UUV trajectory tracking control method based on predetermined performance adaptive fast integral sliding mode

Abstract

The invention discloses a UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode, and belongs to the technical field of underwater robot control, and the method comprises the following steps: giving an initial state and an expected trajectory of a UUV; introducing the ocean current motion model based on frequency analysis into kinematics and dynamics models of the UUV; designing a virtual reference speed and an actual reference speed to construct a speed error; performing performance constraint on the constructed speed error through a predetermined performance function; and designing an adaptive continuous fast integral sliding mode control dynamic controller to drive the UUV to complete finite time speed tracking. According to the method, on the premise that speed and motor performance constraints, internal model uncertainty and external disturbance caused by ocean currents in autonomous underwater robot trajectory tracking control are comprehensively considered, rapid and accurate convergence of tracking errors is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of underwater robot control, in particular to a UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode. Background Art

[0002] Autonomous underwater vehicles (UUVs) have attracted much attention due to their importance in the development of marine exploration equipment. In order to perform marine operations excellently, recent research has focused on developing high-performance trajectory tracking controllers in an optimal way while satisfying speed constraints. During operation, the transient performance of the system and the limitations of the hardware structure need to be considered to avoid overload and wear of the thrusters. At the same time, model uncertainties, hydrodynamic coefficients, and environmental disturbances caused by ocean currents are difficult to measure or estimate in real marine environments, which also makes the design of UUV tracking controllers more challenging.

[0003] There are many advanced control methods for trajectory tracking control of autonomous underwater vehicles, such as adaptive control, predicted performance control (PPC), sliding mode control (SMC), proportional integral derivative (PID) control, etc. Usually, due to the simple design and easy implementation of the classic proportional derivative (PD) or PID controller, they are often used in practical applications of autonomous underwater vehicles, but they may not be able to handle constraints such as state and speed. Among the above control methods, PPC can be used to improve the transient performance of the system and handle complex underwater tasks according to appropriate and effective solutions. However, for the three-dimensional motion control of autonomous underwater vehicles in real marine environments, the uncertainty of the model and the external disturbances caused by ocean currents and tides are the main difficulties for PPC controllers to accurately track the trajectory.

[0004] By introducing PPF, SMC and adaptive control into trajectory tracking control, the new adaptive non-singular integral sliding mode control (ANISMC) not only uses PPF to limit the velocity error, but also improves its transient and steady-state performance, making it easier to meet hardware constraints. The converted velocity error is introduced into the proposed integral sliding mode surface, which effectively reduces the arrival stage of the sliding mode surface without the need for system acceleration information, saves system energy and improves the robustness of the sliding mode surface. For a class of time-varying disturbances in an underwater environment with an upper limit in the form of a power function polynomial, a timing stability adaptive law is designed without knowing the specific form of the disturbance.

[0005] The traditional PPF and logarithmic function transform the position error in a form that the transformed position error needs to satisfy the domain restriction of the transformation function, so that the position error is limited to the range specified by the PPF. However, they do not consider the motor current and performance constraints of the autonomous underwater robot. When the speed error is large, the output torque of the controller increases, causing the motor current to increase. The actual current of the motor exceeds the rated current of the motor, causing serious damage to the motor. In view of the strong disturbances and model uncertainties in the underwater environment, how to realize the timed integral sliding mode synchronization control of the autonomous underwater robot under the condition of speed constraints is an unresolved problem. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode, which solves the problem of difficult trajectory tracking control of existing UUVs under motor constraints, internal model uncertainty and ocean current motion interference, and better realizes finite-time three-dimensional trajectory tracking control.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0008] A UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode comprises the following steps:

[0009] S1, given the initial state and desired trajectory of the UUV;

[0010] S2. Introduce the ocean current motion model based on frequency analysis into the kinematic and dynamic model of UUV;

[0011] S3, designing the virtual reference speed and the actual reference speed to construct the speed error;

[0012] S4, performing performance constraints on the constructed speed error through a predetermined performance function;

[0013] S5. Design an adaptive continuous sliding mode control dynamic controller to drive the UUV to complete finite time speed tracking.

