CN109857124B - Unmanned ship accurate path tracking control method based on speed and course dual guidance - Google Patents

Unmanned ship accurate path tracking control method based on speed and course dual guidance Download PDF

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CN109857124B
CN109857124B CN201910222678.7A CN201910222678A CN109857124B CN 109857124 B CN109857124 B CN 109857124B CN 201910222678 A CN201910222678 A CN 201910222678A CN 109857124 B CN109857124 B CN 109857124B
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unmanned ship
speed
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王宁
潘婷
焦宇航
孙卓
李贺
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Dalian Maritime University
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Abstract

The invention discloses an unmanned ship accurate path tracking control method based on speed and course dual guidance, which comprises the following steps: calculating path tracking error dynamics; designing a speed and course dual guidance law; designing a finite time unknown observer; the non-smooth controller is designed based on a finite time unknown observer. The invention provides a dual guidance law which can simultaneously guide speed and course angle according to tracking error, so that the position error of the unmanned ship can be stabilized to zero in limited time, the operation burden of a rudder is reduced, and the operation flexibility and the integrity of a guidance system are improved; according to the invention, speed and course dual guidance laws are designed to improve the operation flexibility and integrity of the guidance system, the finite time unknown observer accurately observes complex external disturbance and internal uncertainty and compensates in the unsmooth speed and course controller, so that the tracking accuracy of the path tracking control system is greatly improved.

Description

Unmanned ship accurate path tracking control method based on speed and course dual guidance
Technical Field
The invention belongs to the field of unmanned ships, and particularly relates to an accurate path tracking control method for an unmanned ship.
Background
With the wide application of the automation theory and practice in ocean engineering, the under-actuated water surface unmanned ship can flexibly and conveniently complete a series of high-risk ocean tasks as a highly autonomous unmanned vehicle. The high-precision path tracking control technology plays a crucial role in developing the autonomy of the under-actuated surface unmanned ship. In fact, by combining guidance with control, the path tracking problem can be solved well. In the design of the guidance subsystem, the effectiveness of line-of-sight guidance is widely accepted by theory and experiments, and proportional line-of-sight guidance calculates the expected heading angle by setting an arctangent function related to the lateral error. Integral line-of-sight guidance on the basis of proportional line-of-sight guidance, the disturbance of a constant or slowly time-varying sideslip angle is counteracted by an integral term. Self-adaptive sight guidance solves the sideslip problem through a self-adaptive compensation method. The relative speed sight guidance considers the ocean current influence on the basis of sight guidance. In the design of a control system, a backstepping method, a singular perturbation method, a fuzzy partition method, a neural network method and various self-adaptive control methods have been effectively applied to ship motion control, but these control methods have difficulty in realizing efficient estimation and compensation of external complex disturbances, thereby reducing the accuracy of the control system.
In existing guidance methods, the drone is typically required to preset a constant or strictly positive speed, which makes the drone speed uncontrolled by guidance, but only by the rudder, thus reducing the integrity and flexibility of the maneuver. In the control subsystem, uncertain accurate estimation caused by external disturbance and internal parameter perturbation cannot be realized, so that the influence of the complicated uncertainties on the system cannot be eliminated from tracking, and the precision of the unmanned ship path tracking control system is reduced.
The invention adopts a speed and course dual guidance method, reduces the operation burden of the rudder and improves the operation flexibility and decision efficiency of the guidance system. The finite time uncertainty observer is used for accurately observing complex external disturbance and internal uncertainty, and compensation is performed during controller design, so that the working efficiency of the path tracking control system is greatly improved. Therefore, the tracking precision of the path tracking control system is greatly improved.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an unmanned ship accurate path tracking control method based on speed and course dual guidance, which can improve the accuracy of a path tracking control system.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the unmanned ship accurate path tracking control method based on speed and course dual guidance comprises the following steps:
Figure BDA0002004127870000021
Figure BDA0002004127870000022
Figure BDA0002004127870000023
in the formula, x represents the abscissa of the motion position of the unmanned ship in the inertial coordinate system, y represents the ordinate of the motion position of the unmanned ship in the inertial coordinate system, and psi represents the course of the unmanned ship in the inertial coordinate system;
Figure BDA0002004127870000024
is the derivative of x and is,
Figure BDA0002004127870000025
is the derivative of y and is the sum of,
Figure BDA0002004127870000026
is the derivative of ψ; u represents the forward speed of the unmanned ship under the body fixed coordinate system, v represents the transverse speed of the unmanned ship under the body fixed coordinate system, and r represents the course angular speed of the unmanned ship under the body fixed coordinate system.
