Tracking control method for underwater vehicle with state constraints under input saturation

Abstract

The present invention discloses a tracking control method for an underwater vehicle with state constraints under input saturation. First, based on the kinematic and dynamic models of the AUV, the present invention constructs an AUV control system containing model uncertainty and unknown disturbances to obtain a reference trajectory for the tracking target. Then, in combination with an error conversion function, an error model of the AUV control system is established, and design variables related to the position tracking error are obtained. Simultaneously, design variables related to the velocity tracking error are derived. Based on the design variables related to the position tracking error, a fixed-time integral sliding mode lumped disturbance observer is constructed. Finally, the fixed-time integral sliding mode lumped disturbance observer is combined with the design variables related to the velocity tracking error to construct a trajectory tracking control system. A sliding mode controller with fixed-time convergence is designed using a continuous input signal and a position-velocity adaptive law. The present invention achieves stabilization of the tracking error to zero within a fixed time and continuous control input.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater robot control, and in particular relates to an underwater vehicle tracking control method with state constraints under input saturation. Background Art

[0002] The motion control system of underwater vehicles is an active research field. The environment they face is unknown and complex, and their own state variables, such as speed and angular velocity, are subject to physical limits.

[0003] These practical problems jointly affect the trajectory tracking of underwater vehicles in terms of control performance, and may even lead to unstable operation. Trajectory tracking control, as the main control technology requirement for the horizontal motion of underwater vehicles (autonomous underwater vehicles, AUVs), plays a key role in completing operational tasks. However, external interference increases the difficulty of AUV horizontal control. Especially in the under-actuated AUV working environment, due to complex and harsh conditions, trajectory tracking becomes more difficult, which can easily lead to inaccurate tracking and thus fail to successfully complete the desired task. With the widespread application of AUVs and the continuous improvement of their intelligence, AUV motion control technology has achieved rapid development, making it gradually mature in engineering applications. However, due to the incompleteness and coupling of AUV models, interference from the external environment and the application requirements in complex scenarios, AUV motion tracking control technology still has a lot of room for improvement and enhancement. Summary of the Invention

[0004] To address these issues, this paper proposes a tracking control method for underwater vehicles with state constraints under input saturation, achieving precise convergence of the constrained steady-state response with lumped uncertainty. Based on kinematic and dynamic models, an underwater three-degree-of-freedom motion control system is established. Then, a fixed-time disturbance observer is designed by combining fixed-time control and disturbance observer techniques to estimate and correct the system's lumped disturbances. A fixed-time nonsingular terminal sliding mode control is designed, and an auxiliary system is introduced to address the input saturation problem caused by fixed-time control. An improved reaching law is used to address the sliding mode chattering problem. Finally, the system stability is proven using Lyapunov functions.

[0005] The technical solutions of the present invention are as follows:

[0006] A tracking control method for an underwater vehicle with state constraints under input saturation is provided, the method comprising the following steps:

[0007] S1. Based on the kinematic and dynamic models of the AUV, an AUV control system with model uncertainty and unknown interference is constructed to obtain the reference trajectory of the tracking target.

[0008] S2. By combining the error conversion function, an error model of the AUV control system is established. Based on this error model, the reference trajectory of the tracking target obtained in step S1 is compared with the actual output trajectory of the AUV system to obtain the design variables related to the position tracking error. At the same time, the velocity vector of the AUV is combined with the control input signal in the kinematic model to derive the design variables related to the velocity tracking error.

[0009] S3. Based on the design variables related to the position tracking error obtained in step S2, a fixed-time integral sliding mode lumped disturbance observer is constructed;

[0010] S4. Combining the fixed-time integral sliding mode lumped disturbance observer constructed in step S3 and the design variables related to the velocity tracking error obtained in step S2, a trajectory tracking control system is constructed, and a fixed-time convergent sliding mode controller is designed using a continuous input signal and a position-velocity adaptive law.