[0014] A further improvement of the technical solution of the present invention is that in S1, the initial state and the desired trajectory of the given UUV specifically include:

[0015] The inertial position and attitude of the UUV with inertial and body frames are expressed as:

[0016] η=[x,y,z,ψ] T (1)

[0017] The constant expressions of linear velocity and angular velocity are:

[0018] μ=[u,v,w,r]T (2)

[0019] The above basic parameters include the coordinate values ​​of the autonomous underwater robot in the robot coordinate system and the longitudinal sway velocity u, the transverse sway velocity v and the heave velocity w, the yaw angular velocity r of the autonomous underwater robot in the robot coordinate system, the coordinates x, y and z of the autonomous underwater robot in the inertial coordinate system and the bow angle ψ in the inertial coordinate system; η = [x, y, z, ψ] T Represents the position and heading vector of the inertial coordinate system; μ = [u, v, w, r] T represents the linear and angular velocity vectors in the body frame;

[0020] In the three-dimensional trajectory tracking problem, given the desired spiral tracking trajectory η d ∈R 4 Select as:

[0021]

[0022] Assume that the initial conditions for position and orientation values ​​are:

[0023] η(0)=[0.5m,0m,0m,0rad] (4)

[0024] The initial velocity is:

[0025] μ(0)=[0.5m / s,0m / s,0m / s,0rad / s] (5)

[0026] Where μ(0) represents the initial velocity of the UUV.

[0027] The further improvement of the technical solution of the present invention is that in S2, the kinematic and dynamic models of the UUV based on the ocean current motion model based on frequency analysis are introduced as follows:

[0028]

[0029] Where J(ψ) is the coordinate transformation matrix; V xy =[V x ,V y ,0,0] T represents the ocean current speed in the inertial coordinate system; M = M 0 +ΔM,C(μ r )=C 0 (μ r )+ΔC(μ r ),D(μ r )=D 0 (μ r )+ΔD(μ r ),g(η)=g 0 (η)+Δg(η),M0 and ΔM represent the nominal mass matrix and uncertainty mass matrix of UUV, respectively. 0 (μ r ) and ΔC(μ r ) represent the nominal matrix and uncertainty matrix of rigid Coriolis force and centripetal force, respectively, D 0 (μ r ) and ΔD(μ r ) represent the nominal and uncertain viscous resistance matrices, g 0 (η) and Δg(η) represent the nominal value and uncertainty of UUV buoyancy and weight, respectively; F = [τ u ,τ v ,τ w ,τ r ] T represents the control force and torque of the UUV; d = [d u ,d v ,d w ,d r ] T represents external disturbance; η=[x,y,z,ψ] T Represents the position and heading vector of the inertial coordinate system; μ r =[u r ,v r ,w r ,r r ] T represents the velocity vector relative to the ocean current and the fuselage, where u r =uu c ,v r =vv c ,w r =w,r r = r, μ = [u, v, w, r] T represents the linear velocity and angular velocity vector in the body frame; u c represents the speed of the surge current encountered by the UUV in the real ocean environment; v c Represents the swaying current speed encountered by UUV in real ocean environment.

[0030] A further improvement of the technical solution of the present invention is that the surge current velocity u encountered by the UUV in the real ocean environment c and the swing current velocity v c The sea current speed to which the fuselage is subjected is converted through the following conversion relationship:

[0031]

[0032] Among them, V x and V yare the velocity components of the ocean current expressed in the x- and y-directions of the inertial reference frame, as follows:

[0033]

[0034] The parameters λ and κ determine the degree of chaotic mixing of the ocean current. 1 , b 2 and b 3 is a sensitive variable related to underwater environmental fluctuations, b 4 and b 5 represents a random variable.

[0035] A further improvement of the technical solution of the present invention is that in S3, the specific process of constructing the speed error is:

[0036]

[0037] Position and heading are defined as: x = [x, y, z, ψ] T , the control input is: u=[u,v,w,r] T In order to use the PPF function to constrain the speed error, the speed error needs to occur and maintain a uniform error form on the sliding surface, that is, use the converted error; therefore, first a new virtual speed quantity needs to be established; consider a time-varying reference trajectory η d ∈R 4 Define the position tracking error as Combining formula (6), we get:

[0038]

[0039] Where J(η) is the coordinate transformation matrix; μ r Represents the velocity vector of the relative ocean current and the fuselage; η∈R 4 represents the four-degree-of-freedom position and attitude of the UUV; η d ∈R 4 is the desired tracking trajectory;

[0040] μ r As the virtual control input of equation (10), the designed virtual control command acts as a reference speed vector, and the virtual speed is:

[0041]

[0042] Among them, J -1 (η) is the inverse of the coordinate transformation matrix; k 1 =diag(k 11 ,…,k 14 ) and k 2 =diag(k 21 ,…,k24 ) are all constants and positive definite matrices that need to be designed, k 1i , k 2i (i = 1, …, 4) satisfy is the tracking error; then, the velocity tracking error is defined as:

[0043] e = μ - υ c (12)

[0044] where μ represents the linear velocity and angular velocity vectors in the body frame; υ c represents the virtual velocity quantity.

