An underactuated unmanned surface vehicle path following control method based on adaptive sliding mode

Abstract

The application discloses a kind of underactuated unmanned ship track tracking control methods based on adaptive sliding mode, steps are as follows: step 1: according to model parameter uncertainty and external disturbance influence factor, the motion equation of the mathematical model of describing underactuated unmanned ship in horizontal plane three degrees of freedom is established;Step 2: the tracking error dynamic equation is established by tangential trajectory coordinate system;Step 3: based on Lyapunov stability theory, according to tracking error dynamic equation, trajectory tracking guidance law is designed;Step 4: barrier function and super-torsion integral sliding mode method are used, according to the expected bow angle and expected forward speed in trajectory tracking guidance law, motion equation, the sliding mode controller of forward speed and bow angle is designed, and unmanned ship is controlled by the sliding mode controller of forward speed and bow angle.The application obtains expected forward speed and expected bow angle by designing track tracking guidance law, based on Lyapunov stability theory, and then guarantees the convergence of tracking error.

Description

Technical Field

[0001] This invention relates to the field of underactuated unmanned surface vessel (USV) motion control technology, and specifically to a trajectory tracking control method for an underactuated USV based on adaptive sliding mode. Background Technology

[0002] Unmanned surface vessels (USVs), as autonomous marine transport platforms, can perform a wide range of long-duration missions in complex and dangerous marine environments. However, underactuated USVs are only equipped with longitudinal propulsion and steering torque devices, lacking lateral actuators. Furthermore, they are susceptible to uncertainties such as wind, waves, and currents, significantly increasing the difficulty of control.

[0003] The implementation of trajectory tracking control provides a fundamental guarantee for the successful completion of various tasks by unmanned surface vessels (USVs). A good tracking control system can provide USVs with safe, autonomous, accurate, and faster mission completion capabilities. Currently, significant research results have been achieved in trajectory tracking control, including backstepping, dynamic surface control, and sliding mode control. Sliding mode control is widely used in underactuated system control due to its strong robustness and low dependence on system model parameters. For USVs, guidance laws are designed based on the desired velocity from sway and forward velocities. However, the sway velocity is not directly controlled by the control input, making it difficult to guarantee the correct heading of the USV. Typically, the upper bound of the external disturbance needs to be known in advance to ensure system stability by adjusting the sliding mode gain to be greater than this upper bound. However, in practice, the upper bound of the disturbance is usually unknown and difficult to measure. Moreover, discontinuities in the sliding mode controller can cause system chattering, exacerbating mechanical wear on the actuator components. Summary of the Invention

[0004] This invention provides an underactuated unmanned surface vessel (USV) trajectory tracking control method based on adaptive sliding mode, in order to solve the problems of large system chattering, uncertainty of the USV motion system, and unobtainable upper bound of disturbance in the prior art.

[0005] This invention provides a trajectory tracking control method for underactuated unmanned surface vessels based on adaptive sliding mode, comprising the following steps:

[0006] Step 1: Based on the uncertainty of model parameters and the influence of external disturbances, establish the equations of motion for a mathematical model describing the three degrees of freedom of the underactuated unmanned surface vessel in the horizontal plane;

[0007] Step 2: Establish the dynamic equation of tracking error using the tangential trajectory coordinate system;

[0008] Step 3: Based on Lyapunov stability theory and the dynamic equation of tracking error, design the trajectory tracking guidance law;

[0009] Step 4: Using the barrier function and super-torsion integral sliding mode method, based on the desired heading angle and desired forward velocity in the trajectory tracking guidance law and the equation of motion, design a sliding mode controller for the forward velocity and heading angle, and control the unmanned surface vessel through the sliding mode controller for the forward velocity and heading angle.

[0010] Furthermore, the specific formula for the equation of motion in step 1 is as follows:

[0011]

[0012] In the formula, η = [x, y, ψ] T Let v be the pose vector; v = [u, v, r] T It is the velocity vector; M is the rotation matrix; C is the mass matrix; D is the Coriolis matrix; τ = [τ u ,0,τ r ] T ;τ u For longitudinal thrust; τ r For steering torque; Let τ be the sum of the unknown components of the system and external disturbances, ΔM, ΔC(v), and ΔD be the uncertainties of M, C(v), and D, respectively. w =[τ wu , τ wv , τ wr [This is due to external disturbances such as wind, waves, and currents.]

[0013] Furthermore, the specific method for establishing the dynamic equation of tracking error through the tangential trajectory coordinate system is as follows: the tangential trajectory coordinate system is defined as a local translation coordinate system, and the tracking error is established through the local translation coordinate system and the motion equation, as shown in the following specific equation:

[0014]

[0015] In the formula, ψ r =atan2(y′r(t), x′ r (t)) represents the trajectory tangential angle x, y represents the position coordinates; xr and yr represent the coordinates of the trajectory target point.

[0016] Furthermore, the formulas for the desired heading angle and desired forward velocity in the trajectory tracking guidance law are as follows:

[0017]

[0018] In the formula, Δ is the forward sight distance, Δ > 0; k ψ and k x To control the gain; the sideslip angle β = atan2(v, u).

