CN114004035A - Target tracking control method for unmanned surface vehicle - Google Patents

Target tracking control method for unmanned surface vehicle Download PDF

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CN114004035A
CN114004035A CN202111513902.1A CN202111513902A CN114004035A CN 114004035 A CN114004035 A CN 114004035A CN 202111513902 A CN202111513902 A CN 202111513902A CN 114004035 A CN114004035 A CN 114004035A
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黄海滨
陈曦
庄宇飞
梁景凯
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Harbin Institute of Technology Weihai
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Abstract

The invention belongs to the technical field of ship control and regulation systems, relates to a method for optimally controlling and adaptively controlling a ship, and provides a target tracking control method for an unmanned surface vehicle, which is used for acquiring targets in real timetThe method comprises the steps of establishing a three-degree-of-freedom water surface unmanned ship dynamic model, converting the three-degree-of-freedom water surface unmanned ship dynamic model into a nonlinear system capable of similar linear derivation, and solving and tracking the optimal control input of the near-water surface target in real time under the given performance index constraint and the actual system performance index constraint,the method also comprises the step of adaptively adjusting and solving parameters required in the optimal control input process according to a trend function of the unmanned surface vehicle tracking the near-water surface target. When the method is used for tracking control of the unmanned surface vehicle, the control input can be solved with high precision, and the calculation precision and the calculation speed can be coordinated autonomously while the tracking efficiency is ensured.

Description

Target tracking control method for unmanned surface vehicle
Technical Field
The invention belongs to the technical field of ship control and regulation systems, relates to a method for optimally controlling and adaptively controlling a ship, and particularly relates to a control method for optimally and dynamically tracking a near-surface target by an unmanned surface vehicle.
Background
With the increase of the ocean development and the construction strength of marine defense, offshore engineering or military tasks urgently need unmanned carrying platforms with long time, large range and low cost, such as unmanned surface boats and the like, and under certain conditions, the unmanned surface boats are required to be used for automatically tracking targets near the water surface in real time. Due to the fact that offshore supply is difficult, portable energy is limited, the unmanned surface vehicle belongs to a highly nonlinear system, and a control method in the prior art is large in calculation amount and long in resolving time and is not suitable for real-time control of the unmanned surface vehicle on the target tracking near the water surface, so that on-line calculation speed is improved on the basis of guaranteeing tracking accuracy, and meanwhile, optimization of energy consumption is a well-known problem in the field.
Disclosure of Invention
In order to solve the problems in the prior art, the present application aims to provide a method capable of considering both calculation accuracy and calculation speed, so that an unmanned surface vehicle can perform optimal tracking on a near-water target in real time.
The embodiment of the application can be realized by the following technical scheme:
a target tracking control method for unmanned surface vehicle is used for real-time acquisitiontThe system control input of the optimal dynamic tracking of the unmanned surface vehicle to the near-surface target at the moment comprises the following steps:
s100: establishingtThree-degree-of-freedom dynamic model of unmanned surface vehicle at any moment
Figure 879620DEST_PATH_IMAGE001
，
Wherein the content of the first and second substances,Mto add a mass inertia matrix to the hydrodynamic force,C(V) Is an ideal rigid body and a hydrodynamic Coriolis force matrix，D(V) In order to be a hydrodynamic damping matrix,U=[U u ,U v ,U r ] T in order to control the input vector for the system,M、C(V) AndD(V) The concrete form of (A) is as follows:
Figure 390236DEST_PATH_IMAGE002
the values of all elements in the matrix are determined by the actual hull structure of the unmanned surface vehicle andtdetermination of System State at time, V = [ ]u,v,r] T Is an unmanned surface boattThe state of the velocity and the angular velocity at the moment is that the unmanned surface vehicle is ontPosition and angular state of time
Figure 638814DEST_PATH_IMAGE003
The time is derived to obtain the result of the derivation,
Figure 299603DEST_PATH_IMAGE004
is composed ofVThe derivative with respect to time is that of,
Figure 956718DEST_PATH_IMAGE005
，Vform an unmanned surface vehicletState vector of time of day
Figure 248022DEST_PATH_IMAGE006
SaidXDerivative with respect to time
Figure 108531DEST_PATH_IMAGE007
Has the following form:
Figure 776272DEST_PATH_IMAGE008
；
s200: and converting the unmanned ship three-degree-of-freedom dynamic model into a system capable of carrying out quasi-linear derivation by adopting a state correlation coefficient method, wherein the system comprises the following components:
Figure 789359DEST_PATH_IMAGE009
，
wherein the content of the first and second substances,A(X) Is composed oftThe system matrix of the time of day,B(X) Is composed oftAn input matrix of time instants.
