CN113359781B - Networked surface vessel tracking control method, device, equipment and storage medium - Google Patents

Networked surface vessel tracking control method, device, equipment and storage medium Download PDF

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CN113359781B
CN113359781B CN202110577890.2A CN202110577890A CN113359781B CN 113359781 B CN113359781 B CN 113359781B CN 202110577890 A CN202110577890 A CN 202110577890A CN 113359781 B CN113359781 B CN 113359781B
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CN113359781A (en
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张秋月
许坤婷
葛明峰
丁腾飞
梁昌铎
黄凯伦
董玖旺
苏鹏
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China University of Geosciences
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Abstract

The invention provides a networked surface vessel tracking control method, a device, equipment and a storage medium, wherein the method comprises the following steps: modeling is carried out on the surface naval vessel to obtain a dynamics and kinematics model, a virtual leader is set, and the rest are set as followers; establishing a directed topological graph among the surface ships; according to a dynamics and kinematics model and a directed topological graph, a sliding mode surface and a control algorithm under a layered control frame are designed, and the method comprises the following steps: a control algorithm of a distributed estimation layer and a control algorithm of a local control layer; estimating the state of the virtual leader according to a control algorithm of a distributed estimation layer, wherein a follower reaches a formation form at the layer to realize formation control; and driving each surface vessel to track to the virtual leader within a predefined time according to a control algorithm of the local control layer. The formation tracking control of the surface naval vessels is realized by adopting a layered control algorithm, and the system state can be converged to the original point on a new sliding mode surface and can be applied to different complex systems.

Description

Networked surface vessel tracking control method, device, equipment and storage medium
Technical Field
The invention relates to the field of robot control, in particular to a networked surface vessel tracking control method, a networked surface vessel tracking control device, networked surface vessel tracking control equipment and a storage medium.
Background
In the 80's of the 20 th century, the concept of a maritime unmanned system cluster was first proposed in the united states. The offshore unmanned system cluster is used for organically integrating an ocean surface unmanned aerial vehicle cluster and an underwater unmanned robot cluster through intelligent command, cooperative control and information interaction. In recent years, the track tracking control problem of the ocean surface unmanned aerial vehicle is receiving more and more attention, because the track tracking control problem not only conforms to the development trend in the intelligent era, but also meets the requirements which cannot be met by the manned water surface unmanned aerial vehicle.
The application of marine surface unmanned aircraft is mainly focused on dangerous tasks or fields that are not suitable for manned vessels. Such as mine investigation, ocean water quality monitoring, fixed point collection of leaked oil and other application occasions. Among these control problems, the single surface vehicle currently used has a large degree of freedom and working space, but its advantages do not work well when accomplishing some of the more complex problems in highly dynamic waters. The control of networked surface aircraft is considered as one of the most important research topics due to the advantages of more degrees of freedom, larger working space, higher attack resistance and the like compared with a single surface vehicle, and in addition, distributed control generally has the performances of stronger robustness, flexibility, higher efficiency and the like compared with centralized control. Therefore, the networked water surface aircraft can better solve complex problems, each individual in the network system can cooperate with each other to complete tasks, the overall advantages are exerted, and greater contribution is made to the operation tasks on the sea surface.
Disclosure of Invention
In order to solve the technical problems of limited freedom degree and working space of a single surface carrier and lower robustness, flexibility and efficiency of centralized control, the invention provides a networked surface ship tracking control method which is realized based on a hierarchical control algorithm so as to facilitate autonomous definition of users and stabilize a complex system.
In order to achieve the above object: the invention provides a networked surface vessel tracking control method, which specifically comprises the following steps:
performing dynamics and kinematics modeling on N surface ships to obtain dynamics and kinematics models, setting a virtual leader from the N surface ships, and setting the rest of the virtual leader as a follower;
establishing a directed topological graph among the surface ships;
designing a sliding mode surface and a control algorithm under a layered control frame according to the dynamics and kinematics model and the directed topological graph, wherein the control algorithm comprises the following steps: a control algorithm of a distributed estimation layer and a control algorithm of a local control layer;
estimating the state of the virtual leader according to a control algorithm of the distributed estimation layer, and enabling followers to reach a formation form in the distributed estimation layer to realize formation control; and driving each surface vessel to track the virtual leader within a predefined time according to a control algorithm of the local control layer.
