CN113110430A - Model-free fixed-time accurate trajectory tracking control method for unmanned ship - Google Patents

Abstract

The invention provides a model-free fixed-time accurate trajectory tracking control method for an unmanned ship, which comprises the following steps: constructing an USV model with input saturation and complex disturbance; designing a fixed-time lumped observer based on the constructed USV model; designing an adaptive auxiliary system based on the designed fixed-time lumped observer; designing a rapid nonsingular terminal sliding mode based on the designed self-adaptive auxiliary system; and designing a model-free fixed time accurate tracking control strategy based on the designed fixed time lumped observer, the self-adaptive auxiliary system and the fast nonsingular terminal sliding mode. The technical scheme of the invention can ensure that the unmanned ship which suffers from input saturation, complex environment disturbance and completely unknown model dynamics simultaneously tracks the expected track accurately in an expected time, obtains higher convergence speed and tracking precision, and solves the problems of singularity and low convergence speed in the traditional sliding mode strategy.

Description

A model-free fixed-time precise trajectory tracking control method for unmanned ships

technical field

The invention relates to the technical field of fast and precise tracking control of unmanned ships, in particular, to a model-free fixed-time precise trajectory tracking control method for unmanned ships.

Background technique

In recent years, unmanned surface vehicles (USVs) have been widely used in engineering practice and scientific experiments such as water quality monitoring, ocean exploration, and underwater topographic measurement. Due to the above reasons, more and more scholars pay attention to the trajectory tracking of USV, and have achieved some results in this field. In order to ensure that the USV can achieve accurate trajectory tracking under complex ocean conditions, many researchers have designed suitable trackers considering external disturbances, system uncertainties, and actuator dynamics. Due to the good convergence performance and strong anti-disturbance and anti-uncertainty ability, the sliding mode control (SMC) method is adopted to solve the precise trajectory tracking problem. For example, an adaptive SMC method combining a radiation basis function neural network and a disturbance observer is used to deal with the uncertainties and complex disturbances of the USV model, achieving fast response, outstanding convergence performance, and high-precision tracking.

Considering the dynamic uncertainties and time-varying disturbances, a fast non-singular value SMC method is developed for USV to track the reference trajectory and obtain faster convergence than existing non-singular value SMC manifolds. Utilizing the strategy of event-triggered SMC tracking system, the method has external disturbances, which can reduce control updates and guarantee the asymptotic stability of the system and the optimization of resource usage and cost. Furthermore, the SMC method is designed to receive finite-time convergence. A finite-time strategy combined with command filtering SMC has been used for autonomous airships in pursuit of better tracking performance. However, the aforementioned literature ignores the uncertainty of the system, although they achieve good performance in terms of convergence rate. Considering the parameter uncertainty, disturbance and actuator failure of USV trajectory tracking system, a novel finite-time fault-tolerant tracking controller combining adaptive control and time-varying SMC is proposed. The controller can ensure that the USV tracks the reference trajectory for a limited time and does not require known inertial parameters. The researchers separately developed a finite-time SMC method and a finite-time control scheme based on negative homogeneous control combined with observational techniques to remove the negative effects of uncertainty and time-varying disturbances on the trajectory. In addition, the finite-time scheme can achieve good convergence speed, but the convergence time is affected by the initial state. Aiming at this problem, a fixed-time control scheme is proposed, and many achievements have been made in the field of control. A novel fixed-time non-singular sliding-mode manifold is designed based on the double-limit homogeneous theory, which realizes the trajectory tracking of the UAV within the set time, but the upper limit of the disturbance needs to be known in advance. Considering the state constraints and system uncertainty of UAVs, Fu et al. developed a new obstacle Lyapunov function to ensure that the fixed-time stability does not violate the state constraints.