S300: index of structural performanceJ:
Figure 985985DEST_PATH_IMAGE010
，
Whereint 0In order to keep track of the starting moment,t f in order to keep track of the end time,X d is the state vector of the near-surface target,Qin the form of a state variable weight matrix,Ris an energy consumption weight matrix, theQ、RDetermined by the state and performance of the unmanned surface vehicle,
Figure 599369DEST_PATH_IMAGE011
in order to be a function of the terminal error,S(t f ) To be composed ofM(X(t f ),X d (t f ),t f ) A matrix of coefficients expressed in quadratic form, such that the performance indexJMinimum sizeUIs thattSystem control input vector satisfying optimal dynamic tracking of momentsU optimal The concrete form is as follows:
Figure 539643DEST_PATH_IMAGE012
，
wherein the content of the first and second substances,
Figure 905771DEST_PATH_IMAGE013
to make the performance indexJThe smallest co-status vector.
S400: determining the number of LGR points according to a trend function of the unmanned surface vehicle tracking the near-water surface targetNAnd corresponding LGR point
Figure 804457DEST_PATH_IMAGE014
Wherein the LGR is coordinated with a point
Figure 639558DEST_PATH_IMAGE015
Is an equation
Figure 993310DEST_PATH_IMAGE016
Is/are as followsNThe number of +1 zero points is,
Figure 433519DEST_PATH_IMAGE017
is composed ofNOrder Legendre polynomial.
S500: according to the aboveNLGR distribution point
Figure 34264DEST_PATH_IMAGE015
And generating the following matrix equation system in a discrete form by using a pseudo-spectrum method:
Figure 232027DEST_PATH_IMAGE018
，
wherein the content of the first and second substances,A i 、B i 、X i 、X di is that it isA、B、X、X d The value at the ith coordinate point is,
Figure 989522DEST_PATH_IMAGE019
an N +1 order Lagrange differential matrix of the following formula:
Figure 956341DEST_PATH_IMAGE020
；
s600: solving the matrix equation system (5-1) in the discrete form to obtain
Figure 321463DEST_PATH_IMAGE021
，
Figure 475364DEST_PATH_IMAGE022
Will be
Figure 623449DEST_PATH_IMAGE023
Carrying out the formula (3-1) to obtaintSystem control inputs for time instant satisfying optimal dynamic tracking:
Figure 320141DEST_PATH_IMAGE024
。
s700: according to the aboveU optimal And after the unmanned surface vehicle is controlled, re-executing the step S100 to the step S600 at the time of t + 1.
Further, the trend function in step S400 is:
Figure 465951DEST_PATH_IMAGE025
wherein the trend functionkIs the distance between the unmanned surface vehicle and the near-surface targetsAndsthe first derivative, a function of the second derivative,a、b、c、dis a preset constant.
Preferably, the number of LGR dotsNHas a value range of
Figure 169465DEST_PATH_IMAGE026
Wherein, in the step (A),N min the minimum LGR matching point number required by the tracking precision is met.
Preferably, the first and second electrodes are formed of a metal,N min =4。
further, in step S400, the number of LGR nodes is determined according to a trend function of the unmanned surface vehicle tracking the near-water targetNFurther comprising the steps of:
s410: judgment oftWhether the trend function of the moment is in the first state interval or the fourth state interval or not is judged, if the judgment result is true, the number of LGR (light-emitting diode) configuration points is increasedNThen, step S500 is executed, and if the determination result is false, step S420 is executed;
s420: judgment oftWhether the trend function at the moment is in a second state interval or not, and if the judgment result is true, the LG is keptNumber of R matchesNStep S500 is executed without change, and if the determination result is false, step S430 is executed;
s430: determiningtThe trend function at the moment is in a third state interval, and the number of LGR matching points is further judgedNWhether or not greater thanN min If the judgment result is true, the LGR matching point number is decreased and the step S500 is executed, and if the judgment result is false, the LGR matching point number is maintainedNAnd step S500 is not changed and performed.
Further, when the trend function is in the first state interval, the surface drone is far away from the near-surface target; when the trend function is in the second state interval, the unmanned surface vehicle is close to the near-surface target and the motion state of the near-surface target is stable; when the trend function is in the third state interval, the unmanned surface vehicle is close to the near-surface target and the motion state of the near-surface target has slight fluctuation; when the trend function is in the fourth state interval, the unmanned surface vehicle is close to the near-surface target, and the motion state of the near-surface target has obvious change.
Further, the system matrixA(X) The method specifically comprises the following steps:
Figure 183557DEST_PATH_IMAGE027
，
the input matrixB(X) The method specifically comprises the following steps:
Figure 859389DEST_PATH_IMAGE028
，
wherein, a1~a8A total of 8 constants to satisfy the structural requirements of the state correlation coefficient.
Further, the LGR point
Figure 238418DEST_PATH_IMAGE029
With discrete points in time
Figure 6392DEST_PATH_IMAGE030
The corresponding relation is as follows:
Figure 433962DEST_PATH_IMAGE031
。
further, the matrix equation system (5-1) is generated according to the following steps:
the first step is as follows: establishing a Hamiltonian of an error form:
Figure 761038DEST_PATH_IMAGE032
；
the second step is that: and solving partial derivatives under the set boundary condition and the set cross section condition to obtain a continuous matrix equation set:
Figure 373285DEST_PATH_IMAGE033
，
the boundary conditions and the cross-section conditions are as follows:
Figure 254653DEST_PATH_IMAGE034
；
the third step: using the LGR site
Figure 548231DEST_PATH_IMAGE035
With discrete points in timet i And the corresponding relationship ofD ij In thatNApproximating the continuous form matrix equation set at +1 interpolation points to obtain the discrete form matrix equation set (5-1).