[0045] A further improvement of the technical solution of the present invention lies in: in S4, the performance of the constructed velocity error is constrained by a prescribed performance function, specifically including the following:

[0046] Set the error bound, and describe the prescribed performance as:

[0047]

[0048] where ρ(t) is the PPF, b and is described as:

[0049]

[0050] where, is the overshoot exponential constant; e(t) represents the velocity tracking error, and e(0) represents the initial velocity tracking error;

[0051] The prescribed performance function PPF function is as follows:

[0052]

[0053] where 0 < ρ ∞ < |e(0)| < ρ 0 , 0 < T < ∞ and l > 1 are constants selected by the user; the performance indices adopted include: the constant T is the prescribed maximum allowable convergence time for ρ(t) to converge from the given maximum initial error ρ 0 to the maximum allowable steady-state error ρ ∞ ; l represents the prescribed minimum convergence speed; the properties of ρ(t) are summarized as: ρ(t) is a monotonically decreasing bounded smooth positive function, i.e., 0 < ρ ∞ ≤ ρ(t) ≤ ρ 0 , Meanwhile

[0054] The time derivative of ρ(t) is:

[0055]

[0056] Transformation function Introduced as:

[0057]

[0058] ψ(x) is a smooth, increasing bijective mapping that satisfies ψ(0) = 0.

[0059] The derivative υ(x) of ψ(x) with respect to x is:

[0060]

[0061] The inverse function of the ψ(x) function is given by:

[0062]

[0063] Obviously, the inverse function of ψ(x) is is also a smooth increasing bijective mapping, and ψ -1 (0) = 0; define the auxiliary variable θ as:

[0064] θ=e / ρ(22)

[0065] Wherein, e=e(t) represents the speed tracking error; ρ=ρ(t) is the predetermined performance function; the transformed speed error vector ε is introduced, and the formula is as follows:

[0066] ε=ψ(θ)(23)

[0067] The time derivative of the transformed velocity error vector ε is:

[0068]

[0069] Among them, α and β are defined as: β=v(θ) / ρ(t); define B=diag(β 1 ,…,β 4 ).

[0070] The further improvement of the technical solution of the present invention is that: in S5, the adaptive continuous sliding mode control dynamic controller is designed to drive the UUV to complete the finite time speed tracking. The specific process includes:

[0071] In S4, a transformation speed error based on PPF has been designed. When designing the sliding surface, it is necessary to design a sliding surface containing only speed error information for matching; therefore, an integral sliding surface S with finite time specified performance is proposed, as shown below:

[0072]

[0073] Where H(ε)=1+χe -ε , χ>0 is a parameter, the range of H(ε) is (1,1+χ), and H(ε) is a monotonically decreasing function; K 1 ,K 2 >0 constant, ν 1 >1,0 <v 2 <1,sig p (x)=|x| p sign(x), sign(x) is the sign function;

[0074] The time derivative of the integrated sliding surface S is:

[0075]

[0076] Assumption: If the UUV is subject to less severe uncertainties and disturbances and tracks a less complex desired trajectory so that the vehicle thrusters are not frequently saturated, then the lumped system uncertainty Bounded, so that the total disturbance is fitted with a quadratic polynomial about the speed and satisfies the following conditions:

[0077]

[0078] Among them, λ i (i=0,1,2) are the adaptive parameters to be estimated. In addition, it is easy to see in practical applications that is bounded; the control input is The total disturbance is expressed as:

[0079]

[0080] in,

[0081] Based on the design principles of sliding surface and sliding mode controller, the following controller is designed, and the continuous control law is as follows:

[0082]

[0083] in, is the reference velocity vector v c The derivative of -1 B = diag(β 1 ,…,β 4 ) positive definite inverse; H(ε)=1+χe -ε , χ>0 is a parameter, the range of H(ε) is (1,1+χ), H(ε) is a monotonically decreasing function; S is the integral sliding surface; K1 ,K 2 >0 constant, v 1 >1,0 <v 2 <1,sig p (x)=|x| p sign(x), sign(x) is the sign function; L 1 >0,L 2 >0,m 1 >1,0 <m 2 <1;

[0084] In addition, adaptive components are used in the controller to counteract the effects of model parameter uncertainty and external disturbances:

[0085]

[0086] in, is the adaptive parameter λ to be estimated i The estimated value of i=0,1,2;ω is a constant;c 1 >0 and c 2 >0,c 1 and c 2 is a constant adaptive gain.

[0087] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0088] 1. The UUV trajectory tracking control method based on predetermined performance adaptive fast integral sliding mode proposed in the present invention has strong robustness and processing constraint capability under the influence of speed and motor performance constraints, internal model uncertainties and external disturbances of ocean currents on the UUV, and better realizes finite time three-dimensional trajectory tracking control.

