Underwater autonomous vehicle trajectory tracking control method based on fractional order sliding mode control and extended state observer

Abstract

The invention relates to an autonomous underwater vehicle (AUV) trajectory tracking compound control method based on fractional order sliding mode control and an extended state observer. The method is used for high-precision trajectory tracking of an AUV in a complex and uncertain environment. The method comprises the following steps: establishing an AUV six-degree-of-freedom dynamic model; converting the nonlinear model into a linear form through feedback linearization; designing an extended state observer to perform real-time estimation and compensation on lumped disturbance including model uncertainty and external disturbance; designing a fractional order sliding mode controller to improve the tracking precision and suppress buffeting; a Levant differentiator is introduced to provide an accurate differential signal for the control law; and constructing a composite control law and completing the stability analysis of the closed-loop system. Compared with traditional control, the method can improve the dynamic response speed of trajectory tracking, has higher interference suppression capability and robustness, and is suitable for detection and operation scenes of the autonomous underwater vehicle with various uncertain factors such as hydrodynamic coupling, parameter perturbation and external interference.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of underwater robot control, and particularly relates to a control method for trajectory tracking of an underwater autonomous vehicle (AUV), and particularly relates to a high-precision trajectory tracking control method under a feedback linearization framework, which combines disturbance estimation and compensation of an extended state observer (ESO), chattering suppression of a fractional order sliding mode control (FOSMC), and accurate derivative signal generation of a Levant differentiator. BACKGROUND

[0002] AUVs play an increasingly important role in tasks such as ocean resource exploration, environmental monitoring, and seabed mapping. However, AUVs face multiple challenges in actual operations: the hydrodynamic characteristics exhibit strong coupling and nonlinearity, making it difficult to establish an accurate dynamic model; there are problems such as unmodeled dynamics and parameter perturbation in the system; and external environmental disturbances (such as ocean currents and waves) also need to be addressed. These uncertainties seriously restrict the trajectory tracking accuracy and operational reliability of AUVs.

[0003] Existing AUV control methods mainly include active disturbance rejection control (ADRC) and sliding mode control (SMC). Although ADRC can estimate and compensate disturbances, its observer performance decreases when there is a significant mismatch in model parameters, leading to poor control results and large overshoot. Traditional integer order SMC has strong robustness, but its inherent high-frequency switching characteristics cause chattering, affecting actuator life and control accuracy. Although FOSMC can suppress chattering to some extent, its anti-interference ability is limited when facing strong external disturbances and complex model uncertainties. Therefore, there is a need for an AUV trajectory tracking control method that can effectively handle model uncertainties, compensate external disturbances in real time, and ensure tracking accuracy and suppress chattering. SUMMARY

[0004] The present application aims to solve the problems of low trajectory tracking accuracy and insufficient anti-interference ability of underwater autonomous vehicles in complex uncertain environments, and proposes an underwater autonomous vehicle trajectory tracking control method based on fractional order sliding mode control and an extended state observer. This method processes the system nonlinearity through feedback linearization, estimates and compensates the lumped disturbance in real time using an extended state observer, uses a fractional order sliding mode controller to improve tracking accuracy and suppress chattering, and introduces a Levant differentiator to provide a high-precision derivative signal for the control law, thereby achieving high-performance trajectory tracking of AUVs in complex underwater environments.

