CN116859933A - Novel LOS guidance method for path tracking prediction of ultra-large under-actuated ship - Google Patents

Abstract

The invention discloses a novel LOS guidance method for tracking and predicting a path of a super-large under-actuated ship, which comprises the following steps: s1, establishing a ship simulation model containing wind and wave interference and nonlinear terms and a ship design model containing external disturbance; s2, acquiring a high-order nonlinear observer to acquire the ship speed and the external undetermined disturbance; s3: obtaining a virtual reference heading angle of a ship; s4: taking the total path tracking deviation of the path deviation of the current time domain and the path deviation of the future time domain into consideration, and acquiring a predicted LOS virtual heading angle of the ship; s5: and obtaining the control law of the ship so as to control the path of the novel ultra-large underactuated ship. The invention establishes a corresponding navigation strategy aiming at the ultra-large under-actuated ship, and solves the problem of overshoot easily occurring in the track tracking process of the ultra-large under-actuated ship. Provides theoretical guidance for improving the safety of the navigation of the ultra-large ship.

Description

Novel LOS guidance method for path tracking prediction of ultra-large under-actuated ship

Technical Field

The invention relates to the field of ship motion control and guidance, in particular to a novel ultra-large under-actuated ship path tracking prediction LOS guidance method.

Background

With the rapid development of global economy, global sea freight traffic has increased dramatically. The increase of international import and export trade volume stimulates the demand of marine container shift transportation and simultaneously drives the development of large container ships. The development of large vessels presents new challenges for navigation safety. These new challenges are different from the past and even surpass the traditional ideas of the industry. The ultra-large underactuated ship has the characteristics of large inertia and large time lag, and in the traditional guidance method, the phenomenon of overshoot of the ship in the process of tracking the reference track can be caused, so that the ship collides or straddles, and the navigation safety of the ship is affected.

Disclosure of Invention

The invention provides a novel LOS guidance method for tracking and predicting a path of an oversized under-actuated ship, which aims to solve the problems.

The invention comprises the following steps:

a novel LOS guidance method for tracking and predicting a path of a super-large under-actuated ship comprises the following steps:

s1, establishing a ship simulation model containing wind and wave interference and nonlinear terms and a ship design model containing external disturbance;

s2, acquiring a high-order nonlinear observer to acquire the ship speed and the external undetermined disturbance;

s3: according to the ship simulation model, obtaining a virtual reference heading angle of the ship;

s4: according to the ship design model, the ship speed and the virtual reference heading angle of the ship, taking the total path tracking deviation of the path deviation of the current time domain and the path deviation of the future time domain into consideration, and obtaining a predicted LOS virtual heading angle of the ship;

s5: and according to the external undetermined disturbance, acquiring a control law of the ship through the predicted LOS virtual heading angle of the ship so as to control the path of the novel oversized underactuated ship.

Further, the ship simulation model is built as follows:

wherein: x represents the current position abscissa of the ship; y represents the ordinate of the current position of the ship; u represents the longitudinal speed of the ship; v represents the transverse speed of the ship; r represents the bow turning angular speed of the ship; psi represents the ship heading; m represents the mass of the ship; m is m _x Representing additional mass in the heave degrees of freedom; m is m _y Representing additional mass on the cross; x is X _H Representing the forces to which the bare hull is subjected in the heave degrees of freedom; x is X _P Representing the forces to which the propeller is subjected in the heave degrees of freedom; x is X _W Representing the force to which the wind is subjected in the heave degrees of freedom; x is X _WAVE Representing the forces to which the wave is subjected in the heave degrees of freedom; v (V) _c Representing the ocean wave velocity; psi phi type _c Representing the ocean wave flow direction; y is Y _H Representing the forces to which the bare hull is subjected in the lateral degrees of freedom; y is Y _P Representing the forces to which the propeller is subjected in the lateral degrees of freedom; y is Y _W Representing the force exerted by wind on the lateral degrees of freedom; y is Y _WAVE Representing the force exerted by the wave on the lateral swing degree of freedom; i _ZZ Representing the moment of inertia of the vessel about the vertical axis; j (J) _ZZ Representing additional moment of inertia; n (N) _H Representing the forces to which the bare hull is subjected in a bow degree of freedom; n (N) _P Representing the forces exerted by the propeller in the bow freedom; n (N) _R Representing the forces exerted by the rudder on the bow freedom; n (N) _W Representing the force exerted by the wind on the bow freedom; n (N) _WAVE Representing the forces to which the wave is subjected in the bow freedom;representing a derivative operation.

Further, the ship design model is built as follows:

wherein: beta represents the drift angle of the ship; t represents a ship following index; k represents a ship spin index; f (f) _r Representing an externally undetermined disturbance; delta represents the rudder angle.