[0011] Furthermore, step S1 is specifically as follows:

[0012] Considering only the motion in the three directions of sway, pitch and heading, the relationship between the physical quantities in the inertial coordinate system and the carrier coordinate system is established through coordinate transformation:

[0013]

[0014] in, Describes the velocity of the AUV in the inertial coordinate system, They represent the longitudinal linear velocity, transverse linear velocity, and bow angular velocity of the AUV in the inertial coordinate system, respectively. The superscript T represents the transpose of the matrix. μ describes the velocity of the AUV in the carrier coordinate system, μ = [u, v, r] T , where u, v, and r represent the longitudinal velocity, transverse velocity, and bow velocity of the AUV in the carrier coordinate system, respectively, and J(ψ) is a rotation matrix with J -1 (ψ)=J T (ψ) and ||J(ψ)||=1;

[0015]

[0016] Based on the mathematical model of AUV, its dynamic model is established as follows:

[0017]

[0018] in, is the inertial symmetric positive definite matrix including the additional mass; C(v) is the Coriolis centripetal force matrix composed of hydrodynamic parameters; D(v) is the damping coefficient matrix; d represents the time-varying disturbance and dynamic uncertainty generated in the ocean environment, τ = [τu ,τ v ,τ r ] T Indicates the longitudinal control input, lateral control input and heading angle control input, represents the acceleration of the AUV;

[0019] It is assumed that the AUV is a rigid body, and its shape is symmetrical about the horizontal plane and the vertical plane. The weight and buoyancy are equal and the center of buoyancy is located in the vertical plane. The nonlinear hydrodynamic damping term and rolling motion are ignored. The AUV is completely immersed in the fluid medium and is in a fully viscous state.

[0020] Furthermore, step S2 is specifically as follows:

[0021] Define the error transfer function ρ i (t) is:

[0022]

[0023] Where, represents the scheduled time, t is the simulation time; ρ i,0 Represents the initial value of the preset performance function, ρ i,∞ Tracking the boundaries of the steady-state error band for a preset trajectory;

[0024] During the stable operation of the AUV, it outputs the AUV position η, η = [x, y, ψ] T , where x, y, and ψ represent the real-time longitudinal linear displacement, real-time lateral displacement, and real-time azimuth of the AUV in the inertial coordinate system, respectively. The expected value η is obtained by tracking the output AUV position η. d , η d =[x d ,y d ,ψ d ] T , where x d 、y d , ψ d They represent the desired longitudinal position, desired lateral position, and desired heading angle respectively; at the same time, the tracking error e i =η-η d -x1 and the derivative of the error with respect to time Fluctuates within the specified performance range, and x1 is an auxiliary vector. In order to solve the complexity brought by the performance constraint problem in the controller derivation, an error mapping function is introduced to convert the constrained error to the unconstrained space and convert the constraint condition into an error transformation function:

[0025]

[0026] Where i = x, y, ψ, ε i(t) is the new conversion error, S(ε) has the properties of smooth reversibility and strict increasing, e i (t) represents the error between the expected position and the actual position, ρ i (t) represents the error conversion function, R is the change function of the S function;

[0027] Define the error transformation function ε i (t) is:

[0028]

[0029] Derivative of the above formula:

[0030]

[0031] Among them, ρ i represents the error transfer function, represents ρ i The derivative of

[0032] Simplify the above formula and introduce the custom variable α i and β i ,and:

[0033]

[0034]

[0035] We can get:

[0036]

[0037] Furthermore, the S3 is specifically:

[0038] Design a fixed-time lumped disturbance observation and introduce auxiliary variables is the estimated state of the AUV,

[0039]

[0040] Where Ξ(t) is the state error variable, Ξ(t)=[Ξ u Ξ v Ξ r ] T ,Ξ u is the longitudinal linear velocity state error, v is the state error of the transverse linear velocity, r is the rotation angular velocity state error; v(t) represents the system state;

[0041] The integral sliding surface is constructed as follows:

[0042]