[0089] 2. The present invention takes into account the transient performance and hardware structure limitations of the UUV system, limits the speed error through predetermined performance control, improves its transient performance and steady-state performance, and avoids the overload and wear problems of the thruster.

[0090] 3. The present invention introduces the converted speed error into the proposed integral sliding mode surface, which saves system energy and improves the reliability of UUV in completing tasks.

[0091] 4. The present invention solves the trajectory tracking control problem of under-actuated UUV by adaptively estimating model parameter perturbations and external disturbances and compensating them into the UUV, and using fast integral sliding mode control;

[0092] 5. The present invention overcomes the difficulty of UUV tracking control and achieves strict guarantee that the speed, posture and target are known upon arrival, that is, time and space tasks are carried out simultaneously.

[0093] 6. The present invention is reasonably designed and can be easily applied to tasks related to underwater environments, which helps to promote intelligent operations in difficult and complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art are briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative labor.

[0095] Figure 1 is a flow chart of a UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode provided in an embodiment of the present invention;

[0096] Figure 2 is a schematic diagram of a curve of ocean current velocity changes calculated by an ocean current velocity model proposed in an embodiment of the present invention;

[0097] Figure 3 3D trajectory tracking result of UUV without considering the interference of ocean current in an embodiment of the present invention;

[0098] Figure 4 is a schematic diagram of a four-degree-of-freedom trajectory tracking error curve of a UUV in an embodiment of the present invention without considering the interference of ocean currents;

[0099] Figure 5 is a schematic diagram of the three-dimensional trajectory tracking result of the UUV considering the interference of the ocean current in an embodiment of the present invention;

[0100] Figure 6 1 is a schematic diagram of a four-degree-of-freedom trajectory tracking error curve of a UUV considering ocean current interference in an embodiment of the present invention;

[0101] Figure 7 It is a schematic diagram of the speed tracking error curve of the UUV considering the ocean current interference in an embodiment of the present invention. DETAILED DESCRIPTION

[0102] It should be noted that the terms "including" and "having" and any variations thereof in the specification and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or apparatus.

[0103] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the present invention.

[0104] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "several" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0105] The present invention is further described in detail below with reference to the accompanying drawings and embodiments:

[0106] like Figure 1 As shown, a UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode includes the following steps:

[0107] S1, given the UUV initial state and desired trajectory;

[0108] The inertial position and attitude of the UUV with inertial and body frames are expressed as:

[0109] η=[x,y,z,ψ] T (1)

[0110] The constant expressions of linear velocity and angular velocity are:

[0111] μ r =[u r ,v r ,w r ,r r ] T (2)

[0112] The above basic parameters include the coordinate values ​​of the autonomous underwater robot in the robot coordinate system and the longitudinal sway velocity u, the transverse sway velocity v and the heave velocity w, the yaw angular velocity r of the autonomous underwater robot in the robot coordinate system, the coordinates x, y and z of the autonomous underwater robot in the inertial coordinate system and the bow angle ψ in the inertial coordinate system; η = [x, y, z, ψ] T Represents the position and heading vector of the inertial coordinate system; μr =[u r ,v r ,w r ,r r ] T represents the velocity vector relative to the ocean current and the fuselage, where u r =uu c ,v r =vv c ,w r =w,r r = r, μ = [u, v, w, r] T Represents the linear and angular velocity vectors in the body frame.

[0113] In the three-dimensional trajectory tracking problem, given the desired spiral tracking trajectory η d ∈R 4 Select as:

[0114]

[0115] Assume that the initial conditions for position and orientation values ​​are:

[0116] η(0)=[0.5m,0m,0m,0rad] (4)

[0117] The initial velocity is:

[0118] μ(0)=[0.5m / s,0m / s,0m / s,0rad / s] (5)

[0119] S2. Introduce the ocean current motion model based on frequency analysis into the kinematic and dynamic model of UUV;

[0120] The kinematic and dynamic models of UUV after the introduction of the ocean current motion model based on frequency analysis are shown in the following equations:

[0121]