To further deal with the adverse effects of disturbances, researchers have proposed several methods, such as disturbance observers, adaptive fuzzy control, and intelligent learning algorithms. For example, the researchers designed a self-constructing neural that online fuzzy approximation lumped unknowns. Some scholars have studied a disturbance observer to identify and compensate disturbances. In addition, some scholars have designed a fixed-time disturbance observer, which can accurately identify complex disturbances within a fixed time. In practice, actuator saturation often occurs in control systems due to physical limitations. If the actuator is in a saturated state for a long time, it will damage the actuator and seriously reduce the trajectory tracking accuracy. Researchers have used barrier Ryapunov and nonlinear observers to deal with the effects of actuator saturation and disturbance. Considering parameter uncertainty, unknown disturbances, and actuator nonlinearity, the researchers address the input saturation problem by incorporating adaptive control methods. In addition, researchers have designed an auxiliary system to offset the effect of input saturation, but the scheme needs to ensure that the uncertainty is bounded. However, in the field of fixed-time trajectory tracking control of unmanned ships, the existing literature has not dealt with the effects of input saturation, which may significantly reduce the control quality and even cause system instability.

SUMMARY OF THE INVENTION

According to the technical problems raised above, a model-free fixed-time precise trajectory tracking control method for an unmanned ship is provided. The present invention mainly considers the USV model with input saturation and complex disturbance, and designs a fixed-time lumped uncertainty observer. Accurate and fast observation and compensation for it; design a fast non-singular terminal sliding mode with fixed time stability characteristics, and integrate the fixed time idea into the sliding mode control technology; design an adaptive auxiliary system to eliminate the input saturation effect The negative impact caused by the system; design a model-free fixed-time accurate trajectory tracking control strategy, so that the unmanned ship encountering complex ocean current disturbance, completely unknown system dynamics and input saturation can track the desired trajectory within a fixed time.

The technical means adopted in the present invention are as follows:

A model-free fixed-time precise trajectory tracking control method for an unmanned ship, comprising the following steps:

S1. Build a USV model with input saturation and complex perturbations;

S2. Design a fixed-time lumped observer based on the constructed USV model;

S3. Design an adaptive auxiliary system based on the designed fixed-time lumped observer;

S4. Based on the designed adaptive auxiliary system, design a fast non-singular terminal sliding mode;

S5. Based on the fixed-time lumped observer, the adaptive auxiliary system and the fast non-singular terminal sliding mode designed in the above steps S2-S4, a model-free fixed-time precise tracking control strategy is designed.

Further, the step S1 specifically includes:

S11. Consider input saturation and complex disturbances, and construct a USV model as follows:

v＝[u v r]^T表示附体坐标系中的速度向量，G(η,v)＝-C(v)v-D(v)表示系统动态，C(v)表示对角矩阵，

C(v)＝-C^T(v)；D(v)表示阻尼矩阵，

d＝MR^Tδ且δ＝[δ₁,δ₂,δ₃]^T表示复杂的时变扰动，M表示惯性，

M＝M^T＞0；τ表示控制输入受到执行器饱和的限制，

τ_i,max是执行器可以提供的最大扭矩，τ_c,i是理想的控制输入，i＝u,v,r；Among them, η=[xy ψ] ^T represents the position and heading in the earth coordinate system OXY,

v=[uvr] ^T represents the velocity vector in the attached coordinate system, G(η,v)=-C(v)vD(v) represents the system dynamics, C(v) represents the diagonal matrix,

C(v)=-C ^T (v); D(v) represents the damping matrix,

d=MR ^T δ and δ=[δ ₁ ,δ ₂ ,δ ₃ ] ^T represents complex time-varying disturbance, M represents inertia,

M=M ^T >0; τ indicates that the control input is limited by actuator saturation,

τ _i,max is the maximum torque that the actuator can provide, τ _c,i is the ideal control input, i=u,v,r;

S12. Based on the constructed USV model, the following matrix is introduced:

Then the following equation holds:

S13. The desired trajectory equation is given by:

where Q(η _d ,v _d )=-C(v _d )v _d -D(v _d )v _d , η _d =[x _d y _d ψ _d ] ^T and v _d =[u _d v _d r _d ] ^T represents the desired position and velocity vector, respectively;

S14. Introduce the following transformations to ν and ν _d in the above formula:

代表引入的辅助变量，

代表期望状态下的辅助变量，

R代表与实际状态相关的变量矩阵，R＝R(ψ),R_d代表与期望状态相关的变量矩阵，R_d＝R(ψ_d)；in,

represents the introduced auxiliary variable,

represents the auxiliary variable in the desired state,

R represents the variable matrix related to the actual state, R=R(ψ), R _d represents the variable matrix related to the desired state, R _d =R(ψ _d );