[0043] in, s is the constructed sliding surface, satisfy Variables; α and β are constants satisfying 0<α<1, β>1;

[0044] Take the derivative of the sliding surface:

[0045]

[0046] Where d is the external interference, is the expected interference, a>0, then The estimated value of is:

[0047]

[0048] Among them, s [α] =|s| α sign(s),s [β] =|s| β sign(s), k0, k1, k2 are all constants greater than 0, and k0 satisfies

[0049] Furthermore, the S4 operation is specifically as follows:

[0050] For fixed-time control technology, faster transient response results in larger control force or torque to drive the AUV. Therefore, thruster saturation is more likely to occur. To alleviate the input saturation problem, a following adaptive auxiliary system is designed:

[0051]

[0052] Where x1=[x 1u ,x 1v ,x 1r ] T is the auxiliary vector mentioned above, x2=[x 2u ,x 2v ,x 2r ] T is another auxiliary vector. The subscripts u, v, and r represent the longitudinal velocity, transverse velocity, and heading angular velocity, respectively. To ensure that t→∞, x1 and x2 approach 0. c1 and c2 are the designed positive definite parameter matrices, and Δτ=τ c -τ is the difference between the control input and the actual input; JM -1 It is a variation of the previous formula;

[0053] Introduce variables δ1 and δ2 to construct a fixed-time non-singular terminal sliding mode:

[0054] s=δ2+μ1|δ1|γ sign(δ1)+μ2|δ1| λ sign(δ1)

[0055] Among them, δ1=z1-x1=[δ 1u ,δ 1v ,δ 1r ] T , μ1, μ2>0, γ, λ are set constants and satisfy γ>λ, 1<λ<2; z1 is the error with preset performance constraints, z2 is the derivative of z1, that is,

[0056] Taking the derivative of the above formula, we can get:

[0057]

[0058] In order to improve the convergence speed of the sliding mode variable and suppress chattering, a special reaching law based on the hyperbolic tangent function tanh(s / σ1) is designed as a switching term instead of the sign function. The improved special reaching law is:

[0059]

[0060] In the formula, ρ1>0, k>0 and σ1>0 are all positive gain numbers, where the size of σ1 determines the speed of change of the inflection point of the hyperbolic tangent smooth function, and s is the designed sliding mode surface. Combining the two equations, we can get the sliding mode control law as follows:

[0061]

[0062] in, is the estimated value of the disturbance observer; is the symmetric positive definite matrix of inertia including the additional mass; is the Coriolis centripetal force matrix composed of hydrodynamic parameters; is the damping coefficient matrix; the remaining parameters are the same as described above.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] 1) Considering the complex disturbances encountered by underwater vehicles, this paper designs a tracking control method for underwater vehicles with state constraints under input saturation. The designed fixed-time disturbance observer can accurately observe external disturbances and stabilize the tracking error to zero within a fixed time.

[0065] 2) Aiming at the constrained state, the present invention proposes a preset performance fixed control, introduces the converted error function into the fixed-time non-singular terminal sliding mode control, and selects the improved hyperbolic tangent function as the reaching law. This not only ensures that the system can converge within a fixed time, but also reduces the chattering of the control input, realizes the continuity of the control input, and thus improves the robustness of the system.

[0066] 3) This paper proposes a state-constrained tracking control method for underwater vehicles under input saturation, targeting horizontal trajectory tracking control of underwater vehicles. A saturation state auxiliary system is introduced to ensure continuous and smooth control input. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a schematic flow chart of the present invention;

[0068] Figure 2 It is a schematic diagram of the inertial coordinate system and the attached coordinate system;

[0069] Figure 3 is the horizontal plane trajectory tracking curve;

[0070] Figure 4 is the longitudinal control input curve;

[0071] Figure 5 is the lateral control input curve;

[0072] Figure 6 is the heading angle control input curve;

[0073] Figure 7 is the longitudinal displacement tracking error curve;

[0074] Figure 8 is the lateral displacement tracking error curve;

[0075] Figure 9 is the heading angle tracking error curve;

[0076] Figure 10 is the longitudinal disturbance observation error curve;

[0077] Figure 11 is the lateral disturbance observation error curve;

[0078] Figure 12 is the heading angle disturbance observation error curve. DETAILED DESCRIPTION

[0079] The present invention will be further described below with reference to the accompanying drawings.