[0122] Where J(ψ) is the coordinate transformation matrix; V xy =[V x ,V y ,0,0] T represents the ocean current speed in the inertial coordinate system; M = M 0 +ΔM,C(μ r )=C 0 (μ r )+ΔC(μ r ),D(μ r )=D 0 (μ r )+ΔD(μ r ),g(η)=g 0(η)+Δg(η),M 0 and ΔM represent the nominal mass matrix and uncertainty mass matrix of UUV, respectively. 0 (μ r ) and ΔC(μ r ) represent the nominal matrix and uncertainty matrix of rigid Coriolis force and centripetal force, respectively, D 0 (μ r ) and ΔD(μ r ) represent the nominal and uncertain viscous resistance matrices, g 0 (η) and Δg(η) represent the nominal value and uncertainty of UUV buoyancy and weight, respectively; F = [τ u ,τ v ,τ w ,τ r ] T represents the control force and torque of the UUV; d = [d u ,d v ,d w ,d r ] T represents external disturbance; η=[x,y,z,ψ] T Represents the position and heading vector of the inertial coordinate system; μ r =[u r ,v r ,w r ,r r ] T represents the velocity vector relative to the ocean current and the fuselage, where u r =uu c ,v r =vv c ,w r =w,r r = r, μ = [u, v, w, r] T represents the linear velocity and angular velocity vector in the body frame; u c represents the speed of the surge current encountered by the UUV in the real ocean environment; v c Represents the swaying current speed encountered by UUV in real ocean environment.

[0123] Furthermore, the surge current velocity u encountered by the UUV in the real ocean environment c and the sway current velocity v c The sea current speed to which the fuselage is subjected is converted through the following conversion relationship:

[0124]

[0125] Among them, V x and V y are the velocity components of the ocean current expressed in the x and y directions of the inertial reference frame,

[0126]

[0127] The parameters λ and κ determine the degree of chaotic mixing of the ocean current. 1 , b 2 and b 3 is a sensitive variable related to underwater environmental fluctuations, b 4 and b 5 represents a random variable.

[0128] S3, designing the virtual reference speed and the actual reference speed to construct the speed error;

[0129] Specifically include the following:

[0130]

[0131] Position and heading are defined as: x = [x, y, z, ψ] T , the control input is: u=[u,v,w,r] T In order to use the PPF function to constrain the speed error, the speed error needs to occur and maintain a uniform error form on the sliding surface, that is, use the converted error; therefore, first a new virtual speed quantity needs to be established; consider a time-varying reference trajectory η d ∈R 4 Define the position tracking error as Combining formula (6), we get:

[0132]

[0133] Where J(η) is the coordinate transformation matrix; μ r Represents the velocity vector of the relative ocean current and the fuselage; η∈R 4 represents the four-degree-of-freedom position and attitude of the UUV; η d ∈R 4 is the desired tracking trajectory.

[0134] μ r As the virtual control input of equation (10), the designed virtual control command acts as a reference speed vector, and the virtual speed is:

[0135]

[0136] Among them, J -1 (η) is the inverse of the coordinate transformation matrix; k 1 =diag(k 11 ,…,k 14 ) and k 2 =diag(k 21 ,…,k24 ) are all constants and positive definite matrices that need to be designed, k 1i , k 2i (i = 1, …, 4) satisfy is the tracking error; a dot above a character represents differentiation. Then, define the velocity tracking error as:

[0137] e = μ - υ c (12)

[0138] where μ represents the linear velocity and angular velocity vectors in the body frame; υ c represents the virtual velocity quantity.

[0139] S4. Perform performance constraints on the constructed velocity error through a predetermined performance function;

[0140] Specifically, it includes the following content:

[0141] Set the error bound and describe the specified performance as:

[0142]

[0143] where ρ(t) is the PPF, b and are described as:

[0144]

[0145] where is the overshoot exponential constant; e(t) represents the velocity tracking error, and e(0) represents the initial velocity tracking error;

[0146] The predetermined performance function PPF is as follows:

[0147]

[0148] where 0 < ρ ∞ <|e(0)| < ρ 0 , 0 < T < ∞ and l > 1 are constants selected by the user; the performance metrics adopted include: the constant T is the predetermined maximum allowable convergence time for ρ(t) to converge from the given maximum initial error ρ 0 to the maximum allowable steady-state error ρ ∞ ; l represents the predetermined minimum convergence speed; the properties of ρ(t) are summarized as: ρ(t) is a monotonically decreasing bounded smooth positive function, i.e., 0 < ρ ∞ ≤ ρ(t) ≤ ρ 0 , Meanwhile

[0149] The time derivative of ρ(t) is:

[0150]

[0151] Transformation function Introduced as:

[0152]

[0153] ψ(x) is a smooth, increasing bijective mapping that satisfies ψ(0) = 0.

[0154] The derivative υ(x) of ψ(x) with respect to x is:

[0155]

[0156] The inverse function of the ψ(x) function is given by:

[0157]

[0158] Obviously, the inverse function of ψ(x) is is also a smooth increasing bijective mapping, and ψ -1 (0) = 0; define the auxiliary variable θ as:

[0159] θ=e / ρ (22)

[0160] Wherein, e=e(t) represents the speed tracking error; ρ=ρ(t) is the predetermined performance function; the transformed speed error vector ε is introduced, and the formula is as follows:

[0161] ε=ψ(θ) (23)

[0162] The time derivative of the transformed velocity error vector ε is:

[0163]

[0164] Among them, α and β are defined as: β=v(θ) / ρ(t); define B=diag(β 1 ,…,β 4 ).