S15. Combine the above formulas (1), (3) and (5) to obtain:

where H(η,ν) represents the introduced intermediate variable,

S16. Combine the above formulas (3), (4) and (5) to obtain:

Among them, Γ(η _d ,ν _d ) represents the intermediate variable introduced to simplify the operation

S17. According to the above formulas (6) and (7), the trajectory tracking error control system of the unmanned ship is obtained as follows:

Ω＝Ω(η,ν,η_d,ν_d,δ)表示包含了未知扰动和未建模动态的集总未知项，具体表示如下：in,

Ω=Ω(η,ν,η _d ,ν _d ,δ) represents the lumped unknown term including unknown disturbances and unmodeled dynamics, which is specifically expressed as follows:

Ω(·)=RM ⁻¹ G(η, ν)+dR _d M ⁻¹ τ _d −R _d M ⁻¹ Q(η _d , ν _d ).

Further, the fixed-time lumped observer designed in the step S2 is as follows:

Ω(·)的估计值。Among them, the observer coefficients λ ₁ , λ ₂ , λ ₃ represent constant parameters satisfying certain constraints, respectively, λ ₁ , λ ₂ , λ ₃ >0, λ ₃ >d, β ₁ , β ₂ represent the observer power exponents, respectively , β ₁ , β ₂ satisfy β ₁ >1, 0<β ₂ <1, the observer variables z ₁ , z ₂ respectively represent

Estimated value of Ω(·).

Further, the adaptive assistance system designed in the step S3 is specifically as follows:

Wherein, χ ₁ =[χ _1,u χ _1,v χ _1,r ] ^T ,χ ₂ =[χ _2,u χ _2,v χ _2,r ] ^T represents auxiliary variables, and c ₁ ,c ₂ represents appropriate The parameter matrix of Δτ=τ _c −τ, τ _c and τ represent the control input without considering the actuator constraints and the actuator constraints, respectively.

Further, the step S4 specifically includes:

S41. Design a fixed-time fast non-singular terminal sliding mode as follows:

γ₁,γ₂＞0,n₁＞1，f(e₁)表示如下：where σ=[σ _u σ _v σ _r ] ^T , e ₁ =η _e -χ ₁ =[e _1,u e _1,v e _1,r ] ^T ,

γ ₁ , γ ₂ >0, n ₁ >1, f(e ₁ ) is expressed as follows:

Among them, ε is a very small constant, 0<n ₂ <1, 1<n ₃ <n ₄ , n ₁ , n ₂ , n ₃ , n ₄ , γ ₁ , γ ₂ have the following relationship:

S42, derivation of the designed fixed-time fast non-singular terminal sliding mode, to obtain:

可描述为：in,

can be described as:

in:

Further, the model-free fixed-time precise tracking control strategy designed in the step S5 is as follows:

Among them, α _j represents a constant parameter satisfying a certain condition, α _j >0 (j=1, 2, 3), m ₁ , m ₂ are positive odd numbers and satisfy m ₁ >m ₂ .

Further, the step S5 also includes the step of introducing an auxiliary variable g _sat to eliminate the potential jitter caused by the discontinuity of the symbol, specifically:

Among them, g _sat represents auxiliary variables, and φ, χ, and σ all represent constant coefficients that satisfy certain conditions.

Compared with the prior art, the present invention has the following advantages:

1. The model-free fixed-time precise trajectory tracking control method for an unmanned ship provided by the present invention can ensure that an unmanned ship that encounters input saturation, complex environmental disturbances and completely unknown model dynamics at the same time can accurately track a desired trajectory within a desired time period, Get faster convergence and tracking accuracy and greater robustness.

2. The model-free fixed-time precise trajectory tracking control method provided by the present invention overcomes the problems of singularity and slow convergence speed in the traditional sliding mode strategy. At the same time, the external disturbances and unmodeled dynamic items in the trajectory tracking control system of the unmanned ship are regarded as lumped uncertain items, and a fixed-time lumped observer is designed to quickly identify and compensate them within a predetermined time. Thus, precise trajectory tracking control without relying on the unmanned ship model is realized. Strict mathematical proof and simulation experiments verify the effectiveness and superiority of the designed trajectory tracking control strategy.