Further, the higher order nonlinear observer is obtained as follows:

in the formula ：representing the estimated value; psi represents the heading angle; g _u Representing a known portion of the longitudinal velocity model; g _v Representing a known portion of the transverse velocity model; g _r Representing a known portion of the yaw rate model; l (L) _x 、l _y 、l _ψ 、l _ux 、l _uy 、l _vx 、l _vy 、l _r 、l _fux 、l _fuy 、l _fvx 、l _fvy and l_fr All are positive design parameters; f (f) _u Disturbance f representing the longitudinal speed direction of a vessel _v Representing a disturbance in the transverse velocity direction of the vessel; f (f) _r Representing disturbance of the ship in the direction of the turning bow angular velocity;

the observation error of the high-order nonlinear observer is obtained as follows:

in the formula ：representing estimation error +.>

Further, the method for obtaining the virtual reference heading angle of the ship comprises the following steps:

in the formula ：ψ_los Representing a virtual reference heading angle of the vessel; θ _k Representing a reference path angle; y is _e Representing a path deviation;

wherein ,

R＝k ₁ |y _e |+k ₂ L (6)

wherein: l represents the hull length; y is _e Representing a path deviation; k (k) ₁ Representing a positive parameter for adjusting the tracking speed; k (k) ₂ Representing a positive parameter for preventing the arc from disjointing the reference path.

Further, the method for obtaining the predicted LOS virtual heading angle of the ship is as follows;

s41: discretizing the ship design model to obtain a step length calculation value of a future time domain:

in the formula ：a ship position calculation value representing a future nth time domain; y (k) represents the current time-domain step size calculation value; t (T) ₁ Representing a sampling period; j represents the number of the future time domain, j is less than or equal to n;

s42: constructing a path deviation of the future time domain according to the step length calculated value of the future time domain:

in the formula ：y_d (k+n) represents a reference path calculation value of the nth time domain in the future;representing a path deviation of a future nth time domain;

s43: acquiring a total path tracking bias taking into account a path bias in the current time domain and a path bias in the future time domain to obtain a virtual reference heading angle psi of the vessel _los Obtaining a predicted LOS virtual heading angle of a ship;

the total path tracking bias is obtained as follows:

in the formula ：y_E (y,y _d ) Representing a total path tracking bias;representing the path deviation of the current time domain;

representing the total path deviation of n time domains in the future; p represents the weight of the path deviation of the current time domain; q represents the weight of the total path deviation of the n time domains in the future;

according to the virtual reference heading angle psi of the ship _los Is obtained by the calculation formula of (1):

in the formula ：ψ_pre-los Representing a reference heading angle based on the predicted LOS;

thus, the first and second light sources are connected,

in the formula ：ψ_d Representing a predicted LOS virtual heading angle of the ship;

wherein ,

in the formula ：an estimated value representing the drift angle of the ship.

Further, the method for obtaining the control law of the ship comprises the following steps:

s51: construction of fast sliding modes of recursive structures

in the formula ：s₀ Representing a 0 th order recursive slip plane; s is(s) ₁ Representing a 1 st order recursive slip plane; psi phi type _e Representing a heading angle deviation; a, a ₀ Representing a positive design parameter; beta ₀ Representing a positive design parameter; q ₀ Representing a positive design parameter; p is p ₀ Representing a positive design parameter;

for s ₁ Regarding time derivative:

wherein ,a₀ ＞0,β ₀＞0 and q₀ ＜p ₀ Order-makingThe control law of the ship is obtained as follows:

wherein: phi represents the designed sliding mode surface parameter; gamma represents the designed sliding mode surface parameter; wherein phi and gamma are more than 0;

when the system is in stateReaching the slide surface s ₁ When (t) =0, the time for the ship design model to reach stability is as follows:

wherein p represents a positive design parameter; q represents a positive design parameter; where q < p is a positive odd number.

The beneficial effects are that: according to the novel path tracking prediction LOS guidance method for the ultra-large under-actuated ship, the predicted LOS virtual heading angle of the ship is obtained by considering the path deviation of the current time domain and the total path tracking deviation of the path deviation of the future time domain, the control law is designed, the corresponding navigation strategy is formulated for the ultra-large under-actuated ship, and the problem of overshoot easily occurring in the track tracking process of the ultra-large under-actuated ship is solved. Provides theoretical guidance for improving the safety of the navigation of the ultra-large ship.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort to a person skilled in the art.