[0080] like Figure 1Figure 2 shows a schematic diagram of the inertial coordinate system and the attached coordinate system. The inertial coordinate system E-XYZ uses the Earth as its origin, with EZ pointing to the Earth's center. EX, EY, and EZ are perpendicular to each other. The attached coordinate system O-xyz uses the center of the underwater robot as its origin. Ox points forward of the underwater robot, Oy points to the right of the underwater robot, and Oz points downward perpendicular to the xOy plane. Because Newton's laws cannot be applied to the attached coordinate system, variables in the attached coordinate system must be converted to the inertial coordinate system for calculation.

[0081] 1) The state-constrained tracking control method for an underwater vehicle under input saturation of the present invention only considers motion in the three directions of sway, pitch, and heading. The relationship between the physical quantities in the two coordinate systems is established through coordinate transformation:

[0082]

[0083] in, Describes the velocity of the AUV in the inertial coordinate system, They represent the longitudinal linear velocity, transverse linear velocity, and bow angular velocity of the AUV in the inertial coordinate system, respectively. The superscript T represents the transpose of the matrix. μ describes the velocity of the AUV in the carrier coordinate system, μ = [u, v, r] T , where i, v, and r represent the longitudinal velocity, transverse velocity, and bow velocity of the AUV in the carrier coordinate system, respectively, and J(ψ) is a rotation matrix with J -1 (ψ)=J T (ψ) and ||J(ψ)||=1;

[0084]

[0085] Based on the mathematical model of AUV, its dynamic model is established as follows:

[0086]

[0087] in, is the inertial symmetric positive definite matrix including the additional mass; C(v) is the Coriolis centripetal force matrix composed of hydrodynamic parameters; D(v) is the damping coefficient matrix; d represents the time-varying disturbance and dynamic uncertainty generated in the ocean environment, τ = [τ u ,τ v ,τ r ] T Indicates the longitudinal control input, lateral control input and heading angle control input, represents the acceleration of the AUV.

[0088] Assume that the AUV is a rigid body with symmetry about the horizontal and vertical planes, equal weight and buoyancy, and a center of buoyancy located in the vertical plane. Ignore nonlinear hydrodynamic damping and rolling motion. The AUV is completely immersed in the fluid medium and is in a fully viscous state. To facilitate the design of the subsequent controller, the dynamic model is mapped to the inertial coordinate system through coordinate transformation, as follows:

[0089]

[0090] Therefore, the dynamic model in the inertial coordinate system established in this paper is:

[0091]

[0092] In order to facilitate the design of the subsequent preset performance function, error transformation function and terminal sliding surface, the tracking error of the AUV trajectory tracking system is specified as:

[0093] e=η-η d =[e x e y e ψ ] T

[0094] Define the error transfer function ρ i (t) is:

[0095]

[0096] Where, represents the scheduled time, t is the simulation time; ρ i,0 Represents the initial value of the preset performance function, ρ i,∞ Track the boundaries of the steady-state error band for a preset trajectory.

[0097] The error transformation function is defined as:

[0098]

[0099] This transformation ensures that the system states before and after the transformation have the same monotonicity. Therefore, based on this transformation, as long as the transformed system is stable, it is guaranteed that the original system also meets the performance requirements.