The dynamic model of the unmanned ship is as follows:
Figure BDA0002004127870000027
Figure BDA0002004127870000028
Figure BDA0002004127870000029
wherein, tauuFor available control input of forward thrust, taurIn order to input the steering torque for the available control,
Figure BDA00020041278700000210
in the formula (d)11Is a hydrodynamic damping parameter, d, in the forward velocity dimension of the unmanned ship22Is a hydrodynamic damping parameter in the transverse velocity dimension of the unmanned ship, d33The hydrodynamic damping parameter is the hydrodynamic damping parameter on the unmanned ship course angular velocity dimension; m11 is the quality parameter in the dimension of the forward speed of the unmanned ship, m22Is a quality parameter, m, in the transverse velocity dimension of the unmanned ship33The quality parameter of the unmanned ship in the course angular speed dimension; tau isuTo control forward thrust in the input, τrTo control the steering torque in the input; tau isδuIs the external disturbance on the forward speed of the unmanned ship, tauδvIs the external disturbance of the unmanned ship in the transverse speed, tauδrThe unmanned ship is subjected to external disturbance on the navigation angular velocity.
The control method comprises the following steps:
A. computing path tracking error dynamics
Defining a moving virtual ship on the parameterized path tracking curve of the unmanned ship, wherein the horizontal coordinate of the position of the ship is x under the inertial coordinate systempOrdinate is yp，xp、ypIs about a time variable
Figure BDA0002004127870000031
Taking the point as a tracking target and establishing a path tangent coordinate system, wherein the rotation angle of the path tangent coordinate system relative to an inertial coordinate system is phip. The error of the actual position of the unmanned ship relative to the position of the moving virtual ship in the direction of the path tangent coordinate abscissa is xeError in ordinate direction is yeThen the tracking error expression is:
Figure BDA0002004127870000032
the dynamic expression state of the path tracking error is as follows:
Figure BDA0002004127870000033
Figure BDA0002004127870000034
usis the speed of the moving virtual vessel on the path, expressed in the form:
Figure BDA0002004127870000035
in the formula (I), the compound is shown in the specification,
Figure BDA0002004127870000036
is a time-dependent path variable,
Figure BDA0002004127870000037
Figure BDA0002004127870000038
B. dual guidance law for designed speed and course
According to the dynamic expression of the path tracking error, the following speed and course guidance law is designed, so that the path tracking error can be gradually stabilized to zero:
Figure BDA0002004127870000039
Figure BDA00020041278700000310
βd＝arctan(v/ud)
utar＝k2xe+Udcos(ψ-φp+βd)
in the formula (I), the compound is shown in the specification,
Figure BDA00020041278700000311
ideal speed of unmanned ship, parameter k1K > 0 is a constant value in the forward velocity guidance law2U is a constant value in course guidance law > 0dIs a reference value of forward speed, psi, of the unmanned shipdIs a reference value of the heading angle, beta, of the unmanned shipdAn ideal sideslip angle. And gradually converging the error between the actual motion track of the unmanned ship and the designed path to zero by using the designed guidance law.