[0005] To achieve the above purpose, the technical solutions provided by the present application are as follows: Step 1: Establish a six-degree-of-freedom dynamics and kinematics model of the AUV, considering model parameter uncertainty and external disturbance τ dUnder the condition of the presence of compound disturbances, a kinetic error model containing compound disturbances is constructed: Where: v is the velocity vector in the body coordinate system, η is the position and attitude vector in the inertial coordinate system, M is the total mass matrix, C(v) is the centripetal force and Coriolis force matrix, D(v) is the hydrodynamic damping matrix, g(η) is the static water force and torque vector that the AUV receives, Δ(·) is the deviation between the actual value and the nominal value, τ p is the control input, is the compound disturbance containing model uncertainty τ um and external disturbances τ d (current, wave, cable force, etc.); In addition, is the relationship between the geodetic coordinate system and the body coordinate system, where Where φ, θ and ψ are the roll angle, pitch angle and yaw angle, respectively; Step 2: The nonlinear AUV kinetic model is converted into a linear form through feedback linearization processing, and the feedback linearization term τ1 is defined to compensate for the known nonlinear dynamics: The linearized system model is obtained: Where: τ η = J(η) -T τ p , and and are positive definite matrices, τ c = τ p - τ1, f T = f un + f d is the total disturbance, Step 3: An extended state observer (ESO) is designed for the linearized system model to extend the total disturbance f T into a new state variable for real-time estimation: Where: h1 = η, h3 = f T , is the estimated value of the corresponding state, is the position estimation error, and βi Observer gain; Step 4: Design the fractional order sliding mode controller (FOSMC), build the sliding surface containing fractional order differential to improve the convergence performance and suppress chattering: Where: e = η d -η is the tracking error, η d is the desired trajectory, c1, c2 are positive real numbers, μ is the fractional order and 0 < μ < 1, D μ-1 represents the fractional order differential operator; Step 5: Introduce Levant differentiator to provide the required high-precision differential signal for the control law, estimate the derivatives of various orders of system states through the sliding mode differentiator structure: In the formula, r is the input signal to be differentiated; λ1, λ2, λ3 and λ4 are adjustment coefficients for adjusting the performance of the differentiator; m1, m2, m3 and m4 are respectively the estimated values of the zero-order, first-order, second-order and third-order derivatives of the signal, and sign(·) is the sign function, where m2 can be directly used to replace the state quantity Adapt the related formula to the use requirements of the state quantity; Step 6: Integrate the feedback linearization term τ1, the disturbance compensation term and the fractional order sliding mode control term τ3 to build the final composite control law: τ = τ1 + τ2 + τ3 Where: k, ε are the parameters of the sliding mode controller; Step 7: Based on the Lyapunov stability principle, select the Lyapunov function containing the sliding surface and the observation error, and analyze the stability of the closed-loop system composed of ESO and FOSMC, to prove that the system state is uniformly ultimately bounded and the tracking error converges under the condition that the disturbance is bounded.

[0006] Further, the ESO design of step 3 has a workflow including the following steps: Step 3.1: Define the state variable h1 = η, h3 = f T , convert the system to state space form: Step 3.2: Design the linear ESO structure: Step 3.3: Determine the observer gain using the pole placement method, and configure all poles at -ω o : where ω o > 0 is the observer bandwidth; Step 3.4: Based on the observer's estimated value of total disturbance Construct the disturbance compensation term:

[0007] Further, the fractional order sliding mode controller design of step 4, the work flow includes the following steps: Step 4.1: Define the trajectory tracking error e = η d - η and its derivative where η d is the desired trajectory; Step 4.2: Build a fractional order sliding surface: Where: c1 > 0, c2 > 0 is the sliding surface parameter, μ ∈ (0, 1) is the fractional order; Step 4.3: Design the control law based on the exponential reaching law: Where: k > 0, ε > 0 is the reaching law parameter; Step 4.4: Derive the control input τ3 in combination with the system dynamics model:

[0008] Further, the Levant differentiator design of step 5, the work flow includes the following steps: Step 5.1: Build the Levant differentiator system equation: Step 5.2: Take the AUV position signal η as input r, estimate its first order derivative in real time through the differentiator Step 5.3: Adjust the differentiator parameters λ1, λ2, λ3 and λ4 to balance the tracking accuracy and noise suppression performance; Step 5.4: Use the estimated for the calculation of feedback linearization term τ1 and fractional order sliding mode controller τ3.