Based on the above reasons, the present invention can be widely promoted in the fields of fast and precise tracking control of unmanned ships.

Description of drawings

In order to illustrate the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description These are some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without any creative effort.

Fig. 1 is the flow chart of the method of the present invention.

FIG. 2 is a three-degree-of-freedom mathematical model of an unmanned ship provided by an embodiment of the present invention.

FIG. 3 is a frame diagram of a control strategy provided by an embodiment of the present invention.

FIG. 4 is a trajectory tracking curve diagram provided by an embodiment of the present invention.

FIG. 5 is a position tracking curve diagram provided by an embodiment of the present invention.

FIG. 6 is a position tracking error curve diagram according to an embodiment of the present invention.

FIG. 7 is a speed tracking curve diagram provided by an embodiment of the present invention.

FIG. 8 is a speed tracking error curve diagram provided by an embodiment of the present invention.

FIG. 9 is a graph of a lumped unknown observation provided by an embodiment of the present invention.

FIG. 10 is a speed tracking error curve diagram provided by an embodiment of the present invention.

FIG. 11 is a graph of a saturation control input provided by an embodiment of the present invention.

FIG. 12 is a trajectory tracking curve diagram under different initial states provided by an embodiment of the present invention.

FIG. 13 is a position tracking curve diagram under different initial states provided by an embodiment of the present invention.

FIG. 14 is a position tracking error curve diagram under different initial states provided by an embodiment of the present invention.

FIG. 15 is a speed tracking curve diagram under different initial states provided by an embodiment of the present invention.

FIG. 16 is a speed tracking error curve diagram under different initial states provided by an embodiment of the present invention.

Detailed ways

In order to make those skilled in the art better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only Embodiments are part of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

It should be noted that the terms "first", "second" and the like in the description and claims of the present invention and the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific sequence or sequence. It is to be understood that the data so used may be interchanged under appropriate circumstances such that the embodiments of the invention described herein can be practiced in sequences other than those illustrated or described herein. Furthermore, the terms "comprising" and "having" and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those expressly listed Rather, those steps or units may include other steps or units not expressly listed or inherent to these processes, methods, products or devices.

As shown in FIG. 1 , the present invention provides a model-free fixed-time precise trajectory tracking control method for an unmanned ship, including the following steps:

S1. Construct a USV model with input saturation and complex disturbances; as shown in FIG. 2 , a schematic diagram of a three-degree-of-freedom mathematical model of an unmanned ship provided by an embodiment of the present invention is shown.

During specific implementation, as a preferred embodiment of the present invention, the step S1 specifically includes:

S11. Consider input saturation and complex disturbances, and construct a USV model as follows:

v＝[u v r]^T表示附体坐标系中的速度向量，G(η,v)＝-C(v)v-D(v)表示系统动态，C(v)表示对角矩阵，

C(v)＝-C^T(v)；D(v)表示阻尼矩阵，

d＝MR^Tδ且δ＝[δ₁,δ₂,δ₃]^T表示复杂的时变扰动，M表示惯性，

M＝M^T＞0；τ表示控制输入受到执行器饱和的限制，

τ_i,max是执行器可以提供的最大扭矩，τ_c,i是理想的控制输入，i＝u,v,r；Among them, η=[xy ψ] ^T represents the position and heading in the earth coordinate system OXY,

v=[uvr] ^T represents the velocity vector in the attached coordinate system, G(η,v)=-C(v)vD(v) represents the system dynamics, C(v) represents the diagonal matrix,

C(v)=-C ^T (v); D(v) represents the damping matrix,

d=MR ^T δ and δ=[δ ₁ ,δ ₂ ,δ ₃ ] ^T represents complex time-varying disturbance, M represents inertia,

M=M ^T >0; τ indicates that the control input is limited by actuator saturation,

τ _i,max is the maximum torque that the actuator can provide, τ _c,i is the ideal control input, i=u,v,r;