The target tracking control method for the unmanned surface vehicle provided by the embodiment of the application at least has the following beneficial effects:
(1) aiming at a highly nonlinear water surface unmanned ship dynamics model, a state correlation matrix coefficient parameterization thought is utilized to convert the model into a nonlinear system capable of carrying out quasi-linear derivation, a discrete system state matrix equation is solved by utilizing a pseudo-spectrum method to solve the optimal control problem of the system, the calculation speed is improved, the consumption of calculation resources is reduced, and the effect of acquiring the optimal control input for tracking a near-water surface target in real time and with high precision is achieved;
(2) the number of LGR distribution points required by solving a discrete system state matrix equation is adaptively adjusted according to the trend of the unmanned surface vehicle tracking the near-surface target, and the tracking efficiency is guaranteed while the calculation precision and the calculation speed are autonomously coordinated.
Drawings
FIG. 1 is a schematic diagram illustrating a coordinate description of a surface unmanned ship model;
fig. 2 is a flowchart of a target tracking control method for an unmanned surface vehicle according to the present application;
FIG. 3 illustrates a state range and a corresponding function value range of a trend function according to an embodiment of the present disclosure;
FIG. 4 is a setting of kinetic and control parameters according to an embodiment of the present application;
FIG. 5 is a flow chart of a control method implementation according to an embodiment of the present application;
FIG. 6 is a simulation result of surface unmanned vehicle control input vectors according to an embodiment of the present application;
FIG. 7 is a trend of tracking error over time according to an embodiment of the present application;
FIG. 8 is a schematic illustration of a surface drone tracking trajectory according to one embodiment of the present application;
fig. 9 is a comparison of simulation results for different LGR fitting point number settings according to an embodiment of the present application.
Detailed Description
Hereinafter, the technical solutions of the present application will be clearly and completely described in conjunction with a plurality of embodiments of the present application and with reference to the accompanying drawings, and it should be noted that the embodiments described below are for enabling those skilled in the art to better understand the technical solutions of the present application, and do not represent all the embodiments of the present application. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The use of "first," "second," and the like in the description, claims, and drawings of this application is for the purpose of distinguishing between similar elements or objects, and is not intended to limit the order or sequence in which a particular element or sequence is claimed, or to imply relative importance. Furthermore, the terms "comprises," "comprising," and any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, or article that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, or article.
Unless expressly stated or limited otherwise, the terms "disposed," "connected," and "connected" are to be construed broadly and encompass, for example, fixed, removable, or integral connections; they may be mechanically coupled, directly coupled, indirectly coupled through intervening media, or may be interconnected between two elements. The specific meaning of the above terms in the present application will be specifically understood by those skilled in the art.
First, a specific application scenario of the present application will be briefly described.
The near-water surface target is an underwater target moving close to the water surface, and the change of the position of the underwater target along the depth direction can be ignored and only the motion state of the underwater target along the horizontal plane can be concerned in the process of tracking the underwater target by the unmanned surface vehicle. Under the condition that the motion state of a near-water surface target is changed in real time, the optimal control input to the unmanned surface vehicle needs to be obtained as fast as possible so as to meet the real-time tracking requirement of the near-water surface target.
FIG. 1 shows a coordinate description of a three-degree-of-freedom model of an unmanned surface vehicle, at any one timetIts position and angle vector are
Figure 808443DEST_PATH_IMAGE036
(
Figure 466957DEST_PATH_IMAGE037
Is time of daytIs expressed in its entirety as
Figure 632359DEST_PATH_IMAGE038
For simplicity of presentation, omission when no processing of time variables is involvedtThe following pairV、X、X d 、UThe time-related vectors are expressed in the same way), and the velocity and angular velocity vectors areV=[u,v,r]T，
Figure 526366DEST_PATH_IMAGE037
AndVjointly form the unmanned surface vehicletState vector of time of day
Figure 93613DEST_PATH_IMAGE039
。
In addition, near surface targets aretState vector of time of dayX d The real-time acquisition can be realized through measuring equipment or other technical means arranged on the unmanned surface vehicle.
According to the optimal control theory, the optimal control of the unmanned surface vehicle to track the near-surface target can be described as obtaining the optimal control inputUThe control input enabling the system to control the operation of the electronic devicetState transition of time of daytThe minimum performance index is met during the state at time + 1. In the prior art, the method for acquiring the optimal control input is difficult to meet the requirements of solving precision and solving speed at the same time, so that a method capable of calculating the optimal control input of the surface unmanned ship for tracking the near-surface target in real time is needed.