[0019] Furthermore, the formula for the forward look-ahead distance in the trajectory tracking guidance law is as follows:

[0020]

[0021] In the formula, Δ min ,Δ max These are the minimum and maximum forward sight distances, respectively, with gain parameters γ1 > 0, γ2 > 0, and γ3 > 0.

[0022] Furthermore, a sliding mode controller for the forward velocity error is designed, wherein the sliding surface is:

[0023]

[0024] In the formula, the speed error e u =u d -u, integral gain parameter λ u >0;

[0025] The control input for the equivalent sliding mode control is:

[0026] τ u =τ ueq +τ usw

[0027] In the formula,

[0028]

[0029]

[0030]

[0031] k1 and k2 are control gain parameters.

[0032] Furthermore, a sliding mode controller for the bow angle error is designed, wherein the sliding surface is:

[0033]

[0034] In the formula, the heading angle error e ψ =ψ d -ψ, gain parameter λ ψ >0;

[0035] The control input for the equivalent sliding mode control is:

[0036]

[0037]

[0038]

[0039] In the formula, k ψ >0 represents the gain constant; The adjustment parameter ε > 0 and satisfies |s ψ (0) | < ε; finite time t ψ >0; k3 and k4 are control gain parameters.

[0040] The beneficial effects of this invention are:

[0041] This invention designs a trajectory tracking guidance law based on Lyapunov stability theory to obtain the desired forward velocity and desired heading angle, thereby ensuring the convergence of tracking errors. A sliding mode control method is employed to directly control longitudinal thrust and steering torque, reducing the computational complexity of the controller design. Simultaneously, by utilizing barrier function technology and a super-twisting algorithm, the sliding mode gain is adaptively adjusted even when the upper bound of the disturbance is unknown, ensuring that the gain is not overestimated. Furthermore, the sliding variable converges within a finite time and remains within a predefined zero region, guaranteeing the performance of ship trajectory tracking. Attached Figure Description

[0042] The features and advantages of the invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way. In the drawings:

[0043] Figure 1 This is a block diagram of a specific embodiment of the system of the present invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] This invention provides a method for trajectory tracking control of an underactuated unmanned surface vessel based on adaptive sliding mode.

[0046] Figure 1This paper describes the unmanned surface vessel (USV) trajectory tracking control system model of the present invention. The desired trajectory is given to the USV guidance system, a local trajectory coordinate system is established, and the dynamic changes in trajectory tracking error are calculated. Using the moving local trajectory coordinate system and Lyapunov stability theory, the desired forward velocity and desired heading angle of the USV are calculated. Then, using sensors such as GPS and compass, the current actual velocity and heading angle of the USV are measured, and the speed and heading errors are calculated. Finally, using barrier function theory, adaptive parameters for the super-torsion adaptive sliding mode control method are designed to achieve trajectory tracking of the USV under unknown disturbance conditions.

[0047] The specific steps are as follows:

[0048] Step 1: Incorporate model parameter uncertainties and the effects of external disturbances to establish the equations of motion describing the three-degree-of-freedom mathematical model of the underactuated unmanned surface vessel in the horizontal plane, as follows:

[0049]

[0050]

[0051] In the formula, η = [x, y, ψ] T Let v be the pose vector; v = [u, v, r] T It is the velocity vector; M is the rotation matrix; C is the mass matrix; D is the Coriolis matrix; τ = [τ u ,0,τ r ] T ;τ u For longitudinal thrust; τ r For steering torque; The sum of the unknown parts of the system and external disturbances can also be expressed as δ = [δ u δ v δ r ] T Let ΔM, ΔC(v), where ΔD represents the uncertainty components of M, C(v), and D, respectively, and τ w =[τ wu , τ wv , τ wr This indicates external disturbances such as wind, waves, and currents.

[0052] The equations of motion can be expanded as follows:

[0053]

[0054] Step 2: Establish the tracking error equation:

[0055] First, define the tangential trajectory coordinate system as a local translation coordinate system. At the trajectory target point P... r (x r(t), y r The trajectory at point (t) is rotated clockwise by the inertial coordinate system. The tangential angle ψ of this trajectory is... r This yields the tangential track coordinate system. Therefore, the tracking error equation x is established using the local moving coordinate system and the equations of motion. e y e It can be represented as follows:

[0056]

[0057] Where, ψ r =atan2(y′) r (t), x′ r (t) is the tangential angle of the trajectory.

[0058] Differentiating the above equation, we get

[0059]

[0060] In the formula, the unmanned surface vessel speed Sideslip angle β = atan2(v, u).

[0061] Step 3: Design the trajectory tracking guidance law:

[0062] To ensure tracking error x e y e Approaching zero, the desired heading angle and desired forward velocity in the trajectory tracking guidance law are designed as follows:

[0063]

[0064] In the formula, k ψ and k x To control the gain; with forward look-ahead distance Δ > 0, the forward look-ahead distance is designed as a function of lateral tracking error and airspeed:

[0065]

[0066] In the formula, Δ min ,Δ max These are the minimum and maximum forward sight distances, respectively, with parameters γ1 > 0, γ2 > 0, and γ3 > 0.