Preferably, the expression of the kinetic and kinematic model is:
Figure GDA0003608041390000021
wherein i ∈ {1,2, …, N } represents the serial number of the surface vessel,
Figure GDA0003608041390000022
indicating the location of the earth's fixed point (X)i,Yi) (viii), (Ψ)i) Is the angle of the course direction and is,
Figure GDA0003608041390000023
represents a set of real numbers that are,
Figure GDA0003608041390000024
representing an n-dimensional euclidean space;
Figure GDA0003608041390000025
representing a velocity vector (v) of the objectxi,υyi) (ω) of (C)i) Is the angular velocity;
Figure GDA0003608041390000026
representing the velocity/angular velocity vector in earth fixed coordinates;
Figure GDA0003608041390000027
is a control input;
Figure GDA0003608041390000028
is a perturbation vector in which, among other things,
Figure GDA0003608041390000029
Mi，Ci(υi) And Di(υi) Respectively an inertia matrix, a Coriolis and centripetal matrix and a hydrodynamic damping matrix;
Figure GDA00036080413900000210
is a transformation matrix;
the expression of the reference track of the virtual leader in the earth fixed coordinate is as follows:
Figure GDA00036080413900000211
wherein,
Figure GDA00036080413900000212
respectively, a position/attitude vector, a velocity/angle vector, and an acceleration vector of the virtual leader in earth fixed coordinates.
Preferably, the directed topology is G ═ ν, ∈, a }, where ν ═ {1,2, … N }, { (i, j) | i, j ∈ i ≠ j } ∈ ν × ν, a ═ v ═ j }, and,
Figure GDA00036080413900000213
Respectively representing a surface ship set, an edge set and a weight adjacency matrix which are formed by N surface ships, wherein aijRepresenting the weight between the surface vessel i and the surface vessel j; the side (i, j) belongs to epsilon, which indicates that the jth surface vessel is a neighbor of the ith surface vessel, and the ith surface vessel can directly receive information from the jth surface vessel, then aij> 0, otherwise aij＝0；NiDefining the [ j belongs to nu (i, j) belongs to epsilon ] as a neighbor set of the ith surface ship; determining a Laplace matrix L of the directed topological graph according to the weighted adjacency matrix A, wherein the Laplace matrix L is defined as
Figure GDA0003608041390000031
lijFor elements in the matrix L, when i ≠ j ∈ v, Lij＝-aij(ii) a When i ∈ v,
Figure GDA0003608041390000032
j is NiA node in (1); BETA ═ diag { b1,b2,...,bNDenotes a diagonal weight matrix of the directed topology graph illustrating the interaction of the surface vessel with the virtual leader, where biN is an element in the B matrix, B if the ith surface vessel can directly receive information from the virtual leaderiIs greater than 0; otherwise, for
Figure GDA0003608041390000033
bi＝0。
Preferably, after the step of performing dynamics and kinematics modeling on the N surface vessels to obtain dynamics and kinematics models, the method further includes:
defining the error function as:
Figure GDA0003608041390000034
wherein eηiAnd eυiRespectively, a position tracking error and a speed tracking error in earth fixed coordinates; eta0＝[X0,Y0,Ψ0]TAnd upsilon0＝[υx0,υy0,ω0]TRespectively representing the position and velocity states of the virtual leader; etai＝[Xi,Yi,Ψi]TAnd upsiloni＝[υxi,υyi,ωi]TRespectively representing the position and speed state of each follower; h isiRepresenting a formation offset;
according to the error function, the dynamics and kinematics model is converted into:
Figure GDA0003608041390000035
wherein Qi(ηi,υi)＝-Ci(υi)υi-Di(υi)υi，
Figure GDA0003608041390000036
Is the transformation matrix of the virtual leader.