[0100] Taking the derivative of the above formula, we can get:

[0101]

[0102] That is, the transformed system model is obtained as follows:

[0103]

[0104] 2) Design a disturbance observer

[0105] In order to improve the anti-interference ability of the trajectory tracking control system, a fixed-time disturbance observer is designed, which is described as follows:

[0106] Introducing auxiliary variables is the estimated state of the AUV,

[0107]

[0108] Where Ξ(t) is the state error variable, Ξ(t)=[Ξ u Ξ v Ξ r ] T ,Ξ u is the longitudinal linear velocity state error, v is the state error of the transverse linear velocity, r is the rotation angular velocity state error; v(t) represents the system state;

[0109] The integral sliding surface is constructed as follows:

[0110]

[0111] in, s is the constructed sliding surface, satisfy Variables; α and β are constants satisfying 0<α<1, β>1;

[0112] Take the derivative of the sliding surface:

[0113]

[0114] Where d is the external interference, is the expected interference, a>0, then The estimated value of is:

[0115]

[0116] Among them, s [α] =|s| α sign(s),s [β] =|s| β sign(s), k0, k1, k2 are all constants greater than 0, and k0 satisfies

[0117] 3) Design of adaptive sliding mode tracking controller

[0118] For fixed-time control technology, faster transient response results in larger control force or torque to drive the AUV. Therefore, thruster saturation is more likely to occur. To alleviate the input saturation problem, a following adaptive auxiliary system is designed:

[0119]

[0120] Where x1=[x 1u ,x 1v ,x 1r ] T is the auxiliary vector mentioned above, x2=[x 2u ,x 2v ,x 2r ] T is another auxiliary vector. The subscripts u, v, and r represent the longitudinal velocity, transverse velocity, and heading angular velocity, respectively. To ensure that t→∞, x1 and x2 approach 0. c1 and c2 are the designed positive definite parameter matrices, and Δτ=τ c -τ is the difference between the control input and the actual input; JM -1 It is a variation of the previous formula;

[0121] Introduce variables δ1 and δ2 to construct a fixed-time non-singular terminal sliding mode:

[0122] s=δ2+μ1|δ1| γ sign(δ1)+μ2|δ1| λ sign(δ1)

[0123] Among them, δ1=z1-x1=[δ 1u ,δ 1v ,δ 1r ] T , μ1, μ2>0, γ, λ are set constants and satisfy γ>λ, 1<λ<2; z1 is the error with preset performance constraints, z2 is the derivative of z1, that is,

[0124] Taking the derivative of the above formula, we can get:

[0125]

[0126] In order to improve the convergence speed of the sliding mode variable and suppress chattering, a special reaching law based on the hyperbolic tangent function tanh(s / σ1) is designed as a switching term instead of the sign function. The improved special reaching law is:

[0127]

[0128] In the formula, ρ1>0, k>0 and σ1>0 are all positive gain numbers, where the size of σ1 determines the speed of change of the inflection point of the hyperbolic tangent smooth function, and s is the designed sliding mode surface. Combining the two equations, we can get the sliding mode control law as follows:

[0129]

[0130] in, is the estimated value of the disturbance observer; is the symmetric positive definite matrix of inertia including the additional mass; is the Coriolis centripetal force matrix composed of hydrodynamic parameters; is the damping coefficient matrix; the remaining parameters are the same as described above.

[0131] In order to prove that the present invention is stable at a fixed time, the following steps are performed:

[0132] Step 1 Select the following Lyapunov equation:

[0133] Derivative of the above formula:

[0134]

[0135] Substituting the control law into the above formula, we can get:

[0136]

[0137] Where,

[0138] Step 2: When the sliding mode reaches the sliding surface, there is

[0139] s≡0,

[0140] Combined, we can know that δ2+μ1|δ1| γ sign(δ1)+μ2|δ1| λ sign(δ1)=0.

[0141]

[0142] The above formula satisfies the fixed time lemma.

[0143] In summary, the system consisting of a fixed-time disturbance observer and a preset performance trajectory tracking sliding mode control is globally asymptotically stable.