Define the first Lyapunov equation:
Figure BDA0002004127870000041
the derivative of the lyapunov equation is solved:
Figure BDA0002004127870000042
substituting the designed dual guidance law into the equation to obtain:
Figure BDA0002004127870000043
wherein k is 2min k1,k2And the Lyapunov derivative substituted into the double guidance law is negative, so that the gradual stability condition is met, and the global asymptotic stability of the guidance system is ensured. Thus, the path tracking error x in the equatione、yeGradually stabilizes to zero, so that the speed and the heading can be guided by the designed dual guidance law.
C. Observer for designing finite time unknowns
The dynamic model of the unmanned ship is arranged into the following form:
Figure BDA0002004127870000044
wherein: m ═ diag (M)11,m22,m33)
f(ν)＝[fu,fv,fr]
τ＝[τu,0,τr]
Figure BDA0002004127870000045
fu＝m22vr-d11u
fv＝-m11ur-d22v
fr＝-(m22-m11)uv-d33r
The finite time unknown observer is designed in the following form:
Figure BDA0002004127870000051
Figure BDA0002004127870000052
Figure BDA0002004127870000053
an estimate of the external disturbance in the velocity dimension,
Figure BDA0002004127870000054
is an estimate of the external disturbance in the heading angular velocity dimension.
To demonstrate that the complex unknowns are accurately determined under this observer, the following observation errors are defined:
Figure BDA0002004127870000055
Figure BDA0002004127870000056
differentiating the observation error of a finite time unknown observer based on design:
Figure BDA0002004127870000057
Figure BDA0002004127870000058
according to Levant's theorem, it is ensured that the observation error is stable in a limited time, i.e. there is a time 0 < TδInfinity, such that
Figure BDA0002004127870000059
D. Non-smooth controller designed based on finite time unknown observer
D1 designing non-smooth speed controller based on finite time unknown observer
Based on a finite time unknown observer and a non-smooth control theory, the non-smooth speed controller is designed into the following form:
Figure BDA00020041278700000510
in the formula, a forward speed error ue＝u-udParameter ku＞0，0＜p1/q1＜1。
Defining a second Lyapunov equation:
Figure BDA0002004127870000061
and solving the derivative of the Lyapunov equation, and substituting the designed unsmooth speed controller and a finite time observer into the equation to obtain:
Figure BDA0002004127870000062
since the found lyapunov derivative is negative, the forward speed error ue can be stabilized to zero at a finite time according to the global finite time stability theorem, where the finite time is:
Figure BDA0002004127870000063
from this, it is concluded that the velocity can be accurately tracked in a limited time.
D2 designing unsmooth course controller based on finite time unknown observer
Based on a finite time unknown observer and a non-smooth control theory, the non-smooth course controller is designed into the following form:
Figure BDA0002004127870000064
ψe＝ψ-ψdrepresenting the course angle tracking error, re＝r-rdRepresenting a heading angular velocity tracking error. SψIs a nonsingular terminal sliding mode expression, SψThe representation is as follows:
Figure BDA0002004127870000065
in the formula, σ1＞0，q2＜p2＜2q2，p3＜q3。
Define a third Lyapunov equation:
Figure BDA0002004127870000066
substituting the designed speed controller and the limited time observer into the system to obtain the derivative of the Lyapunov equation, and substituting the designed unsmooth course controller and the limited time observer into the equation to obtain the following result:
Figure BDA0002004127870000071
wherein:
Figure BDA0002004127870000072
when r iseWhen not equal to 0, the Lyapunov derivative is negative definite, and S is obtained according to the global finite time stability theoremψStable for a limited time; when r iseWhen equal to 0, there is
Figure BDA0002004127870000073
According to Levant' S lemma, nonsingular terminal sliding mode SψCan converge to zero for a finite time, which is expressed as:
Figure BDA0002004127870000074
when reaching the sliding surface, the heading angle tracking error psieIs stable to zero for a finite time, which is:
Figure BDA0002004127870000075
so that
Figure BDA0002004127870000076
ψe(t)≡0
Therefore, the conclusion that the heading angle is accurately tracked in a limited time is obtained.