Preferably, the sliding form surface under the layered control frame comprises: the sliding mode surface of the distributed estimation layer and the sliding mode surface under the local control layer are respectively as follows:
Figure GDA0003608041390000037
Figure GDA0003608041390000038
wherein,
Figure GDA0003608041390000039
for the sliding-mode faces of the distributed estimation layer,
Figure GDA00036080413900000310
for the sliding surface of the local control layer, first the definition
Figure GDA00036080413900000311
Is Xi,Yi,Ψi,θXi,θYi,ωiIs determined by the estimated value of (c),
Figure GDA00036080413900000312
Figure GDA0003608041390000041
are each ηi,
Figure GDA0003608041390000042
υiAn estimated value of (d); then define
Figure GDA0003608041390000043
Figure GDA0003608041390000044
Figure GDA0003608041390000045
hiRepresenting formation offset, γs1,Υs2Predefined time, and y, of the distributed estimation layer and the local control layer, respectivelys1＞0,Υs2＞0；γ1，γ2Is a normal number, and 0 < gamma1＜1，0＜γ2＜1。
Preferably, based on the predefined time stability, y, if present in the controller designfAnd if the following formula is established, the predefined time formation tracking of the networked surface vessels is realized:
Figure GDA0003608041390000046
wherein the kinematic error eηi＝ηi-η0-hi、eυi＝υi-υoRespectively position tracking error and velocity tracking error in earth's fixed coordinates, hiIndicating a formation offset.
Preferably, the control algorithm of the distributed estimation layer is:
Figure GDA0003608041390000047
wherein 0 < xi1< 1 is a normal number, γc1> 0 is the predefined time of the distributed estimation layer in the algorithm.
Preferably, the control algorithm of the local control layer is as follows:
Figure GDA0003608041390000051
ρeq,idenotes the equivalent control term, ps,iRepresenting a sliding mode cancellation term; 1nDenotes an n-dimensional vector with all elements 1, 13A 3-dimensional vector representing all elements as 1; degree is a value according to Hadamard's theorem if x is ═ x1,x2,…xn]T，y＝[y1,y2,…yn]TThen, then
Figure GDA0003608041390000052
sig(x)mIs defined as sig (x)m＝[sgn(x1)|x1|m,sgn(x2)|x2|m,…,sgn(xn)|xn|m]TWhere | x | ═ x1|,|x2|,…,|xn|]TSgn (x) is a sign function, and m is a normal number.
Figure GDA0003608041390000053
Figure GDA0003608041390000054
Qi(ηi,υi)＝-Ci(υi)υi-Di(υi)υi，0＜ξ2< 1 is a normal number, γc2The more than 0 is the predefined time of a local control layer in the algorithm;
Figure GDA0003608041390000055
is a diagonal positive definite gain matrix.
In addition, in order to achieve the above object, the present invention further provides a networked surface vessel tracking control device, including the following modules:
the model building module is used for carrying out dynamic and kinematic modeling on the N surface vessels to obtain dynamic and kinematic models, setting a virtual leader from the N surface vessels, and setting the rest as followers;
the directed graph building module is used for building a directed topological graph among the surface ships;
the algorithm design module is used for designing a sliding mode surface and a control algorithm under a layered control frame according to the dynamics and kinematics model and the directed topological graph, and the control algorithm comprises a control algorithm of a distributed estimation layer and a control algorithm of a local control layer;
the tracking control module is used for estimating the state of the virtual leader according to a control algorithm of the distributed estimation layer, and the followers reach a formation form in the distributed estimation layer to realize formation control; and driving each surface vessel to track the virtual leader within a predefined time according to a control algorithm of the local control layer.
In addition, in order to achieve the above object, the present invention further provides a networked surface vessel tracking control device, where the networked surface vessel tracking control device includes a memory, a processor, and a networked surface vessel tracking control program stored in the memory and operable on the processor, and the networked surface vessel tracking control program, when executed by the processor, implements the steps of the networked surface vessel tracking method.
In addition, in order to achieve the above object, the present invention further provides a storage medium, where a networked surface vessel tracking control program is stored on the storage medium, and when the networked surface vessel tracking control program is executed by a processor, the steps of the networked surface vessel tracking control method are implemented.