[0165] S5. Design an adaptive continuous sliding mode control dynamic controller to drive the UUV to complete finite time speed tracking.

[0166] Specifically include the following:

[0167] In S4, a transformation speed error based on PPF has been designed. When designing the sliding surface, it is necessary to design a sliding surface containing only speed error information for matching; therefore, an integral sliding surface S with finite time specified performance is proposed, as shown below:

[0168]

[0169] Where H(ε)=1+χe -ε , χ>0 is a parameter, the range of H(ε) is (1,1+χ), and H(ε) is a monotonically decreasing function; K 1 ,K 2 >0 constant, ν 1 >1,0<ν 2 <1,sig p (x)=|x| p sign(x), sign(x) is the sign function;

[0170] The time derivative of the integrated sliding surface S is:

[0171]

[0172] Assumption: If the UUV is subject to less severe uncertainties and disturbances and tracks a less complex desired trajectory so that the vehicle thrusters are not frequently saturated, then the lumped system uncertainty Bounded, so that the total disturbance is fitted with a quadratic polynomial about the speed and satisfies the following conditions:

[0173]

[0174] Among them, λ i (i=0,1,2) are the adaptive parameters to be estimated. In addition, it is easy to see in practical applications that is bounded; the control input is The total disturbance is expressed as:

[0175]

[0176] here,

[0177] Based on the design principles of sliding surface and sliding mode controller, the following controller is designed, and the continuous control law is as follows:

[0178]

[0179]

[0180] in, is the reference velocity vector vc The derivative of -1 B = diag(β 1 ,…,β 4 ) positive definite inverse; H(ε)=1+Xe -ε , χ>0 is a parameter, the range of H(ε) is (1,1+χ), H(ε) is a monotonically decreasing function; S is the integral sliding surface; K 1 ,K 2 >0 constant, v 1 >1,0 <v 2 <1,sig p (x)=|x| p sign(x), sign(x) is the sign function; L 1 >0,L 2 >0,m 1 >1,0 <m 2 <1.

[0181] In addition, adaptive components are used in the controller to counteract the effects of model parameter uncertainty and external disturbances:

[0182]

[0183] in, is the adaptive parameter λ to be estimated i The estimated value of i=0,1,2; ω is a constant; S is the integral sliding surface; c 1 >0 and c 2 >0,c 1 and c 2 is a constant adaptive gain.

[0184] In order to verify the effectiveness of the UUV trajectory tracking control method based on the predetermined performance adaptive fast integral sliding mode proposed in the present invention, a simulation experiment is carried out using MATLAB, and the detailed description is as follows:

[0185] In the simulation, the desired spiral tracking trajectory is chosen as:

[0186] x d (t) = -sin(0.5t)

[0187] y d (t) = sin(0.5t)

[0188] z d (t)=0.05t

[0189] ψ d (t) = atan2(yd ,x d )

[0190] Assume that the initial conditions of position and orientation are η(0) = [0.5m, 0m, 0m, 0rad]; and the initial velocity is μ(0) = [0.5m / s, 0m / s, 0m / s, 0rad / s]. In this three-dimensional trajectory tracking problem, 20% uncertainty is added to each dynamic model parameter and the external disturbance is:

[0191] d u =2sin(0.1t)N

[0192] d v =sin(0.1t)N

[0193] d w =3sin(0.2t)N

[0194] d r =2cos(0.1t)N·m

[0195] Figure 2 The ocean current velocity model proposed in this invention is a curve diagram of ocean current velocity change calculated based on ocean current velocity data at different depths at the entrance of Gowanus Bay, New York, USA. Next, the trajectory tracking control performance of the proposed control scheme under the influence of model uncertainty, external disturbance and ocean current is studied through the three-dimensional tracking control problem.

[0196] Under the influence of model uncertainty and external disturbance, the three-dimensional spiral tracking results and four-degree-of-freedom tracking errors are shown as follows: Figure 3 , Figure 4 As shown, from Figure 4 It can be seen that the position and heading tracking errors along the X, Y, and Z axes converge within about 2 seconds. After considering the ocean current interference in the kinematic model and the dynamic model, Figure 5 , Figure 6 It is confirmed that the proposed control scheme maintains good tracking performance under ocean current disturbances. Figure 7 The velocity tracking error produced by the proposed control scheme is demonstrated, where the maximum error convergence time of velocity tracking is approximately 2s.