[0009] Further, the stability analysis method of step 7, the work flow includes the following steps: Step 7.1: Select the Lyapunov function: Where: s is the sliding surface vector, e = [e1, e2, e3] T is the observer error vector, P is a positive definite symmetric matrix; Step 7.2: Derive the Lyapunov function and substitute the control law and observer error dynamics: Step 7.3: Scale by Young's inequality and parameter conditions to obtain: where α > 0, δ2 is the upper bound of the disturbance rate of change; Step 7.4: Prove that when the system state is uniformly ultimately bounded, and when δ2 → 0, the system is asymptotically stable. The underwater autonomous vehicle trajectory tracking control method based on fractional order sliding mode control and extended state observer proposed by the application has the following advantages compared with the prior art:

[0010] 1. Improve trajectory tracking accuracy and response speed: To solve the chattering phenomenon of traditional sliding mode control and the problem of large overshoot of active disturbance rejection control, a fractional order sliding mode controller is introduced, and a fractional order derivative term is added in the sliding mode surface design to realize fast convergence and smooth adjustment of tracking error. Compared with traditional integer order sliding mode control and active disturbance rejection control, this method realizes no overshoot tracking in step response, smaller tracking error in sinusoidal and circular trajectory tracking, shorter adjustment time, and faster dynamic response; 2. Enhance the robustness and anti-interference ability of the system to compound disturbance: To solve the problem of coexistence of model uncertainty, parameter perturbation and external disturbance in underwater environment and difficult accurate modeling, an extended state observer is designed to extend the lumped disturbance to a new system state for real-time estimation and compensation. Simulation experiments show that under the condition of existing external continuous disturbance and significant model mismatch (up to 500%), this method can still maintain stable tracking of trajectory, while traditional active disturbance rejection control cannot converge under this condition. This method effectively suppresses the influence of disturbance on tracking performance and exhibits strong robustness; 3. Ensure the engineering realizability and real-time performance of the control algorithm: To solve the problem of dependence of feedback linearization and sliding mode controller on system state derivative signal, Levant differentiator is introduced to provide high-precision and strong-robustness derivative signal estimation for the control law, avoiding dependence on precise speed sensor and reducing system hardware cost and complexity. At the same time, the observer gain is designed by pole placement method to ensure the balance between observer bandwidth and system noise suppression ability, making the algorithm easier to deploy and apply in actual engineering. BRIEF DESCRIPTION OF DRAWINGS

[0011] Figure 1 The complete flowchart of the underwater autonomous vehicle trajectory tracking control method based on fractional order sliding mode control and extended state observer of the application is shown in the figure. ​Figure 2 The complete system control block diagram of the underwater autonomous vehicle trajectory tracking control method based on fractional order sliding mode control and extended state observer of the application; Figure 3 The schematic diagram of the inertial coordinate system and the carrier coordinate system; Figure 4 The tracking performance comparison diagram of the Levant differentiator on the AUV velocity signal Figure 5 The X-axis position tracking response curve diagram of the four controllers on the step reference signal under the accurate model; Figure 6 The Y-axis position tracking response curve diagram of the four controllers on the step reference signal under the accurate model; Figure 7 The Z-axis position tracking response curve diagram of the four controllers on the step reference signal under the accurate model; Figure 8 The position tracking response curve diagram of the four controllers on the step reference signal under the noise-containing working condition; Figure 9 The position tracking response curve diagram of the four controllers on the sinusoidal reference signal under the accurate model; Figure 10 The position tracking response curve diagram of the four controllers on the sinusoidal reference signal under the noise-containing working condition; Figure 11 The tracking trajectory comparison diagram of the four controllers on the circular reference trajectory under the accurate model; Figure 12 The tracking trajectory comparison diagram of the four controllers on the circular reference trajectory under the noise-containing working condition; Figure 13 The tracking trajectory comparison diagram of the four controllers on the circular reference trajectory under the 50% model uncertainty; Figure 14 The tracking trajectory comparison diagram of the four controllers on the circular reference trajectory under the noise-containing 50% model uncertainty; Figure 15 The tracking trajectory comparison diagram of the three controllers (SMC, FOSMC, FOSMC-ESO) on the circular reference trajectory under the 500% model uncertainty (ADRC has failed); Figure 16 The Bode diagram of the discrete approximation implementation of the fractional order differential operator and the comparison diagram with the theoretical value; Figure 17 The waveform diagram of the random noise signal injected in the simulation. DETAILED DESCRIPTION