FIG. 1 is a flow chart of a novel method for LOS guidance for path tracking prediction of a very large under-actuated ship;

FIG. 2 is a schematic diagram of a conventional LOS guidance method;

FIG. 3 is a graph of a path followed by an oversized underactuated ship based on predicted LOS;

FIG. 4 is an enlarged view of a portion of the track following diagram of FIG. 3;

FIG. 5 is a path tracking bias duration curve;

FIG. 6 is a course angle and rudder angle duration plot;

FIG. 7 is an enlarged view of a portion of the course angle and rudder angle duration curves of FIG. 5;

FIG. 8 is an observation of speeds u, v, and r based on a high order nonlinear observer;

FIG. 9 is a disturbance f based on a high order nonlinear observer _u 、f _v and f_r Is a result of observation of (a);

FIG. 10 is an observation based on a high order nonlinear observer for drift angle estimation;

FIG. 11 is a schematic diagram of the overall framework of a novel oversized underactuated marine path tracking predictive LOS guidance method of the present invention.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

The embodiment provides a novel ultra-large under-actuated ship path tracking prediction LOS guidance method, which is shown in fig. 1 and 11 and comprises the following steps:

s1, establishing an MMG model containing wind and wave interference and nonlinear terms as a ship simulation model, and a Nomoto model containing external disturbance as a ship design model;

specifically, oversized vessels generally refer to bulk carriers with a load of more than 20 ten thousand tons;

the MMG model is widely applied to simulation experiments due to high precision, so that the MMG model is established as a ship simulation model. In order to simplify the controller design and to meet maritime reality, a Nomoto model is built as a ship design model.

Preferably, the ship simulation model is built as follows:

wherein: x represents the current position abscissa of the ship; y represents the ordinate of the current position of the ship; u represents the longitudinal speed of the ship; v represents the transverse speed of the ship; r represents the bow turning angular speed of the ship; psi represents the ship heading; m represents the mass of the ship; m is m _x Representing additional mass in heave degrees of freedom；m _y Representing additional mass on the cross; x is X _H Representing the forces to which the bare hull is subjected in the heave degrees of freedom; x is X _P Representing the forces to which the propeller is subjected in the heave degrees of freedom; x is X _W Representing the force to which the wind is subjected in the heave degrees of freedom; x is X _WAVE Representing the forces to which the wave is subjected in the heave degrees of freedom; v (V) _c Representing the ocean wave velocity; psi phi type _c Representing the ocean wave flow direction; y is Y _H Representing the forces to which the bare hull is subjected in the lateral degrees of freedom; y is Y _P Representing the forces to which the propeller is subjected in the lateral degrees of freedom; y is Y _W Representing the force exerted by wind on the lateral degrees of freedom; y is Y _WAVE Representing the force exerted by the wave on the lateral swing degree of freedom; i _ZZ Representing the moment of inertia of the vessel about the vertical axis; j (J) _ZZ Representing additional moment of inertia; n (N) _H Representing the forces to which the bare hull is subjected in a bow degree of freedom; n (N) _P Representing the forces exerted by the propeller in the bow freedom; n (N) _R Representing the forces exerted by the rudder on the bow freedom; n (N) _W Representing the force exerted by the wind on the bow freedom; n (N) _WAVE Representing the forces to which the wave is subjected in the bow freedom;representing a derivative operation;

preferably, the ship design model is built as follows:

in particular, since the MMG model of the ship has nonlinear terms, it is difficult to directly apply to the controller design. In addition, the ship model is affected by various states and external disturbances during navigation. To simplify the controller design and to meet maritime reality, the Nomoto model is used as a ship design model. The Nomoto model is expressed as:

wherein: beta represents the drift angle of the ship; t represents a ship following index; k represents a ship spin index; f (f) _r Representing an externally undetermined disturbance; delta represents the rudder angle;

s2, acquiring a high-order nonlinear observer to acquire the ship speed and the external undetermined disturbance;

in particular, since most vessels do not have a speed sensor, the speed of the vessel during voyage is unknown. Even vessels equipped with speed sensors may fail during voyage. Thus, a high-order nonlinear observer is designed to estimate the longitudinal speed u of the vessel, the transverse speed v of the vessel and the angular speed r of the vessel's bow, and external disturbances, including disturbances f in the direction of the longitudinal speed of the vessel _u Disturbance f of the transverse velocity direction of the vessel _v And disturbance f in the direction of the angular velocity of the ship turning bow _r And obtaining the drift angle of the ship in the course of sailing by using the estimated speed value, and compensating the drift angle in the predicted LOS design.