In order to achieve the above object, an embodiment of the present application provides a method for tracking and controlling a target of an unmanned surface vehicle, fig. 2 is a flowchart of the method, and hereinafter, the steps of the method provided by the present application and a specific implementation manner thereof are described in detail in conjunction with a preferred embodiment of the present application.
As shown in fig. 2, step S100 is a step of building a kinetic model.
Specifically, in the embodiments of the present application, the above unmanned surface vehicle is used at any timetThe three free kinetic model of (a) can be constructed by:
Figure 923029DEST_PATH_IMAGE040
，
in the above formula, the first and second carbon atoms are,Mto add a mass inertia matrix to the hydrodynamic force,C(V)for an ideal rigid body and hydrodynamic coriolis force matrix,D(V)in order to be a hydrodynamic damping matrix,U=[U u ,U v ,U r ] T in order to control the input vector for the system,
Figure 152891DEST_PATH_IMAGE041
is composed ofVDerivative with respect to time.
In some specific embodiments of the present application,M、C(V) AndD(V) The concrete form of (A) is as follows:
Figure 725955DEST_PATH_IMAGE042
the values of all elements in the matrix are determined by the actual hull structure of the unmanned surface vehicle andtthe system state at the moment of time.
In some specific embodiments of the present application,M、C(V)、 D(V) Can be further determined by the following kinetic and control parameters:
Figure 882130DEST_PATH_IMAGE043
Figure 7080DEST_PATH_IMAGE044
in some specific embodiments of the present application,Xderivative with respect to time
Figure 84758DEST_PATH_IMAGE045
Has the following form:
Figure 523829DEST_PATH_IMAGE046
。
as shown in fig. 2, step S200 is a process of converting the three-degree-of-freedom dynamical model of the surface unmanned surface vehicle into a nonlinear system capable of performing quasi-linear derivation.
The three-degree-of-freedom dynamic model of the unmanned surface vehicle obtained in the step S100 has high nonlinearity, the calculation step for directly solving the optimal control input is complex, the calculation time is long, and the requirement of real-time control cannot be met, so that the parameterization idea of the state correlation matrix coefficient is utilized to convert the model into a nonlinear system capable of carrying out quasi-linear derivation.
Specifically, in the embodiments of the present application, a state correlation coefficient method is adopted, for
Figure 613139DEST_PATH_IMAGE045
The expression of (2) is subjected to identity transformation, so that the system complexity is increased on the aspect of mathematical expression, and the system controllability and the system observability can be met. The specific method is to increase or decrease the same term, multiply or divide the same non-zero term, and introduce a set of 8 constants a between 0 and 11~a8The following can be obtained:
Figure 846675DEST_PATH_IMAGE047
converted into matrix form to obtain system matrixA(X) And an input matrixB(X) Comprises the following steps:
Figure 411648DEST_PATH_IMAGE027
Figure 451148DEST_PATH_IMAGE028
the matrix representation of the mathematical model of the surface unmanned boat can be written in the form of:
Figure 581915DEST_PATH_IMAGE048
at the moment, under the condition of not changing the nonlinear nature of the unmanned surface vehicle system, the energy controllability of any state can be ensured, and the input vector is controlledUChanging any state.
As shown in FIG. 2, steps S300 to S600 are specifically solved at any timetOptimal control input vector of unmanned surface vehicleU optimal The solving process is as follows: the position and speed state information of the unmanned surface vehicle and the near-surface target is used, under the action of given performance index constraint and actual system performance constraint, a self-adaptive parameter adjusting method is introduced based on the numerical calculation principle of a pseudo-spectrum method, and the optimal control input vector of the tracking dynamic near-surface target is solved in real time.
Specifically, step S300 is to construct a performance indexJIn the embodiments of the present application, the performance index is in the form of:
Figure 189614DEST_PATH_IMAGE049
，
in the above formula, the first and second carbon atoms are, t 0in order to keep track of the starting moment,t f in order to keep track of the end time,X d is the state vector of the near-surface target,Qin the form of a state variable weight matrix,Rweighting matrices for energy consumptionQ、RThe value of (2) is determined by the state and performance of the unmanned surface vehicle,M(X(t f ),X d (t f ),t f ) Is a terminal error function and can be expressed in a quadratic form:
Figure 350206DEST_PATH_IMAGE050
，S(t f ) To be composed ofM(X(t f ),X d (t f ),t f ) A matrix of coefficients expressed in quadratic form to give the above propertiesControl input vector with minimum indexUI.e. the optimal control input vectorU optimal 。
Step S400 is to determine the number of matched points of LGR (Legendre-Gauss-Radau) according to the states of the unmanned surface vehicle and the near-surface targetNAccording to the determination of step S500NAnd (3) constructing a discrete system state matrix equation set by matching points of the LGRs.