[0012] ​The application will be described in detail below with specific embodiments. The following examples will help those skilled in the art to further understand the application, but do not limit the application in any form. It should be pointed out that for those skilled in the art, without departing from the concept of the application, a number of modifications and improvements can be made. These belong to the protection scope of the application. Example 1

[0013] The application discloses a trajectory tracking control method for an underwater autonomous vehicle based on a fractional order sliding mode control and an extended state observer, comprising the following steps: Step 1: Establishing a six-degree-of-freedom dynamics and kinematics model of an AUV, and constructing a dynamics error model containing a compound disturbance under the condition of considering model parameter uncertainty and external disturbance τ d Wherein, ν is a velocity vector in a body coordinate system, η is a position and attitude vector in an inertial coordinate system, M is a total mass matrix, C(ν) is a centripetal force and Coriolis force matrix, D(ν) is a hydrodynamic damping matrix, g(η) is a static water force and torque vector received by the AUV, Δ(·) is a deviation between an actual value and a nominal value, τ p is a control input, is a compound disturbance containing model uncertainty τ um and external disturbance τ d (current, wave, cable force, etc.); In addition, is a description of the relationship between the geodetic coordinate system and the body coordinate system, and here Wherein, φ, θ and ψ are roll angle, pitch angle and yaw angle, respectively; Step 2: The nonlinear AUV dynamics model is converted into a linear form through feedback linearization processing, and a feedback linearization term τ1 is defined to compensate for the known nonlinear dynamics: The linearized system model is obtained as follows: Wherein: τ η =J(η) -T τ p , and and are positive definite matrices, τ c =τ p ​-τ1,f T =f un +f d For the total disturbance, Step 3: Design an extended state observer (ESO) for the linearized system model, and measure the total disturbance f. T Extend to real-time estimation of new state variables: Where: h1 = η, h3 = f T , This is an estimate of the corresponding state. For the position estimation error, β i For observer gain; Step 4: Design a fractional-order sliding mode controller (FOSMC) and construct a sliding surface containing fractional derivatives to improve convergence performance and suppress chattering. Where: e = η d -η represents the tracking error, η d Let D be the desired trajectory, c1 and c2 be positive real numbers, μ be a fractional order and 0 < μ < 1. μ-1 Represents a fractional differential operator; Step 5: Introduce a Levant differentiator to provide the required high-precision differential signal for the control law, and estimate the derivatives of the system state through the sliding mode differentiator structure: In the formula, r is the input signal to be differentiated; λ1, λ2, λ3, and λ4 are adjustment coefficients used to adjust the performance of the differentiator; m1, m2, m3, and m4 are the estimated values ​​of the zeroth, first, second, and third derivatives of the signal, respectively; sign(·) is the sign function, where m2 can be directly used to replace the state variables. Adapt to the relevant formulas to meet the usage requirements of this state variable; Step 6: Integrate the feedback linearization term τ1 and the disturbance compensation term And the fractional sliding mode control term τ3, to construct the final composite control law: τ=τ1+τ2+τ3 in: k and ε are sliding mode controller parameters; Step 7: Based on the Lyapunov stability principle, select a Lyapunov function that includes the sliding surface and observation error, and perform stability analysis on the closed-loop system composed of ESO and FOSMC. Prove that under the condition of bounded perturbation, the system state is consistent and eventually bounded and the tracking error converges.

[0014] Furthermore, the ESO design described in step 3 includes the following workflow steps: Step 3.1: Define the state variable h1 = η, h3 = f T The system is converted into a state-space form: Step 3.2: Design the linear ESO structure: Step 3.3: Determine the observer gain using the pole placement method, placing all poles at -ω. o Location: Where ω o >0 represents the observer bandwidth; Step 3.4: Estimation of total disturbance based on observers Construct disturbance compensation terms:

[0015] Furthermore, the workflow of the fractional-order sliding mode controller design described in step 4 includes the following steps: Step 4.1: Define the trajectory tracking error e = η d -η and its derivative Where η d For the desired trajectory; Step 4.2: Construct the fractional-order sliding surface: Where: c1>0, c2>0 are sliding surface parameters, and μ∈(0,1) is the fractional order; Step 4.3: Design a control law based on the law of exponential reaching: Where: k > 0, ε > 0 are the parameters of the reaching law; Step 4.4: Derive the control input τ3 using the system dynamics model:

