to drive the AUV to track the desired trajectory.

2. The method according to claim 1, characterized in that, In step S1, the three-degree-of-freedom kinematic model of the horizontal plane is as follows: ， in,( () represents the position in the inertial coordinate system. For heading angle, , , These are the sway velocity, roll velocity, and bow angular velocity in the carrier coordinate system, respectively. It is a rotation matrix; The dynamic model, considering the uncertainties in hydrodynamic parameters and external disturbances, is expressed as follows: ， in, The inertia matrix includes the added mass. For the Coriolis and centripetal force matrices, Here is the damping matrix. , To control the input, For lumped disturbances; The position tracking error and Defined in the carrier coordinate system as: ， in,( ) represents the position of the desired trajectory.

3. The method according to claim 2, characterized in that, In step S2, the equation of the reduced-order extended state observer is: ， in, For sway speed The estimated value, is the observer gain, and p is an intermediate variable. Let be the reference velocity constructed from the differential of the desired trajectory, and >

0.

4. The method according to claim 3, characterized in that, In step S3, the desired oscillation velocity generated by the adaptive fixed-time guidance law... and expected heading angle for: ， ， in, For reference heading angle, , > 0, β1> 0, q1 > 1 is a design parameter. , , > 1 is a constant; The intermediate variable Θ is defined as follows: ， Where ω is the adaptive compensation term, and its adaptive law is: , >0 represents adaptive gain; Ξ is a variable representing the dynamic gain adjustment parameter. .

5. The method according to claim 4, characterized in that, In step S3, the guidance law is improved by introducing a smoothing parameter. Ensure that |Θ| ≤ 1, the Defined as: ， in, , , It is a positive number.

6. The method according to any one of claims 1-5, characterized in that, In step S4, the tracking error of the sway velocity is addressed. and heading angle tracking error The designed fixed-time sliding surfaces are as follows: ， ， in, .

7. The method according to claim 6, characterized in that, In step S4, the derived nominal control law of the actuator is... and for: ， in, and This is the nominal nonlinear term in the dynamic model. For control parameters, and These are the upper limits of the disturbances in the oscillation and turning channels, respectively. It is the hyperbolic tangent function. It is a small positive number.

8. The method according to claim 1, characterized in that, In step S5, the actuator fault model is as follows: The actual control input is represented as: Where ρ u , ρ r ∈(0, 1] represents the unknown actuator efficiency factor. An actuator efficiency factor of 1 indicates a healthy state, while a factor of less than 1 indicates a partial failure.

9. The method according to claim 8, characterized in that, In step S4, based on the output of the reduced-order extended state observer (step S2), an adaptive law for fault diagnosis is designed to estimate the efficiency loss factor online. Wherein: γ u , γ r > 0 represents adaptive gain; s u , s ψ The fixed-time sliding surface as described in claim 6; Ψ u ,Ψ r As an intermediate variable, it is defined as: 。 10. The method according to claim 9, characterized in that, In step S5, the reconstructed fault-tolerant control law is: Where δ > 0 is a small constant to prevent division by zero; This refers to the nominal control law.

11. The method according to claim 1, characterized in that, The method constructs a cascaded fault-tolerant control architecture through the reduced-order extended state observer, adaptive fixed-time guidance law, fixed-time sliding mode controller, and actuator fault diagnosis and fault-tolerant compensation module, so that the entire closed-loop system still has fixed-time stability under actuator partial failure, that is, the upper bound of the convergence time of the system state is independent of the initial state and the degree of failure.

12. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1 to 11.

13. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 11.

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