[0144] Next, in order to verify the effectiveness of the underwater vehicle tracking control method with state constraints under input saturation proposed by the present invention, MATLAB is used for simulation verification and explanation. Figure 3 is the horizontal plane trajectory tracking control curve, the solid line represents the actual tracking curve obtained under the method of the present invention, and the dotted line represents the expected trajectory. It can be seen from the figure that the method proposed in the present invention can achieve accurate trajectory tracking. Figure 4 、 56 are the longitudinal, lateral and heading angle control input curves. It can be seen from the figure that the method proposed in the present invention can obtain a smooth control input curve and effectively reduce buffeting. Figure 7 、 8 9 are the tracking error curves of lateral displacement, longitudinal displacement and heading angle. It can be seen from the figure that the method proposed in the present invention can stabilize the error to zero within a fixed time. Figure 10 、 11 1 and 12 are the longitudinal, lateral and heading angle disturbance observation error curves. It can be seen from the figure that the method proposed in the present invention can accurately observe external disturbances so that the observation error can be stabilized to zero within a fixed time.

Claims

1. A tracking control method for an underwater vehicle with state constraints under input saturation, characterized in that: The method comprises the following steps: S1. Based on the kinematic and dynamic models of the AUV, an AUV control system with model uncertainty and unknown interference is constructed to obtain the reference trajectory of the tracking target. S2. By combining the error conversion function, an error model of the AUV control system is established. Based on this error model, the reference trajectory of the tracking target obtained in step S1 is compared with the actual output trajectory of the AUV system to obtain the design variables related to the position tracking error. At the same time, the velocity vector of the AUV is combined with the control input signal in the kinematic model to derive the design variables related to the velocity tracking error. S3. Based on the design variables related to the position tracking error obtained in step S2, a fixed-time integral sliding mode lumped disturbance observer is constructed; S4. Combining the fixed-time integral sliding mode lumped disturbance observer constructed in step S3 and the design variables related to the velocity tracking error obtained in step S2, a trajectory tracking control system is constructed, and a fixed-time convergent sliding mode controller is designed using a continuous input signal and a position-velocity adaptive law; Step S2 is specifically as follows: Define the error transfer function ρ i (t) is: Where, represents the scheduled time, and t is the simulation time; ρ i,0 Represents the initial value of the preset performance function, ρ i,∞ Tracking the boundaries of the steady-state error band for a preset trajectory; During the stable operation of the AUV, it outputs the AUV position η, η = [x, y, ψ] T , where ψ, y, and ψ represent the real-time longitudinal linear displacement, real-time lateral displacement, and real-time azimuth of the AUV in the inertial coordinate system, respectively. The expected value η is obtained by tracking the output AUV position η. d , η d =[x d ,y d ,ψ d ] T , where x d 、y d , ψ d They represent the desired longitudinal position, desired lateral position, and desired heading angle respectively; at the same time, the tracking error e i =η-η d -x1 and the derivative of the error with respect to time Fluctuates within the specified performance range, and x1 is an auxiliary vector. In order to solve the complexity brought by the performance constraint problem in the controller derivation, an error mapping function is introduced to convert the constrained error to the unconstrained space and convert the constraint condition into an error transformation function: Where i = x, y, ψ, ε i (t) is the new conversion error, S(ε) has the properties of smooth reversibility and strict increasing, e i (t) represents the error between the expected position and the actual position, ρ i (t) represents the error conversion function, R is the change function of the S function; Define the error transformation function ε i (t) is: Derivative of the above formula: Among them, ρ i represents the error transfer function, represents ρ i The derivative of Simplify the above formula and introduce the custom variable α i and β i ,and: have to: The S3 is specifically: Design a fixed-time lumped disturbance observation and introduce auxiliary variables is the estimated state of the AUV, Where Ξ(t) is the state error variable, Ξ(t)=[Ξ u Ξ v Ξ r ] T ,Ξ u is the longitudinal linear velocity state error, v is the state error of the transverse linear velocity, r is the rotation angular velocity state error; v(t) represents the system state; The integral sliding surface is constructed as follows: in, s is the constructed sliding surface, satisfy Variables; α and β are constants satisfying 0<α<1, β>1; Take the derivative of the sliding surface: Where d is the external interference, is the expected interference, a>0, then The estimated value of is: Among them, s [α] =|s| α sign(s),s [β] =|s| β sign(s), k0, k1, k2 are all constants greater than 0, and k0 satisfies 2. The underwater vehicle tracking control method with state constraints under input saturation according to claim 1, characterized in that: Step S1 is specifically as follows: Considering only the motion in the three directions of sway, pitch and heading, the relationship between the physical quantities in the inertial coordinate system and the carrier coordinate system is established through coordinate transformation: in, Describes the velocity of the AUV in the inertial coordinate system, They represent the longitudinal linear velocity, transverse linear velocity, and bow angular velocity of the AUV in the inertial coordinate system, respectively. The superscript T represents the transpose of the matrix. μ describes the velocity of the AUV in the carrier coordinate system, μ = [u, v, r] T , where u, v, and r represent the longitudinal linear velocity, transverse linear velocity, and bow angular velocity of the AUV in the carrier coordinate system, respectively, and J(ψ) is a rotation matrix with J -1 (ψ)=J T (ψ) and ||J(ψ)||=1; Based on the mathematical model of AUV, its dynamic model is established as follows: in, is the inertial symmetric positive definite matrix including the additional mass; C(v) is the Coriolis centripetal force matrix composed of hydrodynamic parameters; D(v) is the damping coefficient matrix; d represents the time-varying disturbance and dynamic uncertainty generated in the ocean environment, τ = [τ u ,τ v ,τ r ] T Indicates the longitudinal control input, lateral control input and heading angle control input, represents the acceleration of the AUV; It is assumed that the AUV is a rigid body, and its shape is symmetrical about the horizontal plane and the vertical plane. The weight and buoyancy are equal and the center of buoyancy is located in the vertical plane. The nonlinear hydrodynamic damping term and rolling motion are ignored. The AUV is completely immersed in the fluid medium and is in a fully viscous state.