In conclusion, the designed non-smooth speed and heading controller based on the finite time unknown observer accurately tracks the guidance signals of the speed and the heading angle.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides a dual guidance law capable of simultaneously guiding speed and course angle according to tracking error, so that the position error of the unmanned ship can be stabilized to zero within a limited time, the operation burden of a rudder is reduced, and the operation flexibility and the integrity of a guidance system are improved.
2. According to the method, the finite time unknown observer is constructed, the unknown disturbance is accurately estimated in a complex unknown environment, and effective compensation is implemented in the designed speed and course controller according to the estimation quantity, so that the tracking error is quickly and stably converged to zero, and the limitation of bounded observation and progressive observation is overcome.
3. The invention designs the unsmooth speed and course controller on the basis of the finite time unknown observer, so that the control system can accurately track the guidance signal under the condition of complex interference.
4. In conclusion, the speed and course dual guidance law is designed to improve the operation flexibility and the integrity of the guidance system, the finite time unknown observer accurately observes complex external disturbance and internal uncertainty and compensates in the unsmooth speed and course controller, and therefore the tracking accuracy of the path tracking control system is greatly improved.
Drawings
FIG. 1 is an unmanned ship path tracking control geometry.
FIG. 2 is a block diagram of a finite-time path tracking control system of an unmanned ship based on dual guidance of speed and heading.
FIG. 3 is a design flow diagram of the present invention.
Fig. 4 is a real scene simulation tracking diagram of a large connected seaport.
Fig. 5 is a graph of path lateral tracking error.
Fig. 6 is a graph of path longitudinal tracking error.
FIG. 7 is a graph of path heading tracking error.
Fig. 8 is a velocity tracking graph.
Fig. 9 is a velocity tracking error graph.
FIG. 10 is a forward speed disturbance observation graph.
FIG. 11 is a lateral velocity external disturbance observation graph.
FIG. 12 is a plot of an observation of an external disturbance of heading angular velocity.
FIG. 13 is a forward speed disturbance observation error graph.
FIG. 14 is a lateral velocity external disturbance observation error graph.
FIG. 15 is a graph of heading angular velocity external disturbance observation error.
Fig. 16 is a schematic view of forward thrust.
Fig. 17 is a steering torque diagram.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Fig. 1 is a schematic diagram showing the relationship between the inertial coordinate system and the body-fixed coordinate system and the positions of the mobile virtual ship and the unmanned ship in step a.
FIG. 2 is a block diagram of a path tracking control system, a tracking error dynamic equation is obtained by an under-actuated unmanned ship dynamic model and the actual position error of a virtual ship and an unmanned ship, and a speed and course dual guidance law is designed on the basis of the tracking error dynamic equation. And designing a finite time observer according to an unknown uncertainty, and designing a corresponding non-smooth controller to control the under-actuated unmanned ship to meet the requirement of accurate path tracking.