[0067] Step 4: Using the barrier function and the super-torsion integral sliding mode method, based on the desired heading angle and desired forward velocity in the trajectory tracking guidance law, and based on the kinematic equations of the unmanned surface vessel, a sliding mode controller for the forward velocity and heading angle is designed, and the unmanned surface vessel is controlled by the sliding mode controller for the forward velocity and heading angle.

[0068] Among them, a sliding mode controller for the forward velocity error is designed, wherein the sliding surface is:

[0069] s u =e u +λ u ∫e u dτ

[0070] In the formula, the speed error e u =u d -u, integral gain parameter λ u >0.

[0071] Differentiating with respect to the sliding surface, we get:

[0072]

[0073] Using the equivalent sliding mode control method, the control input can be selected in the following forms:

[0074] τ u =τ ueq +τ usw ,

[0075] The equivalent term in sliding mode control is:

[0076]

[0077] The switching options in sliding mode control are:

[0078]

[0079] In the formula, control gain parameters k1 and k2 are control gain parameters.

[0080] The sliding mode adaptive gain is:

[0081]

[0082] In the formula, k u >0 is a constant. The barrier function is a positive semi-definite function with parameter ε > 0. The properties of the barrier function guarantee that for all sliding mode variables at initial time s... u (0), s u (t) can be performed in a finite time t u Converging to less than Within the range, and for all t≥t u At any time, there is |s u (t)|<ε holds.

[0083] Among them, a sliding mode controller for the bow angle error is designed, wherein the sliding mode surface is:

[0084]

[0085] In the formula, the heading angle error e ψ =ψd -ψ, gain parameter λ ψ >0,

[0086] Differentiating with respect to the sliding surface, we get:

[0087]

[0088] Similar to calculating the longitudinal thrust, an equivalent sliding mode control method is used, with the control input selected in the following form:

[0089] τ r =τ req +τ rsw

[0090] in,

[0091]

[0092]

[0093] In the formula, control gain parameters k3 and k4 are control gain parameters.

[0094] The sliding mode adaptive gain is:

[0095]

[0096] In the formula, k ψ >0 is a constant. The parameter ε > 0. For all t ≥ t u At any time, there is |s u (t)|<ε holds.

[0097] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. An adaptive sliding mode based underactuated USV path following control method, characterized in that, The method comprises the following steps: Step 1: according to the model parameter uncertainty and external disturbance influence factors, a mathematical model of the motion equation of the underactuated unmanned surface vehicle in the horizontal plane three degrees of freedom is established; Step 2: a tracking error dynamic equation is established through a tangential trajectory coordinate system; Step 3: a trajectory tracking guidance law is designed based on the Lyapunov stability theory according to the tracking error dynamic equation; Step 4: a forward speed and a bow angle sliding mode controller are designed according to the expected bow angle and the expected forward speed in the trajectory tracking guidance law, the motion equation and the barrier function and the super-twisting integral sliding mode method, and the unmanned surface vehicle is controlled through the forward speed and the bow angle sliding mode controller, Wherein, the formula of the expected bow angle and the expected forward speed in the trajectory tracking guidance law is as follows: ； wherein ; Δ is a forward distance, Δ > 0; and k x is a control gain; side slip angle ; The formula of the forward distance is as follows: ； where Δ min , Δ max are the minimum and maximum values of the look-ahead distance, respectively, and the gain parameter , , ; The sliding surface of the forward speed sliding mode controller is: ； where the velocity error e u = u d - u, the integral gain parameter ; Wherein, the control input of the equivalent sliding mode control is: ； In the formulae, ; ; ； k1 and k2 are control gain parameters; The sliding surface of the bow angle sliding mode controller is: ； wherein the bow angle error , gain parameter ; Wherein, the control input of the equivalent sliding mode control is: ； ； ； wherein is a gain constant; ; adjustment parameters and satisfies ; finite time ; k3, k4 are control gain parameters.

2. The adaptive sliding mode based underactuated USV path following control method of claim 1, wherein, The specific formula of the motion equation in the step 1 is as follows: ； wherein is a pose vector; is a velocity vector; is a rotation matrix; M is the mass matrix; C is the Coriolis matrix; D is the damping matrix; ; is the longitudinal thrust force; is the steering moment; is the sum of the unknown part of the system and the external disturbance, ΔM, ΔC(v), ΔD are the uncertainty parts of M, C(v), D, respectively, is the external disturbance such as wind, wave, current, etc.

3. The adaptive sliding mode based underactuated USV path following control method of claim 1, wherein, The specific method for establishing the tracking error dynamic equation through the tangential trajectory coordinate system is that the tangential trajectory coordinate system is defined as a local moving coordinate system, and the tracking error is established through the local moving coordinate system and the motion equation, and the specific equation is as follows: ； In the formula, is the trajectory tangential angle x, y is the position coordinate; x r , y r is the coordinate of the trajectory target point.

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