[0016] Furthermore, the Levant differentiator design described in step 5 includes the following steps in its workflow: Step 5.1: Construct the equations for the Levant differentiator system: Step 5.2: Using the AUV position signal η as input r, estimate its first derivative in real time using a differentiator. Step 5.3: Adjust the differentiator parameters λ1, λ2, λ3 and λ4 to balance tracking accuracy and noise suppression performance; Step 5.4: Calculate the estimated... Used for the calculation of the feedback linearization term τ1 and the fractional sliding mode controller τ3.

[0017] Furthermore, the stability analysis method described in step 7 includes the following steps in its workflow: Step 7.1: Select the Lyapunov function: Where: s is the sliding mode surface vector, e = [e1, e2, e3] T Let P be the observer error vector, and let P be a positive definite symmetric matrix. Step 7.2: Differentiate the Lyapunov function and dynamically substitute the control law and observer error into it: Step 7.3: By scaling using Young's inequality and parameter conditions, we obtain: Where α > 0, and δ2 is the upper bound of the rate of change of the disturbance; Step 7.4: Prove that when hour The system state is uniformly bounded, and the system is asymptotically stable when δ2→0.

[0018] The following simulation is performed on the underwater autonomous vehicle trajectory tracking control method based on fractional sliding mode control and extended state observer disclosed in this application to verify its effectiveness and feasibility. Figure 2 The diagram shows the complete system control block diagram of the control method proposed in this invention, illustrating the collaborative architecture of feedback linearization, extended state observer, fractional sliding mode controller, and Levant differentiator. Figure 3 A schematic diagram of the inertial coordinate system and the carrier coordinate system is provided, clarifying the spatial relationship used in AUV motion modeling. Three reference trajectories—step, sinusoidal, and circular—were set up in the simulation, and comparative analyses were conducted with Active Disturbance Rejection Control (ADRC), Sliding Mode Control (SMC), and Forward Unstable Oriented Mode Control (FOSMC) under conditions of noise-free operation and significant model uncertainty (50% and 500%). The main physical parameters of the AUV dynamic model used in the simulation are shown in Table 1, the relevant hydrodynamic coefficients are shown in Table 2, and the key controller parameter settings are shown in Table 3. Figure 4 Demonstrates the Levant differentiator for AUV speed signals The comparison of tracking performance verified the feasibility of providing high-precision differential signals for control laws. Table 1 Main physical parameters of AUV Parameter Value Unit Dimension 380×267×165 mm Weight 55 N Submersion depth 100 m Moment of inertia [0.12,0.25,0.2] [kg·m 2 ]]> Maximum speed 1.5 m / s Table 2 Hydrodynamic coefficients related to AUV Table 3 Parameter settings for different controllers

[0019] Simulation results are as follows Figures 5 to 15 The corresponding performance table is shown below. Figures 5 to 7 The position tracking response under a step reference trajectory is demonstrated. The results show that, under the exact model assumptions, ADRC has the shortest rise time (approximately 0.3 s) but produces an overshoot of up to 21.3%; SMC and FOSMC have smaller overshoots (0.5%), but both fail to converge to the target value after an external disturbance is injected at 5 s; the proposed FOSMC-ESO method maintains zero overshoot while having a shorter settling time (approximately 0.8 s) than SMC and FOSMC, and exhibits the best disturbance suppression capability after a disturbance occurs, with the smallest position deviation range (only ±0.001 m) and the fastest recovery. Figure 8 The step tracking performance under noisy conditions was demonstrated, and all controllers exhibited consistent noise suppression capabilities.

[0020] Figure 9 The tracking error under a sinusoidal reference trajectory is shown. It is evident that ADRC exhibits significant tracking error (up to 2.59m) due to the degraded observer performance under model mismatch; while FOSMC-ESO demonstrates the smallest tracking error range (less than ±7×10⁻³) under external perturbations. m This verified its excellent tracking accuracy and anti-interference ability.