In order to test the effectiveness of the method provided by the invention, according to the flow shown in FIG. 3, a Cybership I ship is utilized to perform live-action simulation path tracking in the coastal harbors in Dalian City of Liaoning China, and a guidance control method (SHG-FPC for short) provided by the invention is compared with an algorithm frame without a time-limited interference observer, so that the method is further used for checking the effectiveness of the method provided by the inventionThe observation effect of the observer is clear. The ship model parameters are as follows: m is11＝19kg，m22＝35.2kg，m33＝4.2kg，d11＝4kg/s，d22＝1kg/s，d 3310 kg/s. The complex unknown interference hypothesis is as follows:
Figure BDA0002004127870000091
Figure BDA0002004127870000092
λd＝1，δd＝[δdu,δdv,δdr]T∈[-6,6]3for random noise, the initial state of the vessel is set to: [ x (0), y (0), ψ (0)]T＝[345,20,0]T,[u(0),v(0),r(0)]T＝[0,0,0]TThe path variables are set as follows:
Figure BDA0002004127870000093
the set parameters in the algorithm are selected as follows:
k1＝0.4，k2＝1，Δ＝3，L＝diag(300,300,300)，λ1＝0.4，λ2＝0.01，ku＝1.2，kψ＝1.2，σ1＝1，p1＝5，q1＝7，p2＝5，q2＝5，p3＝5，p3＝5，q3＝7。
FIG. 4 is a real-scene simulation training diagram of the present invention, comparing the actual and expected path of the unmanned ship under the control scheme of the present invention and the scheme without the finite time uncertainty observer (abbreviated as SHG-FPC/FUO), it can be seen that the method of the present invention can simultaneously achieve higher path following precision and stronger anti-interference capability. Fig. 5 shows the situation of the path lateral tracking error under the SHG-FPC scheme and the SHG-FPC/FUO scheme, and it can be seen from the figure that the SHG-FPC algorithm can make the lateral error converge to zero more effectively. FIG. 6 shows the path longitudinal tracking error under the SHG-FPC scheme and the SHG-FPC/FUO scheme, and it can be seen from the figure that the SHG-FPC algorithm can make the longitudinal error converge to zero, while the SHG-FPC/FUO algorithm cannot make the longitudinal error converge to zero and has an unstable error. FIG. 7 shows the path tracking error under the SHG-FPC scheme and the SHG-FPC/FUO scheme, and it can be seen from the figure that the SHG-FPC algorithm can quickly make the tracking error converge to zero, while the SHG-FPC/FUO algorithm has a poor tracking effect. Fig. 8 shows a velocity tracking graph, from which it can be seen that the SHG-FPC algorithm can make the unmanned ship's forward velocity track the upper reference velocity very quickly. Fig. 9 shows a velocity tracking error curve, from which it can be seen that the SHG-FPC algorithm can more stably converge the velocity tracking error to zero. 10-12 are external disturbance observation curves in three directions of forward direction, transverse direction and heading angle, and it can be seen from the diagrams that the finite time unknown observer provided by the invention can realize accurate observation of disturbance quantity. Fig. 13-15 are observation curves of the external disturbance error in the three directions of the forward direction, the transverse direction and the heading angle, and it can be seen from the observation curves that the observation error is converged to the zero point by the observer in a short time. FIG. 16 is a schematic representation of the forward thrust of the drone as a forward speed control input, and FIG. 17 is a schematic representation of the turning moment of the drone as a heading control input. Through the above examples, it can be concluded that: the invention can accurately track the reference signal generated by the guidance system and has obvious effectiveness and superiority.
The present invention is not limited to the embodiment, and any equivalent idea or change within the technical scope of the present invention is to be regarded as the protection scope of the present invention.

Claims (1)

1. The unmanned ship accurate path tracking control method based on speed and course dual guidance is characterized by comprising the following steps: the kinematics model of the unmanned ship is as follows:
Figure FDA0003164556830000011
Figure FDA0003164556830000012
Figure FDA0003164556830000013
in the formula, x represents the abscissa of the motion position of the unmanned ship in the inertial coordinate system, y represents the ordinate of the motion position of the unmanned ship in the inertial coordinate system, and psi represents the course of the unmanned ship in the inertial coordinate system;
Figure FDA0003164556830000014
is the derivative of x and is,
Figure FDA0003164556830000015
is the derivative of y and is the sum of,
Figure FDA0003164556830000016