Preferably, the higher order nonlinear observer is obtained as follows:

in the formula ：representing the estimated value; psi represents the heading angle; g _u Representing a known portion of the longitudinal velocity model; g _v Representing a known portion of the transverse velocity model; g _r Representing a known portion of the yaw rate model; l (L) _x 、l _y 、l _ψ 、l _ux 、l _uy 、l _vx 、l _vy 、l _r 、l _fux 、l _fuy 、l _fvx 、l _fvy and l_fr All are positive design parameters; f (f) _u Disturbance f representing the longitudinal speed direction of a vessel _v Representing a disturbance in the transverse velocity direction of the vessel; f (f) _r Representing disturbance of the ship in the direction of the turning bow angular velocity;

the observation error of the high-order nonlinear observer, which can be obtained according to the LOS guidance method, is obtained as follows:

in the formula ：representing estimation error +.>

S3: according to the ship simulation model, obtaining a virtual reference heading angle of the ship;

preferably, the method for obtaining the virtual reference heading angle of the ship is as follows:

specifically, in the present embodiment, the basic idea of converting path tracking into heading control LOS guidance by LOS guidance (line of sight guidance method) is to keep the heading of the ship consistent with the "line of sight angle" so that the unmanned ship automatically approaches to the desired position. The LOS guidance method has the advantages of simplicity, high efficiency, practicability and the like, and is widely applied to the actual engineering development of ships. Picture 2 shows, y _e Represents the path deviation, delta represents the LOS forward distance, theta _k Is the reference path angle. a represents the fixed point turning angle as the included angle between adjacent reference paths, the size of which is 0<a<π。R _m Is an acceptable radius of the circle.

First, by the time when it is aligned with the (k+1) th reference fixed point P _k+1 Each straight line between them constitutes a reference path y _d . Secondly, the actual position P (x, y) of the ship is taken as the center, R is taken as the radius, and a reference path y is drawn _d And (3) intersecting circular arcs. Subsequently, in reference path y _d The intersection point of the straight line closest to the next reference point on the arc is selected as the LOS point P _los . At this time, the coordinate P of the LOS point can be calculated by using simultaneous equations of the circular arc and the straight line _los (x _los ,y _los ). The calculation process is as follows:

acquiring the coordinate P of the LOS point according to the current position of the ship _los (x _los ,y _los ) The method comprises the following steps:

in the formula ：x_los An abscissa representing the LOS point; y is _los An ordinate representing the LOS point; y is _k Representing the current fixed point P _k Is the ordinate of (2); x is x _k The representation represents the current fixed point P _k Is the abscissa of (2); θ _k Representing a reference path angle; r represents a radius centered on the actual position of the vessel, used to determine P _los The location of the point;

based on ship position information, LOS point coordinates and ship path deviation y _e The following virtual reference heading angle is calculated:

in the formula ：ψ_los Representing a virtual reference heading angle of the vessel; θ _k Representing a reference path angle; y is _e Representing a path deviation;

wherein, to ensure that the calculation of the coordinates of the LOS point can be solved, i.e. that there is at least one intersection point between an arc and a straight line, the path deviation y is designed using a curve radius R which varies with time and the length of the hull _e ：

R＝k ₁ |y _e |+k ₂ L (6)

Wherein: l represents the hull length; y is _e Representing a path deviation; k (k) ₁ A positive parameter for adjusting the tracking speed is generally in the range of 1 to 5; k (k) ₂ Representing a positive parameter for preventing the arc from disjoint with the reference path, typically in the range of 0-2;

specifically, another benefit of selecting the variable radius R at this time is that when the path deviation is large, a larger LOS angle can be designed, so that the speed of the ship tracking path is faster; conversely, when the path deviation is smaller, a smaller LOS angle can be designed to reduce the path overshoot.

When the ship moves to the (k+1) th reference fixed point P _k+1 (x _k+1 ,y _k+1 ) Near, accept the (k+1) th parameter in the circular areaExamination fixing point P _k+2 Is a tracking of (a). The switching conditions of the reference points are as follows:

when the ship position P (x, y) satisfies the above condition, the ship starts to follow the next specific point, i.e., k becomes k+1. In general, R is selected _m And designing a virtual reference course for the sum of a plurality of captchas according to the course and the drift angle beta.

S4: based on the ship design model and the virtual reference heading angle ψ of the ship _los Obtaining a predicted LOS virtual heading angle of a ship; to construct a total path deviation by predicting a future time domain position of the vessel;

specifically, the present embodiment predicts a future position of a ship based on an actual position of the current ship, and then designs a new method for predicting visual guidance based on the actual position and the future position of the current ship. First, equation (2) is discretized, and a path y at a future time is predicted by the euler method. The total path deviation is then constructed from the current and future path deviations.