[0021] Figures 11 to 15 The performance of circular trajectory tracking and model robustness are demonstrated. Under an accurate model ( Figure 11 All four controllers can effectively track the trajectory. When the model has 50% uncertainty ( Figure 13 ADRC can still track, but its performance degrades, while FOSMC-ESO performs comparably to SMC and FOSMC, with good trajectory fit. When the model uncertainty increases to 500% ( Figure 15 ADRC has completely failed and cannot converge to the desired trajectory, while FOSMC-ESO, SMC, and FOSMC can still maintain stable tracking, with FOSMC-ESO exhibiting strong robustness similar to SMC and FOSMC. Furthermore, under various noisy operating conditions (…), Figure 8 , 10 (12, 14) FOSMC-ESO maintained good noise suppression capabilities.

[0022] In summary, the simulation results demonstrate that the FOSMC-ESO method proposed in this invention exhibits superior comprehensive performance in terms of tracking accuracy, anti-interference capability, model robustness, and noise suppression, especially in underwater environments with significant uncertainties, thus verifying the effectiveness and feasibility of the method. Figure 16 The comparison between the Bode plot of the discrete approximation of the fractional differential operator and the theoretical value proves the accuracy of the discrete approximation of the fractional differential term in the fractional sliding mode control. Figure 17 The waveform of the random noise signal injected in the simulation clarifies the noise input characteristics used to test the noise immunity performance of the controller in the simulation.

[0023] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions that combine any of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements are also considered within the scope of protection of this invention.

Claims

1. A trajectory tracking control method for underwater autonomous vehicles based on fractional-order sliding mode control and an extended state observer, applicable to high-precision trajectory tracking of underwater autonomous vehicles (AUVs) under uncertain environments such as hydrodynamic coupling, unmodeled dynamics, parameter perturbations, and external disturbances, characterized in that... The proposed method constructs a composite control structure within a feedback linearization framework, incorporating extended state observation, fractional sliding mode control, and precise differential signal generation. Based on feedback linearization, the nonlinear AUV dynamics model is transformed into a linear form. Furthermore, an extended state observer is introduced to estimate and compensate for lumped disturbances, including model uncertainties and external disturbances, in real time. A fractional sliding mode controller is further designed to improve tracking accuracy and suppress chattering, while a Levante differentiator is used to provide the required high-precision differential signal for the control law. Finally, the composite control law drives the AUV to achieve high-performance trajectory tracking under uncertain environments, thereby improving the system's tracking accuracy, robustness, and dynamic response performance under model mismatch, external disturbances, and noise conditions.

2. The underwater autonomous vehicle trajectory tracking control method based on fractional-order sliding mode control and extended state observer according to claim 1, characterized in that, The method includes the following steps: Step 1: Establish a six-degree-of-freedom dynamic and kinematic model of the AUV, considering the uncertainty of model parameters and external disturbances τ. d Under the given conditions, construct a dynamic error model that includes composite disturbances: Where: ν is the velocity vector in the body coordinate system, η is the position and attitude vector in the inertial coordinate system, M is the total mass matrix, C(ν) is the centripetal force and Coriolis force matrix, D(ν) is the hydrodynamic damping matrix, g(η) is the hydrostatic force and torque vector acting on the AUV, Δ(·) is the deviation between the actual value and the nominal value, and τ p To control the input, For models containing uncertainty τ um External interference τ d Complex interference from ocean currents, waves, cable tensions, etc. also, It describes the relationship between the geodetic coordinate system and the body coordinate system. Wherein, φ, θ, and ψ are the roll angle, pitch angle, and yaw angle, respectively; Step 2: Transform the nonlinear AUV dynamics model into a linear form through feedback linearization, defining a feedback linearization term τ1 to compensate for the known nonlinear dynamics: The linearized system model is obtained as follows: in: τ η =J(η) -T τ p , and and τ is a positive definite matrix. c =τ p -τ1,f T =f un +f d For the total disturbance, Step 3: Design an extended state observer (ESO) for the linearized system model, and measure the total disturbance f. T Extend to real-time estimation of new state variables: Where: h1 = η, h3 = f T , This is an estimate of the corresponding state. For the position estimation error, β i For observer gain; Step 4: Design a fractional-order sliding mode controller (FOSMC) and construct a sliding surface containing fractional derivatives to improve convergence performance and suppress chattering. Where: e = η d -η represents the tracking error, η d Let D be the desired trajectory, c1 and c2 be positive real numbers, μ be a fractional order and 0 < μ < 1. μ-1 Represents a fractional differential operator; Step 5: Introduce a Levant differentiator to provide the required high-precision differential signal for the control law, and estimate the derivatives of the system state through the sliding mode differentiator structure: In the formula, r is the input signal to be differentiated; λ1, λ2, λ3, and λ4 are adjustment coefficients used to adjust the performance of the differentiator; m1, m2, m3, and m4 are the estimated values ​​of the zeroth, first, second, and third derivatives of the signal, respectively; sign(·) is the sign function, where m2 can be directly used to replace the state variables. Adapt to the relevant formulas to meet the usage requirements of this state variable; Step 6: Integrate the feedback linearization term τ1 and the disturbance compensation term And the fractional sliding mode control term τ3, to construct the final composite control law: τ=τ1+τ2+τ3 in: k and ε are sliding mode controller parameters; Step 7: Based on the Lyapunov stability principle, select a Lyapunov function that includes the sliding surface and observation error, and perform stability analysis on the closed-loop system composed of ESO and FOSMC. Prove that under the condition of bounded perturbation, the system state is consistent and eventually bounded and the tracking error converges.