is the derivative of ψ; u represents the forward speed of the unmanned ship under the main body fixed coordinate system, v represents the transverse speed of the unmanned ship under the main body fixed coordinate system, and r represents the course angular speed of the unmanned ship under the main body fixed coordinate system;
the dynamic model of the unmanned ship is as follows:
Figure FDA0003164556830000017
Figure FDA0003164556830000018
Figure FDA0003164556830000019
in the formula (d)11Is a hydrodynamic damping parameter, d, in the forward velocity dimension of the unmanned ship22In the transverse velocity dimension of unmanned shipHydrodynamic damping parameter, d33The hydrodynamic damping parameter is the hydrodynamic damping parameter on the unmanned ship course angular velocity dimension; m is11Is a quality parameter, m, in the forward velocity dimension of the unmanned ship22Is a quality parameter, m, in the transverse velocity dimension of the unmanned ship33The quality parameter of the unmanned ship in the course angular speed dimension; tau isuTo control forward thrust in the input, τrTo control the steering torque in the input; tau isδuIs the external disturbance on the forward speed of the unmanned ship, tauδvIs the external disturbance of the unmanned ship in the transverse speed, tauδrExternal disturbance on the navigation angular velocity of the unmanned ship is realized;
the control method comprises the following steps:
A. computing path tracking error dynamics
Defining a moving virtual ship on the parameterized path tracking curve of the unmanned ship, wherein the abscissa of the point is x under the inertial coordinate systempOrdinate is yp，xp、ypIs about a time variable
Figure FDA00031645568300000110
Taking the point as a tracking target and establishing a path tangent coordinate system, wherein the rotation angle of the path tangent coordinate system relative to an inertial coordinate system is phip(ii) a The error of the actual position of the unmanned ship relative to the moving virtual ship in the direction of the path tangent coordinate abscissa is xeError in ordinate direction is yeThen the tracking error expression is:
Figure FDA0003164556830000021
the dynamic expression state of the path tracking error is as follows:
Figure FDA0003164556830000022
Figure FDA0003164556830000023
usis the speed of the moving virtual vessel on the path, expressed in the form:
Figure FDA0003164556830000024
in the formula (I), the compound is shown in the specification,
Figure FDA0003164556830000025
is a time-dependent path variable,
Figure FDA0003164556830000026
B. dual guidance law for designed speed and course
According to the dynamic expression of the path tracking error, the following speed and course guidance law is designed, so that the path tracking error can be gradually stabilized to zero:
Figure FDA0003164556830000027
Figure FDA0003164556830000028
βd＝arctan(v/ud)
utar＝k2xe+Udcos(ψ-φp+βd)
in the formula (I), the compound is shown in the specification,
Figure FDA0003164556830000029
ideal speed of unmanned ship, parameter k1K > 0 is a constant value in the forward velocity guidance law2U is a constant value in course guidance law > 0dIs an unmanned shipReference value of forward velocity, #dIs a reference value of the heading angle, beta, of the unmanned shipdAn ideal sideslip angle; gradually converging the error between the actual motion track of the unmanned ship and the designed path to zero by using the designed guidance law;
C. observer for designing finite time unknowns
The dynamic model of the unmanned ship is arranged into the following form:
Figure FDA00031645568300000210
wherein: m ═ diag (M)11,m22,m33)
f(ν)＝[fu,fv,fr]
τ＝[τu,0,τr]
Figure FDA0003164556830000031
fu＝m22vr-d11u
fv＝-m11ur-d22v
fr＝-(m22-m11)uv-d33r
The finite time unknown observer is designed in the following form:
Figure FDA0003164556830000032
Figure FDA0003164556830000033
Figure FDA0003164556830000034
D. non-smooth controller designed based on finite time unknown observer
D1 designing non-smooth speed controller based on finite time unknown observer
Based on a finite time unknown observer and a non-smooth control theory, the non-smooth speed controller is designed into the following form:
Figure FDA0003164556830000035
in the formula, a forward speed error ue＝u-udParameter ku＞0，0＜p1/q1＜1；
D2 designing non-smooth heading controller based on finite time observer
Based on a finite time unknown observer and a non-smooth control theory, the non-smooth course controller is designed into the following form:
Figure FDA0003164556830000036
in the formula, #e＝ψ-ψdRepresenting the course angle tracking error, re＝r-rdRepresenting a course angular velocity tracking error; sψIs a nonsingular terminal sliding mode expression, SψThe representation is as follows:
Figure FDA0003164556830000037
in the formula, σ1＞0，q2＜p2＜2q2，p3＜q3。
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