S12. Based on the constructed USV model, the following matrix is introduced:

Then the following equation holds:

S13. The desired trajectory equation is given by:

where Q(η _d ,v _d )=-C(v _d )v _d -D(v _d )v _d , η _d =[x _d y _d ψ _d ] ^T and v _d =[u _d v _d r _d ] ^T represents the desired position and velocity vector, respectively;

S14. Introduce the following transformations to ν and ν _d in the above formula:

代表引入的辅助变量，

代表期望状态下的辅助变量，

R代表与实际状态相关的变量矩阵，R＝R(ψ),R_d代表与期望状态相关的变量矩阵，R_d＝R(ψ_d)；in,

represents the introduced auxiliary variable,

represents the auxiliary variable in the desired state,

R represents the variable matrix related to the actual state, R=R(ψ), R _d represents the variable matrix related to the desired state, R _d =R(ψ _d );

S15. Combine the above formulas (1), (3) and (5) to obtain:

where H(η,ν) represents the introduced intermediate variable,

S16. Combine the above formulas (3), (4) and (5) to obtain:

Among them, Γ(η _d ,ν _d ) represents the intermediate variable introduced to simplify the operation

S17. According to the above formulas (6) and (7), the trajectory tracking error control system of the unmanned ship is obtained as follows:

Ω＝Ω(η,ν,η_d,ν_d,δ)表示包含了未知扰动和未建模动态的集总未知项，具体表示如下：in,

Ω=Ω(η,ν,η _d ,ν _d ,δ) represents the lumped unknown term including unknown disturbances and unmodeled dynamics, which is specifically expressed as follows:

Ω(·)=RM ⁻¹ G(η, ν)+dR _d M ⁻¹ τ _d −R _d M ⁻¹ Q(η _d , ν _d ).

Assumption 1: Assume that the lumped unknown in (15) is differentiable and bounded and satisfies:

||Ω(·)||≤d

Among them, the constant d<∞, ||*|| represents the standard Euclidean norm.

In this embodiment, the system dynamic matrices C(v), D(v) and the vector d are completely unknown, and the matrices C(v), D(v) are changed by the changes of wind, wave and current in the ocean. The purpose of the present invention is to design a model-free fixed-time trajectory tracking control scheme for unmanned ships that encounter complex unknown and input saturation effects. This scheme can ensure that the tracking errors η _e , ν _e converge to a small range centered on the origin within a set time, and the closed-loop system is stable for a fixed time.

S2. Design a fixed-time lumped observer based on the constructed USV model;

During specific implementation, as a preferred embodiment of the present invention, in order to obtain high-precision tracking performance, it is necessary to accurately identify and compensate the lumped unknown items in the trajectory tracking error control system. Therefore, the fixed time set designed in step S2 The total observer, as follows:

集总扰动Ω(·)的估计值。Among them, the observer coefficients λ ₁ , λ ₂ , λ ₃ represent constant parameters satisfying certain constraints, respectively, λ ₁ , λ ₂ , λ ₃ >0, λ ₃ >d, β ₁ , β ₂ represent constant exponents satisfying certain constraints power, and β ₁ >1, 0 <β ₂ <1, the observed variables z ₁ , z ₂ represent intermediate variables respectively

An estimate of the lumped disturbance Ω(·).

S3. Design an adaptive auxiliary system based on the designed fixed-time lumped observer;

In fact, due to the limitation of actuator saturation, the actuator often cannot provide sufficient control torque. During specific implementation, as a preferred embodiment of the present invention, in order to deal with input saturation, the adaptive assistance system designed in step S3, specifically as follows:

Wherein, χ ₁ =[χ _1,u χ _1,v χ _1,r ] ^T ,χ ₂ =[χ _2,u χ _2,v χ _2,r ] ^T represents auxiliary variables, and c ₁ ,c ₂ represents appropriate The parameter matrix of Δτ=τ _c −τ, τ _c and τ represent the control input without considering the actuator constraints and the actuator constraints, respectively.