S41: discretizing the ship design model to obtain a step length calculation value of a future time domain:

in the formula ：a ship position calculation value representing a future nth time domain; y (k) represents the current time-domain step size calculation value; t (T) ₁ Representing a sampling period; j represents the number of the future time domain, j is less than or equal to n;

s42: constructing path deviation of the future time domain by utilizing step sizes of different time domains according to the step size calculated value of the future time domain:

in the formula ：y_d (k+n) represents a reference path calculation value representing the nth time domain in the future;representing a path deviation of a future nth time domain;

s43: acquiring a total path tracking bias taking into account a path bias in the current time domain and a path bias in the future time domain to obtain a virtual reference heading angle psi of the vessel _los Obtaining a predicted LOS virtual heading angle of a ship;

the total path tracking bias is obtained as follows:

in the formula ：y_E (y,y _d ) Representing a total path tracking bias;representing the path deviation of the current time domain;

representing the total path deviation of n time domains in the future; p represents the weight of the path deviation of the current time domain; q represents the weight of the total path deviation of the n time domains in the future;

according to the virtual reference heading angle psi of the ship _los Is obtained by the calculation formula of (1):

in the formula ：ψ_pre-los Representing a reference heading angle based on the predicted LOS;

thus, in combination with the LOS guidance method, a novel predictive LOS guidance method is designed as follows:

in the formula ：ψ_d Representing a predicted LOS virtual heading angle of the ship;

wherein ,

in the formula ：an estimate representing the drift angle of the vessel, which is a known parameter in the model; converting the path deviation into course control through the predicted LOS virtual heading angle of the ship;

s5: according to the ship design model, a control law of the ship is obtained through the predicted LOS virtual heading angle of the ship so as to control the path of the novel oversized underactuated ship;

specifically, in the normal sliding mode control, a linear sliding mode surface is selected, and after the system reaches a sliding mode, the tracking error gradually converges to zero. The speed of asymptotic convergence can be adjusted by adjusting the parameters of the sliding mode surface. However, the state tracking error does not converge to zero for a limited time. In order to converge the tracking error to zero, a global fast sliding mode is used to design the controller.

S51: construction of fast sliding modes of recursive structures

in the formula ：s₀ Representing a 0 th order recursive slip plane; s is(s) ₁ Representing a 1 st order recursive slip plane; psi phi type _e Representing a heading angle deviation; a, a ₀ Representing a positive design parameter; beta ₀ Representing a positive design parameter; q ₀ Representing a positive design parameter; p is p ₀ Representing a positive design parameter;

for s ₁ Regarding time derivative:

wherein ,a₀ ＞0,β ₀＞0 and q₀ ＜p ₀ Order-makingThe control law of the ship is obtained as follows:

wherein: phi represents the designed sliding mode surface parameter; gamma represents the designed sliding mode surface parameter; wherein phi and gamma are more than 0;

when the system is in stateReaching the slide surface s ₁ When (t) =0, the time for the ship design model (MMG simulation model) to reach stability is as follows:

wherein p represents a positive design parameter; q represents a positive design parameter; where q < p is a positive odd number.

In the embodiment of the invention, the simulation model is a ship with 3 degrees of freedom, and the control input is single rudder angle input, so that the underspeed ultra-large ship is satisfied, and the path deviation, the stability of the controller and the observer and the simulation verification are as follows:

first, the path deviation is calculated as follows:

in the formula (18)) In (A) _k 、B _k and C_k Are all reference path parameters. The Lyapunov function is selected and its time derivative is determined as follows:

wherein ,V₁ Representing a first lyapunov function; θ _k Representing a reference path angle;

bringing formula (17) into formula (18):

therefore, the stable path deviation y can be obtained based on the reference course angle designed by the LOS guidance technology _e And y is _e And tends to zero.

Considering the controller error, the Lyapunov function is selected as follows:

in the formula ：V₂ Representing a second lyapunov function; theta (theta),χ, η, μ, λ and γ are positive coefficients;

V ₂ the derivative of (2) is expressed as follows:

wherein ,z₁ 、z ₂ 、z ₃ 、z ₄ 、z ₅ 、z ₆ Are all intermediate calculation parameters

Because ofIs strictly boundedThus->σ ₁ Representation definition->Positive parameters of amplitude; since the displacement is greater than the velocity and acceleration, when the design parameter l _x and l_y Above other observer parameters, the sign of the brackets depends on +.> and />Then z ₂ ≤0,z ₃ And is less than or equal to 0. From formula (9), the +_> and />And->Andinversely proportional. By adjusting parameter l _ux and l_uy 、l _vx and l_vy 、l _fux and l_fux L _fvx and l_fvy The ratio between them can be adjusted> and />Feedback amount at different symbols. When->Or->When (I)>Or->Will increase to greater than 0, at which point z ₄ ≤0,z ₅ And is less than or equal to 0. When->Or (b)When (I)>Or->Reduced to greater than 0, z ₃ ≤0,z ₄ And is less than or equal to 0. Therefore, there is a positive number sigma, satisfying z ₄ +z ₅ ≤σ ² Then:

wherein ,σ₁ Is a finite value, and thus the controller and the high-order nonlinear observer are designed to stabilize the system.