According to the optimal control theory, the control input vector can be expressed as:
Figure 68763DEST_PATH_IMAGE051
in the above formulaP(X) To solve the state-dependent differential Riccati equation,
Figure 319616DEST_PATH_IMAGE052
in the process of actually solving the optimal control input for the co-state variable, the optimal control input can be obtained according to the preset parameters by a pseudo-spectral methodNThe LGR nodes discretize the system state to construct 2 × (N+1) dimension of the system state matrix equation set in discrete form, and the discrete matrix equation set is solved through step S600 to obtain the co-state variable which minimizes the performance index
Figure 957271DEST_PATH_IMAGE053
Thereby obtainingU optimal 。
Specifically, to obtain the performance indexJThe minimum system control input, a Hamiltonian of the following error form can be constructed:
Figure 496836DEST_PATH_IMAGE054
，
the Hamiltonian satisfies the following boundary conditions and cross-section conditions:
Figure 815822DEST_PATH_IMAGE055
，
to pairHAnd (3) solving the partial derivatives to obtain a continuous system state matrix equation set:
Figure 999810DEST_PATH_IMAGE056
，
solving the above equation set to obtain
Figure 683732DEST_PATH_IMAGE057
Then the optimal control input vector can be obtainedU optimal 。
To solve the above system state matrix equation set in continuous form, it can be discretized to facilitate the solution.
Specifically, first, let
Figure 241753DEST_PATH_IMAGE058
Is composed ofNOrder Legendre polynomial of
Figure 426746DEST_PATH_IMAGE059
(ii) aN+1) zeros
Figure 386612DEST_PATH_IMAGE060
For LGR dotting, the above-mentioned dotting row includes
Figure 507015DEST_PATH_IMAGE061
. The coordination points are distributed in [ -1,1 [)]And has a corresponding relation with the finite time domain, each point
Figure 395074DEST_PATH_IMAGE062
And a real time point
Figure 993546DEST_PATH_IMAGE063
The following corresponding relations exist:
Figure 135814DEST_PATH_IMAGE064
；
after the LGR point-to-point columns are determined, the system state may be approximated at the interpolation point using the following lagrange polynomial:
Figure 489435DEST_PATH_IMAGE065
，
wherein the content of the first and second substances,Din the form ofNLagrange differential matrix of order + 1:
Figure 225310DEST_PATH_IMAGE066
；
and finally, substituting the discretized system state into the continuous system state matrix equation set to obtain the following discrete system state matrix equation set:
Figure 502839DEST_PATH_IMAGE067
。
the system state matrix equation set in the discrete form contains
Figure 171717DEST_PATH_IMAGE068
The equations obtained by solving the above equation set in step S600
Figure 633923DEST_PATH_IMAGE069
And
Figure 981727DEST_PATH_IMAGE070
therein will be
Figure 984318DEST_PATH_IMAGE071
The expression of the control input vector brought into the unmanned surface vehicle is obtained at any momenttThe optimal control input variable of the unmanned surface vehicle is as follows:
Figure 710966DEST_PATH_IMAGE072
。
in the process of solving the system state matrix equation set by using the pseudo-spectrum method, the selection of the number of LGR distribution points influences the solving speed and the solving precision simultaneously,if the number of the matching points is too small, the obtained control input vector can not reach the optimum actually, and the good tracking of the water surface target can not be realized; too many matching points will result in excessive consumption of computing resources and prolonged computing time, and even real-time tracking cannot be realized, so the LGR matching points need to be determinedNAnd adjusting the number of LGR points according to a trend function between the unmanned surface vehicle and the near-surface target.
Determining LGR ligand counts is described in detail belowNThe process of (1).
Preferably, in embodiments of the present application, the number of LGR dotsNHas a value range of
Figure 406390DEST_PATH_IMAGE073
Wherein, in the step (A),N min the minimum LGR matching point number required by the tracking precision is met.
In some preferred embodiments of the present application,N min the value of (a) is 4, and in some other embodiments of the present application, the value can be determined according to factors such as computing resources, tracking accuracy, and tracking real-time performanceN min The value of (a).
Preferably, in an embodiment of the present application, a trend function of the form:
Figure 225179DEST_PATH_IMAGE074
trend function of abovekIs the distance between the unmanned surface vehicle and the object near the water surfacesAndsthe first derivative, a function of the second derivative,a、b、c、dis a preset constant which reflects the distance between the unmanned surface vehicle and the near-surface target and the relation between the change trends of the distance, and is adjusted by the preset constanta、b、c、dThere may be a preferential choice of factors in tracking with a bias.
In the embodiments of the present application, the number of LGR nodes is determined in S400NThe method can be realized by the following steps:
s410: judgment oftWhether the trend function of the moment is in the first state interval or the fourth state interval or not is judged, if the judgment result is true, the number of LGR (light-emitting diode) nodes is increasedNThen, step S500 is executed, and if the determination result is false, step S420 is executed;
s420: judgment oftWhether the trend function of the moment is in the second state interval or not, if the judgment result is true, keeping the LGR matching point numberNStep S500 is executed without change, and if the determination result is false, step S430 is executed;
s430: determiningtThe trend function of the moment is in a third state interval, and whether the number of LGR configuration points is greater than that of the LGR configuration points is further judgedN min If the judgment result is true, the LGR matching point number is reducedNThen, step S500 is executed, if the determination result is false, the LGR matching point number is maintainedNAnd step S500 is not changed and performed.