S4. Based on the designed adaptive auxiliary system, design a fast non-singular terminal sliding mode;

During specific implementation, as a preferred embodiment of the present invention, the step S4 specifically includes:

S41. Design a fixed-time fast non-singular terminal sliding mode as follows:

γ₁,γ₂＞0,n₁＞1，f(e₁)表示如下：where σ=[σ _u σ _v σ _r ] ^T , e ₁ =η _e -χ ₁ =[e _1,u e _1,v e _1,r ] ^T ,

γ ₁ , γ ₂ >0, n ₁ >1, f(e ₁ ) is expressed as follows:

Among them, ε is a very small constant, 0<n ₂ <1, 1<n ₃ <n ₄ , n ₁ , n ₂ , n ₃ , n ₄ , γ ₁ , γ ₂ have the following relationship:

S42, derivation of the designed fixed-time fast non-singular terminal sliding mode, to obtain:

可描述为：in,

can be described as:

in:

S5. Based on the fixed-time lumped observer, the adaptive auxiliary system and the fast non-singular terminal sliding mode designed in the above steps S2-S4, a model-free fixed-time precise tracking control strategy is designed.

During specific implementation, as a preferred embodiment of the present invention, the model-free fixed-time precise tracking control strategy designed in step S5 is specifically as follows:

Among them, α _j represents a constant parameter satisfying a certain condition, α _j >0 (j=1, 2, 3), m ₁ , m ₂ are positive odd numbers and satisfy m ₁ >m ₂ .

During specific implementation, as a preferred embodiment of the present invention, the step S5 also includes the step of introducing g _sat to eliminate potential jitter caused by symbol discontinuity, specifically:

Among them, g _sat represents auxiliary variables, and φ, χ, and σ all represent constant parameters that satisfy certain conditions.

To sum up, the fixed-time lumped observer designed in the present invention can realize accurate observation of lumped unknown items including environmental disturbances and unmodeled dynamics within a fixed time. The model-free fixed-time trajectory tracking control scheme designed by the present invention can make the unmanned ship that encounters input saturation, complex environmental disturbance and completely unknown model dynamics at the same time accurately track the desired trajectory within a desired time, and the convergence time is different from that of the unmanned ship. The initial state of the man-ship is independent of the designed parameters.

In order to verify the effectiveness and superiority of the method of the present invention, a simulation test was carried out. As shown in Fig. 4-16, the method of the present invention can ensure that the unmanned ship that encounters input saturation, complex environmental disturbance and completely unknown model dynamics at the same time is in an expected Accurately track the desired trajectory in time, and obtain faster convergence speed, tracking accuracy and stronger robustness.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: The technical solutions described in the foregoing embodiments can still be modified, or some or all of the technical features thereof can be equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention. scope.

Claims (7)

1. A model-free fixed-time accurate trajectory tracking control method for an unmanned ship is characterized by comprising the following steps:

s1, constructing a USV model with input saturation and complex disturbance;

s2, designing a fixed time lumped observer based on the constructed USV model;

s3, designing an adaptive auxiliary system based on the designed fixed time lumped observer;

s4, designing a rapid nonsingular terminal sliding mode based on the designed adaptive auxiliary system;

s5, designing a model-free fixed time accurate tracking control strategy based on the fixed time lumped observer, the self-adaptive auxiliary system and the fast nonsingular terminal sliding mode designed in the steps S2-S4.

2. The method for model-free fixed-time accurate trajectory tracking control of an unmanned ship according to claim 1, wherein the step S1 specifically includes:

s11, considering input saturation and complex disturbance, constructing a USV model as follows:

wherein eta is [ x y psi ═ n]^TRepresenting the position and heading in the earth coordinate system OXY,

v＝[u v r]^Trepresents a velocity vector in an attached coordinate system, G (η, v) ═ c (v) v-d (v) represents system dynamics, c (v) represents a diagonal matrix,

C(v)＝-C^T(v) (ii) a D (v) represents a damping matrix,

d＝MR^Tδ and δ ═ δ₁,δ₂,δ₃]^TRepresenting complex, time-varying perturbations, M representing inertia,

M＝M^Tis greater than 0; tau denotes that the control input is limited by actuator saturation,