In order to verify the validity of the proposed algorithm, a simulation method is used for verification. The simulation model adopts a super-large under-actuated ship 'Tianjin' number. The wind and wave interference suffered by the ship is as follows:

equation (23) represents the parameter setting of the ship subjected to wind disturbance in the simulation, where ρ _α Is the air density. Alpha _R Is a phaseFor wind direction angle, U _R Indicating the relative wind speed. A is that _f and A_s Respectively a front projection area and a side projection area above the waterline of the ship, L _oa Is the total length of the ship, C _wx (α _R ) Representing the windup pressure coefficient of the heave degree of freedom; c (C) _wy (α _R ) Representing the windup pressure coefficient of the swinging freedom degree; c (C) _wn (α _R ) Representing the wind pressure coefficient in the self-freedom degree of bow swing;

equation (24) represents the parameter setting of the ship subjected to wave disturbance in the simulation, where λ is the wave wavelength, χ is the wave encounter angle, ρ is the sea water density, α is the wave amplitude, L is the ship length, C _Xw (lambda) represents the wave force coefficient in heave degrees of freedom; c (C) _Yw (lambda) represents the wave force coefficient in the lateral degrees of freedom; c (C) _Nw (lambda) represents the wave force coefficient in the bow freedom;

the parameters of the controller were selected as follows: q=1, p=0.1, k ₁ ＝3、k ₂ ＝0.5、l _x ＝0.95、l _y ＝0.95、l _ψ ＝0.75、l _ux ＝0.75、l _uy ＝0.65、l _vx ＝0.1、l _vy ＝0.65、l _r ＝0.45、l _fux ＝0.08、l _fuy ＝0.08、l _fvx ＝0.05、l _fvy ＝0.1、l _fr ＝0.1、p ₀ ＝9、q ₀ ＝5、p ₁ ＝3、q ₁ ＝1、a ₀ ＝2,β ₀ =1 ship initial state (x, y, ψ, u, v, r) = (0, 200,0,7.2m/s, 0).

IAE provides a numerical measure of tracking performance for the entire error curve. The energy consumption is compared by adopting an ISV standard:

in the formulas (23) and (24), tf represents the total simulation duration. IAE (IAE) _yei Representing a total path deviation value; ye (ye) _i A path deviation indicating the i-th time; ISV (International standards v) _δ Representing a total rudder angle input; delta _i A rudder angle indicating the i-th moment;

the simulation time was set to 3500s. The reference path is a track composed of waypoints.

Table 1 ship reference waypoints

Table 2 comparative quantitative analysis of different predictors

FIG. 2 shows a conventional LOS guidance method, where y _e Represents the path deviation, delta represents the LOS forward distance, theta _k Is the reference path angle. a is the fixed point turning angle, the included angle between adjacent reference paths, and the size of the included angle is 0<a<π。R _m Is an acceptable radius of the circle. First, by the current fixed point P _k With the next fixed point P _k+1 Each straight line between them constitutes a reference path y _d . And secondly, drawing an arc intersecting with the current straight line path by taking the actual position P (x, y) of the ship as a center and taking R as a radius.

FIG. 3 shows the guidance effect of LOS during path tracking of an oversized underactuated vessel, where y ₁ For guiding effect of unpredicted LOS, i.e. predicted value np=0, y ₂ For the path tracking effect when the predicted value np=20, y ₃ For the path tracking effect when the predicted value np=40, y ₄ Path tracking effect when np=60 is the predicted valueAnd (5) fruits. As can be seen from fig. 4, all paths track the reference path well. The designed global quick terminal sliding mode is verified to have a good control effect. And y is ₁ and y₄ In comparison, y ₄ Is faster and y ₁ The ship body has larger mass and obvious overshoot. Contrast y ₁ 、y ₂ 、y ₃ Along with the continuous increase of the predicted value, the overshoot can be effectively reduced. However, when the predicted value reaches a certain threshold, the path-tracking effect is not changed any more. Thus, y ₃ and y₄ Has almost the same path tracking effect. Table 2 shows the quantitative index IAE _yei The path deviation of different predicted values can be obtained more intuitively. As the predicted value increases, the path deviation decreases. However, after the predicted value reaches a certain threshold, the increase in predicted value does not significantly reduce the path deviation.

Fig. 5 shows that when the predicted value np=0, the maximum path deviation does not exceed 100, and the control path deviation gradually decreases as the predicted value increases. This shows that the predictive LOS guidance algorithm proposed herein has good guidance effects, and can significantly reduce the overshoot phenomenon of path tracking.