[0197] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode, characterized in that: The following steps are involved: S1, given the initial state and desired trajectory of the UUV; S2. Introduce the ocean current motion model based on frequency analysis into the kinematic and dynamic model of UUV; S3, designing the virtual reference speed and the actual reference speed to construct the speed error; S4, performing performance constraints on the constructed speed error through a predetermined performance function; S5. Design an adaptive continuous sliding mode control dynamic controller to drive the UUV to complete finite time speed tracking.

2. The UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode according to claim 1 is characterized in that: In S1, the initial state and desired trajectory of the given UUV specifically include: The inertial position and attitude of the UUV with inertial and body frames are expressed as: η=[x,y,z,ψ] T (1) The constant expressions of linear velocity and angular velocity are: μ=[u,v,w,r] T (2) The above basic parameters include the coordinate values ​​of the autonomous underwater robot in the robot coordinate system and the longitudinal sway velocity u, the transverse sway velocity v and the heave velocity w, the yaw angular velocity r of the autonomous underwater robot in the robot coordinate system, the coordinates x, y and z of the autonomous underwater robot in the inertial coordinate system and the bow angle ψ in the inertial coordinate system; η = [x, y, z, ψ] T Represents the position and heading vector of the inertial coordinate system; μ = [u, v, w, r] T represents the linear and angular velocity vectors in the body frame; In the three-dimensional trajectory tracking problem, given the desired spiral tracking trajectory η d ∈R 4 Select as: Assume that the initial conditions for position and orientation values ​​are: η(0)=[0.5m,0m,0m,0rad] (4) The initial velocity is: μ(0)=[0.5m / s,0m / s,0m / s,0rad / s] (5) Where μ(0) represents the initial velocity of the UUV.

3. The UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode according to claim 1 is characterized in that: In S2, the kinematic and dynamic models of UUVs that introduce the ocean current motion model based on frequency analysis are: Where J(ψ) is the coordinate transformation matrix; V xy =[V x ,V y ,0,0] T represents the ocean current velocity in the inertial coordinate system; M = M0 + ΔM, C (μ r )=C0(μ r )+ΔC(μ r ),D(μ r )=D0(μ r )+ΔD(μ r ), g(η)=g0(η)+Δg(η), M0 and ΔM represent the nominal mass matrix and uncertainty mass matrix of UUV, respectively, C0(μ r ) and ΔC(μ r ) represent the nominal matrix and uncertainty matrix of rigid Coriolis force and centripetal force, respectively, D0(μ r ) and ΔD(μ r ) represent the nominal and uncertain viscous drag matrices, respectively, g0(η) and Δg(η) represent the nominal and uncertain values ​​of the UUV buoyancy and weight, respectively; F = [τ u ,τ v ,τ w ,τ r ] T represents the control force and torque of the UUV; d = [d u ,d v ,d w ,d r ] T represents external disturbance; η=[x,y,z,ψ] T Represents the position and heading vector of the inertial coordinate system; μ r =[u r ,v r ,w r ,r r ] T represents the velocity vector relative to the ocean current and the fuselage, where u r =uu c ,v r =vv c ,w r =w,r r = r, μ = [u, v, w, r] T represents the linear velocity and angular velocity vector in the body frame; u c represents the speed of the surge current encountered by the UUV in the real ocean environment; v c Represents the swaying current speed encountered by UUV in real ocean environment.

4. The UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode according to claim 3 is characterized in that: The surge current speed u encountered by UUV in the real ocean environment c and the sway current velocity v c The sea current speed to which the fuselage is subjected is converted through the following conversion relationship: Among them, V x and V y are the velocity components of the ocean current expressed in the x- and y-directions of the inertial reference frame, as follows: Among them, parameters λ and κ determine the chaotic mixing degree of the ocean current, b1, b2 and b3 are sensitive variables related to the underwater environmental fluctuations, and b4 and b5 represent random variables.