FIG. 3 shows the setting of coefficients in a specific embodiment of the present applicationa、b、c、dThe trend function is divided into 4 state intervals, as shown in fig. 3:
(1) when in usekWhen the unmanned surface vehicle is in the first state interval, the unmanned surface vehicle is far away from the target close to the water surface, and the target needs to be approached at a high speed, so that the number of LGR configuration points can be increased, and the input can be more densely and accurately controlled to shorten the distance from the target as soon as possible;
(2) when in usekWhen the unmanned surface vehicle is in the fourth state interval, the unmanned surface vehicle is closer to the near-surface target, and the motion state of the near-surface target is obviously changed, so that the number of LGR points can be increased, and the input can be more densely and accurately controlled to better adapt to the change of the target state;
(3) when in usekWhen the unmanned surface vehicle is in the second state interval, the unmanned surface vehicle is closer to the target close to the water surface, the target motion state is more stable, and the number of LGR points can be kept to continuously follow the target state and gradually reduce the error;
(4) when in usekWhen the unmanned surface vehicle is in the second state interval, the unmanned surface vehicle is close to the near-surface target, the motion state of the target fluctuates but is not obvious, and the number of the counter points can be reduced to reduce the calculation consumption.
In the embodiment of the application, after the LGR matching number is adjusted by using the above specific implementation, the optimal control input vector for tracking the near-water target on the unmanned surface vehicle can be solved through steps S500 and S600:
Figure 969144DEST_PATH_IMAGE075
。
step S700 is a continuous control process by using the value found in step S600U optimal After the unmanned surface vehicle is controlled, the unmanned surface vehicle is arranged ontAnd +1, re-executing the step S100 to the step S600, thereby realizing the continuous control of the unmanned surface vehicle tracking the target close to the water surface.
Example 1
The embodiment shows the situation that the unmanned surface vehicle tracks the near-surface target in a specific motion state by using the method provided by the application, wherein the initial state vector of the unmanned surface vehicleX=[-3,1,0.1,0.1,0.1,0.01] T Initial state vector of near surface targetX d =[3,5,pi/4,1.4142,0,0] T And the near-water target moves along a sinusoidal track.
Fig. 4 shows the detailed settings of the relevant kinetic parameters and control parameters in the present embodiment:
in this embodiment, the state variable weight matrixQ=diag(106, 106, 106, 106, 106, 106) In other embodiments, such as considering the following effect of the x, y coordinates to be more important than the rest of the state, one may considerQIs arranged, for example, asdiag(3×106, 3×106, 106, 106, 106, 106)。
In the present embodiment, the energy consumption weight matrixR=diag(1, 1, 1)，RIs set according to the energy consumption of the physical propulsion device on the actual ship body, wherein the energy consumption degree of the supplied thrust and the torque is considered to be the same, in other embodiments, the energy consumption degree can be set according to the energy consumption of the actual ship bodyPropulsion device performance adjustmentRThe value of (a).
In this embodiment, the number of LGR nodesNLower limit of (2)N min Is 4, such asNLess than 4, the calculation will not meet the accuracy requirement.
In this embodiment, the number of LGR nodesNThe upper limit of (2) is 12, and in other embodiments, the upper limit can also be set according to the actual needs of the tracking targetNThe upper limit of (3).
In the present embodiment, each adjustmentNThe step size of (2) is set to 1, and in other embodiments, other fixed step sizes or variable step sizes may be set according to the actual need of the tracking target.
In the present embodiment, the values of a 1-a 8 are: 0.1,0.12,0.15,0.17,0.2,0.23,0.26,0.29.
After the above setting is completed, the unmanned surface vehicle is controlled to continuously track the target near the water surface in real time according to steps S100 to S700, and fig. 5 shows a specific tracking flow, where "behind" is the first state region or the fourth state region in fig. 3, "steady state" is the second state region in fig. 3, and "fluctuation" is the third state region in fig. 3.
Fig. 6 shows simulation results of the input vector for the surface unmanned surface vehicle control of the present embodiment, and fig. 7 shows simulation results of the tracking error of the surface unmanned surface vehicle of the present embodiment with time.
Example 2
This embodiment presents the case where the surface drone approaches from a distance to the surface drone when the near surface target is in a static state (i.e., a regulator problem), where the initial state vector of the surface droneX=[10,10,1,1,1,0.1] T Initial state vector of near surface targetX d =[0,0,0,0,0,0] T And then the near-surface target continues to remain stationary.
The other settings of the present embodiment are the same as those of embodiment 1.
Fig. 8 shows simulation results of the surface unmanned ship tracking path using the adaptive adjustment LGR fitting point number and using different fixed LGR fitting point numbers, and fig. 9 shows comparison of the simulation results using the adaptive adjustment LGR fitting point number and using different fixed LGR fitting point numbers.