3. The underwater vehicle tracking control method with state constraints under input saturation according to claim 1, characterized in that: The S4 operation is specifically as follows: Design follow-up adaptive assistance system: Where x1=[x 1u ,x 1v ,x 1r ] T is an auxiliary vector, x2=[x 2u ,x 2v ,x 2r ] T is another auxiliary vector; the subscripts u, v, and r represent the longitudinal velocity, transverse velocity, and heading angular velocity, respectively; in order to ensure that t→∞, x1 and x2 approach 0; c1 and c2 are the designed positive definite parameter matrices, Δτ=τ c -τ is the difference between the control input and the actual input; JM -1 It is a variation of the previous formula; Introduce variables δ1 and δ2 to construct a fixed-time non-singular terminal sliding mode: s=δ2+μ1|δ1| γ sign(δ1)+μ2|δ1| λ sign(δ1) Among them, δ1=z1-x1=[δ 1u ,δ 1v ,δ 1r ] T , μ1, μ2>0, γ, λ are set constants and satisfy γ>λ, 1<λ<2; z1 is the error with preset performance constraints, z2 is the derivative of z1, that is, Taking the derivative of the above formula, we can get: In order to improve the convergence speed of the sliding mode variable and suppress chattering, a special reaching law based on the hyperbolic tangent function tanh(s / σ1) is designed as a switching term instead of the sign function. The improved special reaching law is: In the formula, ρ1>0, k>0 and σ1>0 are all positive gain numbers, where the size of σ1 determines the speed of change of the inflection point of the hyperbolic tangent smooth function, and s is the designed sliding mode surface. Combining the two equations, we can get the sliding mode control law as follows: in, is the estimated value of the disturbance observer; is the symmetric positive definite matrix of inertia including the additional mass; is the Coriolis centripetal force matrix composed of hydrodynamic parameters; is the damping coefficient matrix.

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