Fig. 6 shows a continuous curve of the ship heading and rudder angle over time. The amplitude of the course angle fluctuates between-20 degrees and 40 degrees, and the amplitude of the rudder angle fluctuates between-35 degrees and 35 degrees, thereby conforming to the navigation practice. Fig. 6 is a partial enlarged view of fig. 5. As shown in fig. 7, in the path tracking process, no guidance is given to the predicted target value, and a course angle overshoot occurs. The algorithm has a very stable rudder angle, and only a certain degree of shake occurs during turning, so that the algorithm is consistent with the actual navigation condition. By quantizing the index ISV, the predicted value increases and the ISV value decreases continuously. However, after a certain threshold is reached, the value of ISV remains unchanged. Therefore, the algorithm reduces the energy loss of the actuator, and therefore the algorithm has the characteristic of more energy conservation.

FIGS. 8 and 9 show, respectively, the estimation of the velocity values u, v and r based on the higher order nonlinear observer, and the disturbance f _u 、f _v and f_r Is a function of the estimate of (2). From FIG. 7, it canThe nonlinear observer designed has good estimation effect on the speed; therefore, the drift angle obtained from the speed value has higher accuracy. However, in fig. 9, the effect of estimating the external interference is not significant, and there is a certain error. This is because the high-order nonlinear observer is designed based on the MMG model, and the controller is designed based on the Nomoto model. The observation errors of the high-order nonlinear observer only include errors caused by external disturbances, and do not include uncertainty between models. Therefore, it is practical to have a certain deviation.

Fig. 10 shows the drift angle estimate from the velocity estimate.

Through the simulation experiment, the beneficial effects of the invention are as follows: the total path deviation is constructed by predicting a future time domain position of the vessel. The problem of overshoot easily occurs in the track tracking process of the ultra-large under-actuated ship is solved. And a global quick terminal sliding mode design controller is adopted to enable the path deviation to be converged in a limited time. In order to solve the problem of unknown navigational speed, disturbance and yaw angle, a high-order nonlinear observer is designed to estimate the system state to obtain the values of navigational speeds u, v and r and external disturbance f _u 、f _v and f_r The speed and the external interference can be effectively estimated. The drift angle of the ship during sailing is obtained through estimating the sailing speed, so that the problem that the sailing yaw angle is unknown is solved. LOS guidance based on position prediction can significantly reduce overshoot problems in the path tracking process. The prediction effect of different predictors is also different. Along with the continuous improvement of the predicted value, the path tracking precision is also improved.

Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.

Claims (7)

1. The novel LOS guidance method for tracking and predicting the path of the ultra-large under-actuated ship is characterized by comprising the following steps:

s1, establishing a ship simulation model containing wind and wave interference and nonlinear terms and a ship design model containing external disturbance;

s2, acquiring a high-order nonlinear observer to acquire the ship speed and the external undetermined disturbance;

s3: according to the ship simulation model, obtaining a virtual reference heading angle of the ship;

s4: according to the ship design model, the ship speed and the virtual reference heading angle of the ship, taking the total path tracking deviation of the path deviation of the current time domain and the path deviation of the future time domain into consideration, and obtaining a predicted LOS virtual heading angle of the ship;

s5: and according to the external undetermined disturbance, acquiring a control law of the ship through the predicted LOS virtual heading angle of the ship so as to control the path of the novel oversized underactuated ship.

2. The novel ultra-large under-actuated ship path tracking prediction LOS guidance method according to claim 1, wherein the ship simulation model is established as follows:

wherein: x represents the current position abscissa of the ship; y represents the ordinate of the current position of the ship; u represents the longitudinal speed of the ship; v represents the transverse speed of the ship; r represents the bow turning angular speed of the ship; psi represents the ship heading; _m representing the mass of the ship; mx represents the additional mass in the heave degree of freedom; my represents the additional mass on the cross; XH represents the force to which the bare hull is subjected in the heave degree of freedom; XP represents the force to which the propeller is subjected in terms of heave degrees of freedom; x is X _W Representing the force to which the wind is subjected in the heave degrees of freedom; x is X _WAVE Representing the forces to which the wave is subjected in the heave degrees of freedom; v (V) _c Representing the ocean wave velocity; psi phi type _c Representing the ocean wave flow direction; y is Y _H Representing the forces to which the bare hull is subjected in the lateral degrees of freedom; y is Y _P Representing the forces to which the propeller is subjected in the lateral degrees of freedom; y is Y _W Representing the force exerted by wind on the lateral degrees of freedom; y is Y _WAVE Representing the force exerted by the wave on the lateral swing degree of freedom; i _ZZ Representing the moment of inertia of the vessel about the vertical axis; j (J) _ZZ Representing additional moment of inertia; n (N) _H Representing the forces to which the bare hull is subjected in a bow degree of freedom; n (N) _P Representing the forces exerted by the propeller in the bow freedom; n (N) _R Representing the forces exerted by the rudder on the bow freedom; n (N) _W Representing the force exerted by the wind on the bow freedom; n (N) _WAVE Representing the forces to which the wave is subjected in the bow freedom;representing a derivative operation.