As can be seen from fig. 8 and 9, the overall tracking control effect of the adaptive method is better than that of the fixed point number, and the point number matching adaptive strategy can make better compromise between the calculation accuracy and the calculation speed, so as to obtain a better control effect.
While the present invention has been described in detail and with reference to specific embodiments thereof, it will be apparent to one skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope thereof as defined in the appended claims.

Claims (9)

1. A target tracking control method for unmanned surface vehicle is used for real-time acquisitiontThe system control input of the optimal dynamic tracking of the unmanned surface vehicle to the near-surface target at the moment is characterized by comprising the following steps:
s100: establishingtThree-degree-of-freedom dynamic model of unmanned surface vehicle at any moment
Figure DEST_PATH_IMAGE001
，
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE002
to add a mass inertia matrix to the hydrodynamic force,
Figure DEST_PATH_IMAGE003
for an ideal rigid body and hydrodynamic coriolis force matrix,
Figure DEST_PATH_IMAGE004
in order to be a hydrodynamic damping matrix,
Figure DEST_PATH_IMAGE005
in order to control the input vector for the system,
Figure 615780DEST_PATH_IMAGE002
、
Figure 798500DEST_PATH_IMAGE003
and
Figure 109395DEST_PATH_IMAGE004
the concrete form of (A) is as follows:
Figure DEST_PATH_IMAGE006
the values of all elements in the matrix are determined by the actual hull structure of the unmanned surface vehicle andtthe decision of the state of the system at the moment,
Figure DEST_PATH_IMAGE007
is an unmanned surface boat
Figure DEST_PATH_IMAGE008
The state of the velocity and the angular velocity at the moment is that the unmanned surface vehicle is on
Figure 832501DEST_PATH_IMAGE008
Position and angular state of time
Figure DEST_PATH_IMAGE009
The time is derived to obtain the result of the derivation,
Figure DEST_PATH_IMAGE010
，
Figure DEST_PATH_IMAGE011
form an unmanned surface vehicle
Figure 974769DEST_PATH_IMAGE008
State vector of time of day
Figure DEST_PATH_IMAGE012
Said
Figure DEST_PATH_IMAGE013
Derivative with respect to time
Figure DEST_PATH_IMAGE014
Has the following form:
Figure DEST_PATH_IMAGE015
；
s200: and converting the unmanned ship three-degree-of-freedom dynamic model into a system capable of carrying out quasi-linear derivation by adopting a state correlation coefficient method, wherein the system comprises the following components:
Figure DEST_PATH_IMAGE016
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE017
is composed oftThe system matrix of the time of day,
Figure DEST_PATH_IMAGE018
is composed oftAn input matrix of time instants;
s300: index of structural performance
Figure DEST_PATH_IMAGE019
:
Figure DEST_PATH_IMAGE020
，
Wherein
Figure DEST_PATH_IMAGE021
In order to keep track of the starting moment,
Figure DEST_PATH_IMAGE022
in order to keep track of the end time,
Figure DEST_PATH_IMAGE023
is the state vector of the near-surface target,
Figure DEST_PATH_IMAGE024
in the form of a state variable weight matrix,
Figure DEST_PATH_IMAGE025
is an energy consumption weight matrix, the
Figure 577658DEST_PATH_IMAGE024
、
Figure 110270DEST_PATH_IMAGE025
Determined by the state and performance of the unmanned surface vehicle,
Figure DEST_PATH_IMAGE026
in order to be a function of the terminal error,S(t f ) To be composed ofM(X(tf),X d(tf), tf) A matrix of coefficients expressed in quadratic form, such that the performance index
Figure 840329DEST_PATH_IMAGE019
Minimum size
Figure DEST_PATH_IMAGE027
Is that
Figure 305945DEST_PATH_IMAGE008
System control input vector satisfying optimal dynamic tracking of moments
Figure DEST_PATH_IMAGE028
The concrete form is as follows:
Figure DEST_PATH_IMAGE029
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE030
to make the performance index
Figure 627205DEST_PATH_IMAGE019
A minimum co-state vector;
s400: determining the number of LGR points according to a trend function of the unmanned surface vehicle tracking the near-water surface targetNAnd corresponding LGR point
Figure DEST_PATH_IMAGE031
Wherein the LGR is coordinated with a point
Figure DEST_PATH_IMAGE032
Is an equation
Figure DEST_PATH_IMAGE033
Is/are as followsNThe number of +1 zero points is,
Figure DEST_PATH_IMAGE034
is composed ofNOrder Legendre polynomial;
s500: according to the aboveNLGR distribution point
Figure 975010DEST_PATH_IMAGE032
And generating the following matrix equation system in a discrete form by using a pseudo-spectrum method:
Figure DEST_PATH_IMAGE035
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE036
is that it is
Figure DEST_PATH_IMAGE037
The value at the ith coordinate point is,
Figure DEST_PATH_IMAGE038
an N +1 order Lagrange differential matrix of the following formula:
Figure DEST_PATH_IMAGE039
；
s600: solving the matrix equation system (5-1) in the discrete form to obtain
Figure DEST_PATH_IMAGE040
Will be
Figure DEST_PATH_IMAGE041
Carrying out the formula (3-1) to obtaintSystem control inputs for time instant satisfying optimal dynamic tracking:
Figure DEST_PATH_IMAGE042
；
s700: according to the above
Figure DEST_PATH_IMAGE043
After the unmanned surface vehicle is controlled, the unmanned surface vehicle is arranged on
Figure DEST_PATH_IMAGE044
Step S100 to step S600 are executed again at this time.