τ_i,maxis the maximum torque, τ, that the actuator can provide_c,iIs an ideal control input, i ═ u, v, r;

s12, introducing the following matrix based on the constructed USV model:

then the following equation holds true:

s13, the desired trajectory equation is given by:

wherein, Q (η)_d,v_d)＝-C(v_d)v_d-D(v_d)v_d，η_d＝[x_d y_d ψ_d]^TAnd v_d＝[u_d v_d r_d]^TRespectively representing desired position and velocity vectors;

s14, v in the formula_dThe following transformations were introduced:

wherein,

represents the auxiliary variable to be introduced and is,

represents the auxiliary variable in the desired state,

r represents andan extreme state dependent variable matrix, R ═ R (ψ), R_dRepresenting a variable matrix, R, associated with the desired state_d＝R(ψ_d)；

S15, combining the above equations (1), (3) and (5) to obtain:

wherein H (eta, nu) represents an introduced intermediate variable,

s16, combining the above equations (3), (4) and (5) to obtain:

wherein, Γ (η)_d,ν_d) Representing introduced intermediate variables for simplifying operations

S17, obtaining the unmanned ship track tracking error control system according to the formulas (6) and (7) as follows:

wherein,

Ω＝Ω(η,ν,η_d,ν_dδ) represents a lumped unknown term that contains unknown perturbations and unmodeled dynamics, as follows:

Ω(·)＝RM^-1G(η，ν)+d-R_dM^-1τ_d-R_dM^-1Q(η_d，ν_d)。

3. the method for model-free fixed-time accurate trajectory tracking control of an unmanned ship according to claim 1, wherein the fixed-time lumped observer designed in the step S2 is specifically as follows:

wherein the observer coefficient lambda₁,λ₂,λ₃Respectively representing constant parameters, λ, satisfying certain constraints₁,λ₂,λ₃＞0，λ₃＞d，β₁,β₂Denotes a constant exponential power satisfying a certain constraint, and₁＞1,0＜β₂< 1, observation variable z₁,z₂Respectively representing intermediate variables

An estimate of the lumped disturbance Ω (·).

4. The model-free fixed-time accurate trajectory tracking control method for the unmanned ship according to claim 1, wherein the adaptive auxiliary system designed in the step S3 specifically comprises the following steps:

wherein, χ₁＝[χ_1,u χ_1,v χ_1,r]^T,χ₂＝[χ_2,u χ_2，v χ_2，r]^TRepresenting auxiliary variables, c₁,c₂Denotes a suitable parameter matrix, Δ τ ═ τ_c-τ，τ_cAnd τ represent control inputs that do not take into account actuator constraints and actuator constraints, respectively.

5. The method for model-free fixed-time accurate trajectory tracking control of an unmanned ship according to claim 1, wherein the step S4 specifically includes:

s41, designing a fixed-time fast nonsingular terminal sliding mode as follows:

wherein σ ═ σ [ σ ]_u σ_v σ_r]^T,e₁＝η_e-χ₁＝[e_1,u e_1,v e_1,r]^T，

γ₁,γ₂＞0,n₁＞1，f(e₁) Is represented as follows:

wherein ε is a very small normal number, 0 < n₂＜1,1＜n₃＜n₄，n₁,n₂,n₃,n₄,γ₁,γ₂There is the following relationship between:

s42, carrying out derivation on the designed fixed-time fast nonsingular terminal sliding mode to obtain:

wherein,

can be described as:

wherein:

6. the method for model-free fixed-time accurate trajectory tracking control of an unmanned ship according to claim 1, wherein the model-free fixed-time accurate trajectory tracking control strategy designed in step S5 is specifically as follows:

wherein alpha is_jDenotes a constant parameter, alpha, satisfying a certain condition_j＞0(j＝1,2,3)，m₁,m₂Is a positive odd number, and satisfies m₁＞m₂。

7. The method for model-free fixed-time accurate trajectory tracking control of an unmanned ship according to claim 6, wherein the step S5 further comprises introducing a variable g_satThe method comprises the following steps of eliminating potential flutter caused by symbol discontinuity:

wherein, g_satRepresents auxiliary variables, and phi, chi and sigma all represent constant parameters meeting certain conditions.

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