5. The UUV trajectory tracking control method based on predetermined performance adaptive fast integral sliding mode according to claim 1 is characterized in that: In S3, the specific process of constructing the speed error is: Position and heading are defined as: x = [x, y, z, ψ] T , the control input is: u=[u,v,w,r] T ,In order to use the PPF function to constrain the speed error, it is necessary to have the speed error occur, and keep the error in a uniform form on the sliding surface, that is, use the converted error; Therefore, first a new virtual velocity quantity needs to be established; Consider a time-varying reference trajectory η d ∈R 4 Define the position tracking error as Combining formula (6), we get: Where J(η) is the coordinate transformation matrix; μ r Represents the velocity vector of the relative ocean current and the fuselage; η∈R 4 represents the four-degree-of-freedom position and attitude of the UUV; η d ∈R 4 is the desired tracking trajectory; μ r As the virtual control input of equation (10), the designed virtual control command acts as a reference speed vector, and the virtual speed is: Among them, J -1 (η) is the inverse of the coordinate transformation matrix; k1=diag(k 11 ,…,k 14 ) and k2=diag(k 21 ,…,k 24 ) are constants and positive definite matrices that need to be designed, k 1i ,k 2i (i=1,…,4) satisfies is the tracking error; then, the velocity tracking error is defined as: e=μ-υ c (12) where μ represents the linear velocity and angular velocity vector in the body frame; υ c Indicates the virtual speed amount.

6. The UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode according to claim 1 is characterized in that: In S4, the performance constraints are imposed on the constructed speed error through a predetermined performance function, which specifically includes the following contents: Set error limits to describe the specified performance as: where ρ(t) is the PPF, b and Described as: in, is the overshoot exponential constant; e(t) represents the velocity tracking error, and e(0) represents the initial velocity tracking error; The predetermined performance function PPF function is as follows: where 0 < ρ ∞ <|e(0)| < ρ0, 0 < T < ∞ and l > 1 are constants chosen by the user; the performance metrics adopted include: the constant T is the predetermined maximum allowable convergence time for ρ(t) to converge from a given maximum initial error ρ0 to a maximum allowable steady-state error ρ ∞ ; l represents the predetermined minimum convergence rate; the properties of ρ(t) are summarized as: ρ(t) is a monotonically decreasing, bounded, smooth positive function, i.e., 0 < ρ ∞ ≤ ρ(t) ≤ ρ0, while The time derivative of ρ(t) is: Transformation function ψ(·): Introduced as: ψ(x) is a smooth, increasing bijective mapping that satisfies ψ(0) = 0. The derivative υ(x) of ψ(x) with respect to x is: The inverse function of the ψ(x) function is given by: Obviously, the inverse function of ψ(x) is -1 (·): is also a smooth increasing bijective mapping, and ψ -1 (0) = 0; define the auxiliary variable θ as: θ=e / ρ (22) Wherein, e=e(t) represents the speed tracking error; ρ=ρ(t) is the predetermined performance function; the transformed speed error vector ε is introduced, and the formula is as follows: ε=ψ(θ) (23) The time derivative of the transformed velocity error vector ε is: Among them, α and β are defined as: β=υ(θ) / ρ(t); define B=diag(β1,…,β4).

7. The UUV trajectory tracking control method based on a predetermined performance adaptive fast integral sliding mode according to claim 1 is characterized in that: In S5, the adaptive continuous sliding mode control dynamic controller is designed to drive the UUV to complete finite time speed tracking. The specific process includes: In S4, a transformation speed error based on PPF has been designed. When designing the sliding surface, it is necessary to design a sliding surface containing only speed error information for matching; therefore, an integral sliding surface S with finite time specified performance is proposed, as shown below: Where H(ε)=1+χe -ε , χ>0 is a parameter, the range of H(ε) is (1,1+χ), H(ε) is a monotonically decreasing function; K1, K2>0 constants, ν1>1, 0<ν2<1, sig p (x)=|x| p sign(x), sign(x) is the sign function; The time derivative of the integrated sliding surface S is: Assumption: If the UUV is subject to less severe uncertainties and disturbances and tracks a less complex desired trajectory so that the vehicle thrusters are not frequently saturated, then the lumped system uncertainty Bounded, so that the total disturbance is fitted with a quadratic polynomial about the speed and satisfies the following conditions: Among them, λ i (i=0,1,2) are the adaptive parameters to be estimated. In addition, it is easy to see in practical applications that is bounded; the control input is The total disturbance is expressed as: in, Based on the design principles of sliding surface and sliding mode controller, the following controller is designed, and the continuous control law is as follows: in, is the reference velocity vector v c The derivative of -1 It is the positive inverse of B=diag(β1,…,β4); H(ε)=1+Xe -ε , X>0 is a parameter, the range of H(ε) is (1,1+χ), H(ε) is a monotonically decreasing function; S is the integral sliding surface; K1, K2>0 constants, v1>1, 0<ν2<1, sig p (x)=|x| p sign(x), sign(x) is the sign function; L1>0, L2>0, m1>1, 0 <m2<1; In addition, adaptive components are used in the controller to counteract the effects of model parameter uncertainty and external disturbances: in, is the adaptive parameter λ to be estimated i The estimated value of ω is a constant; c1>0 and c2>0, c1 and c2 are constant adaptive gains.

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