2. The surface unmanned ship target tracking control method of claim 1, wherein the trend function in step S400 is:
Figure DEST_PATH_IMAGE045
wherein the trend function
Figure DEST_PATH_IMAGE046
Is the distance between the unmanned surface vehicle and the near-surface target
Figure DEST_PATH_IMAGE047
And
Figure 226868DEST_PATH_IMAGE047
the first derivative, a function of the second derivative,
Figure DEST_PATH_IMAGE048
is a preset constant.
3. The water surface unmanned ship target tracking control method as claimed in claim 2, characterized in that:
the number of LGR dotsNHas a value range of
Figure DEST_PATH_IMAGE049
Wherein, in the step (A),
Figure DEST_PATH_IMAGE050
the minimum LGR matching point number required by the tracking precision is met.
4. The water surface unmanned ship target tracking control method as claimed in claim 3, characterized in that:
the above-mentioned
Figure DEST_PATH_IMAGE051
。
5. The surface unmanned ship target tracking control method as claimed in any one of claims 3 to 4, wherein the step S400 is to determine the number of LGR counter points according to a trend function of the surface unmanned ship tracking the near-surface targetNFurther comprising the steps of:
s410: judgment of
Figure 343729DEST_PATH_IMAGE008
Whether the trend function of the moment is in the first state interval or the fourth state interval or not is judged, if the judgment result is true, the number of LGR (light-emitting diode) configuration points is increasedNThen, step S500 is executed, and if the determination result is false, step S420 is executed;
s420: judgment of
Figure 39153DEST_PATH_IMAGE008
Whether the trend function at the moment is in a second state interval or not, if the judgment result is true, keeping the number of LGR nodesNStep S500 is executed without change, and if the determination result is false, step S430 is executed;
s430: determining
Figure 811936DEST_PATH_IMAGE008
The trend function at the moment is in a third state interval, and the number of LGR matching points is further judged
Figure DEST_PATH_IMAGE052
Whether or not greater than
Figure 618218DEST_PATH_IMAGE050
If the judgment result is true, the LGR matching point number is reduced
Figure 792848DEST_PATH_IMAGE052
Then, step S500 is executed, if the determination result is false, the LGR matching point number is maintainedNAnd step S500 is not changed and performed.
6. The water surface unmanned ship target tracking control method as claimed in claim 5, characterized in that:
when the trend function is in the first state interval, the unmanned surface vehicle is far away from the near-surface target;
when the trend function is in the second state interval, the unmanned surface vehicle is close to the near-surface target and the motion state of the near-surface target is stable;
when the trend function is in the third state interval, the unmanned surface vehicle is close to the near-surface target and the motion state of the near-surface target has slight fluctuation;
when the trend function is in the fourth state interval, the unmanned surface vehicle is close to the near-surface target, and the motion state of the near-surface target has obvious change.
7. The water surface unmanned ship target tracking control method as claimed in claim 1, characterized in that:
the system matrix
Figure 393593DEST_PATH_IMAGE017
The method specifically comprises the following steps:
Figure DEST_PATH_IMAGE053
，
the input matrix
Figure 653673DEST_PATH_IMAGE018
The method specifically comprises the following steps:
Figure DEST_PATH_IMAGE054
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE055
a total of 8 constants to satisfy the structural requirements of the state correlation coefficient.
8. The water surface unmanned ship target tracking control method as claimed in claim 1, characterized in that:
the LGR distribution point
Figure 794805DEST_PATH_IMAGE032
With discrete points in time
Figure DEST_PATH_IMAGE056
The corresponding relation is as follows:
Figure DEST_PATH_IMAGE057
。
9. the surface unmanned ship target tracking control method of claim 8, wherein the matrix equation set (5-1) is generated according to the following steps:
the first step is as follows: establishing a Hamiltonian of an error form:
Figure DEST_PATH_IMAGE058
；
the second step is that: and solving partial derivatives under the set boundary condition and the set cross section condition to obtain a continuous matrix equation set:
Figure DEST_PATH_IMAGE059
，
the boundary conditions and the cross-section conditions are as follows:
Figure DEST_PATH_IMAGE060
；
the third step: using the LGR site
Figure DEST_PATH_IMAGE061
With discrete points in time
Figure DEST_PATH_IMAGE062
And the corresponding relationship of
Figure DEST_PATH_IMAGE063
In thatNApproximating the continuous form matrix equation set at +1 interpolation points to obtain the discrete form matrix equation set (5-1).
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