3. The underwater autonomous vehicle trajectory tracking control method based on fractional-order sliding mode control and extended state observer according to claim 2, characterized in that, The ESO design described in step 3 includes the following steps in its workflow: Step 3.1: Define the state variable h1 = η, h3 = f T The system is converted into a state-space form: Step 3.2: Design the linear ESO structure: Step 3.3: Determine the observer gain using the pole placement method, placing all poles at -ω. o Location: Where ω o >0 represents the observer bandwidth; Step 3.4: Estimation of total disturbance based on observers Construction of disturbance compensation terms:

4. The underwater autonomous vehicle trajectory tracking control method based on fractional-order sliding mode control and extended state observer according to claim 2, characterized in that, The fractional sliding mode controller design described in step 4 includes the following steps in its workflow: Step 4.1: Define the trajectory tracking error e = η d -η and its derivative Where η d For the desired trajectory; Step 4.2: Construct the fractional-order sliding surface: Where: c1>0, c2>0 are sliding surface parameters, and μ∈(0,1) is the fractional order; Step 4.3: Design a control law based on the exponential reaching law: Where: k > 0, ε > 0 are the approach law parameters; Step 4.4: Derive the control input τ3 using the system dynamics model:

5. The underwater autonomous vehicle trajectory tracking control method based on fractional sliding mode control and extended state observer according to claim 2, characterized in that, The Levant differentiator design described in step 5 includes the following steps in its workflow: Step 5.1: Construct the equations for the Levant differentiator system: Step 5.2: Using the AUV position signal η as input r, estimate its first derivative in real time through a differentiator. Step 5.3: Adjust the differentiator parameters λ1, λ2, λ3 and λ4 to balance tracking accuracy and noise suppression performance; Step 5.4: Calculate the estimated... Used for the calculation of the feedback linearization term τ1 and the fractional sliding mode controller τ3.

6. The underwater autonomous vehicle trajectory tracking control method based on fractional-order sliding mode control and extended state observer according to claim 2, characterized in that, The stability analysis method described in step 7 includes the following steps in its workflow: Step 7.1: Select the Lyapunov function: Where: s is the sliding mode surface vector, e = [e1, e2, e3] T Let P be the observer error vector, and let P be a positive definite symmetric matrix. Step 7.2: Differentiate the Lyapunov function and dynamically substitute the control law and observer error into it: Step 7.3: By scaling using Young's inequality and parameter conditions, we obtain: Where α > 0, and δ2 is the upper bound of the rate of change of the disturbance; Step 7.4: Prove that when hour The system state is uniformly bounded, and the system is asymptotically stable when δ2→0.

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