3. The novel ultra-large under-actuated ship path tracking prediction LOS guidance method according to claim 1, wherein the ship design model is established as follows:

wherein: beta represents the drift angle of the ship; t represents a ship following index; k represents a ship spin index; f (f) _r Representing an externally undetermined disturbance; delta represents the rudder angle.

4. The novel oversized underactuated marine path-tracking predictive LOS guidance method of claim 1, wherein the high-order nonlinear observer is obtained as follows:

in the formula ：representing the estimated value; psi represents the heading angle; g _u Representing a known portion of the longitudinal velocity model; g _v Representing a known portion of the transverse velocity model; g _r Representing a known portion of the yaw rate model; l (L) _x 、l _y 、l _ψ 、l _ux 、l _uy 、l _vx 、l _vy 、l _r 、l _fux 、l _fuy 、l _fvx 、l _fvy and l_fr All are positive design parameters; f (f) _u Disturbance f representing the longitudinal speed direction of a vessel _v Representing a disturbance in the transverse velocity direction of the vessel; f (f) _r Representing disturbance of the ship in the direction of the turning bow angular velocity;

the observation error of the high-order nonlinear observer is obtained as follows:

in the formula ：representing estimation error +.>

5. The novel ultra-large under-actuated ship path tracking prediction LOS guidance method according to claim 1, wherein the method for obtaining the virtual reference heading angle of the ship is as follows:

in the formula ：ψ_los Representing a virtual reference heading angle of the vessel; θ _k Representing a reference path angle; y is _e Representing a path deviation;

wherein ,

R＝k ₁ |y _e |+k ₂ L (6)

wherein: l represents the hull length; y is _e Representing a path deviation; k (k) ₁ Representing a positive parameter for adjusting the tracking speed; k (k) ₂ Representing a positive parameter for preventing the arc from disjointing the reference path.

6. The novel ultra-large under-actuated ship path tracking prediction LOS guidance method according to claim 1, wherein the method for obtaining the predicted LOS virtual heading angle of the ship is as follows;

s41: discretizing the ship design model to obtain a step length calculation value of a future time domain:

in the formula ：a ship position calculation value representing a future nth time domain; y (k) represents the current time-domain step size calculation value; t (T) ₁ Representing a sampling period; j represents the number of the future time domain, j is less than or equal to n;

s42: constructing a path deviation of the future time domain according to the step length calculated value of the future time domain:

in the formula ：y_d (k+n) represents a reference path calculation value of the nth time domain in the future;representing a path deviation of a future nth time domain;

s43: acquiring a total path taking into account a path deviation of a current time domain and a path deviation of a future time domainTracking the deviation to obtain a virtual reference heading angle psi of the ship _los Obtaining a predicted LOS virtual heading angle of a ship;

the total path tracking bias is obtained as follows:

in the formula ：y_E (y,y _d ) Representing a total path tracking bias;representing the path deviation of the current time domain; />Representing the total path deviation of n time domains in the future; p represents the weight of the path deviation of the current time domain; q represents the weight of the total path deviation of the n time domains in the future;

according to the virtual reference heading angle psi of the ship _los Is obtained by the calculation formula of (1):

in the formula ：ψ_pre-los Representing a reference heading angle based on the predicted LOS;

thus, the first and second light sources are connected,

in the formula ：ψ_d Representing a predicted LOS virtual heading angle of the ship;

wherein ,

in the formula ：an estimated value representing the drift angle of the ship.

7. The novel ultra-large under-actuated ship path tracking prediction LOS guidance method according to claim 1, wherein the method for obtaining the control law of the ship is as follows:

s51: construction of fast sliding modes of recursive structures

in the formula ：s₀ Representing a 0 th order recursive slip plane; s is(s) ₁ Representing a 1 st order recursive slip plane; psi phi type _e Representing a heading angle deviation; a, a ₀ Representing a positive design parameter; beta ₀ Representing a positive design parameter; q ₀ Representing a positive design parameter; p is p ₀ Representing a positive design parameter;

for s ₁ Regarding time derivative:

wherein ,a₀ ＞0,β ₀＞0 and q₀ ＜p ₀ Order-makingThe control law of the ship is obtained as follows:

wherein: phi represents the designed sliding mode surface parameter; gamma represents the designed sliding mode surface parameter; wherein phi and gamma are more than 0;

when the system is in stateReaching the slide surface s ₁ When (t) =0, the time for the ship design model to reach stability is as follows:

wherein p represents a positive design parameter; q represents a positive design parameter; where q < p is a positive odd number.