The invention adopts a layered control algorithm, realizes formation tracking control of the surface naval vessels by selecting proper control parameters, and the system state of the kinematics and dynamics model can be converged to the original point on a new sliding mode surface, and can be applied to different complex systems.
The invention has the following beneficial effects:
1. the new sliding mode surface enables the state to reach convergence in the predefined time;
2. the method can be applied to different complex systems, and the time parameter of the predefined time is considered, so that the user can define the method independently, and the practicability is higher.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
fig. 1 is a flowchart of a method for tracking and controlling a networked surface vessel of the surface vessel according to an embodiment of the present invention;
figure 2 is a coordinate diagram of a surface vessel provided in an embodiment of the invention;
FIG. 3 is a general framework diagram of a hierarchical control algorithm provided by an embodiment of the present invention;
fig. 4 is a directed topology diagram of a networked surface vessel according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a networked surface vessel eta in accordance with an embodiment of the present inventioni-hiTime evolution graphs;
fig. 6 is a diagram illustrating the evolution of the error of the networked surface vessel over time according to the embodiment of the present invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
Referring to fig. 1, fig. 1 is a flowchart of a networked surface vessel tracking control method for a surface vessel according to an embodiment of the present invention;
s1, performing dynamics and kinematics modeling on the N surface ships to obtain dynamics and kinematics models, setting a virtual leader from the N surface ships, and setting the rest as followers;
the expression of the dynamics and kinematics model is:
Figure GDA0003608041390000071
wherein i ∈ {1,2, …, N } represents the serial number of the surface vessel,
Figure GDA0003608041390000072
indicating the location of the earth's fixed point (X)i,Yi) (viii), (Ψ)i) Is the angle of the course direction and is,
Figure GDA0003608041390000073
represents a set of real numbers and is,
Figure GDA0003608041390000074
representing an n-dimensional euclidean space;
Figure GDA0003608041390000075
representing a velocity vector (v) of the objectxi,υyi) (ω) of (c)i) Is the angular velocity;
Figure GDA0003608041390000076
representing the velocity/angular velocity vector in earth fixed coordinates;
Figure GDA0003608041390000077
is a control input;
Figure GDA0003608041390000078
is a perturbation vector in which, among other things,
Figure GDA0003608041390000079
Mi，Ci(υi) And Di(υi) Respectively an inertia matrix, a Coriolis matrix, a centripetal matrix and a hydrodynamic damping matrix;
Figure GDA00036080413900000710
is a transformation matrix;
the expression of the reference track of the virtual leader in the earth fixed coordinate is as follows:
Figure GDA00036080413900000711
wherein,
Figure GDA00036080413900000712
respectively, a position/attitude vector, a velocity/angle vector, and an acceleration vector of the virtual leader in earth fixed coordinates.
After the step of performing dynamics and kinematics modeling on the N surface vessels to obtain dynamics and kinematics models, the method further comprises the following steps:
defining the error function as:
Figure GDA00036080413900000713
wherein eηiAnd eυiRespectively, a position tracking error and a speed tracking error in earth fixed coordinates; eta0＝[X0,Y0,Ψ0]TAnd upsilon0＝[υx0,υy0,ω0]TRespectively representing the position and speed states of the virtual leader; etai＝[Xi,Yi,Ψi]TAnd upsiloni＝[υxi,υyi,ωi]TRespectively representing the position and speed state of each follower; h isiRepresenting a formation offset;
according to the error function, the dynamics and kinematics model is converted into:
Figure GDA0003608041390000081
wherein Qi(ηi,υi)＝-Ci(υi)υi-Di(υi)υi，
Figure GDA0003608041390000082
Is the transformation matrix of the virtual leader.
Referring to fig. 2, in the present embodiment, a simulation study was conducted on a networked surface vessel system composed of six well-known seebo second Ships (Cyber-Ships II), each of which is a duplicate of a supply vessel in a ratio of 1: 70, and each of which has a mass, a length, and a width of m ═ 23.8kg, L ═ 1.255m, and B ═ 0.29m, respectively.
The trajectory of the virtual leader is set to:
Figure GDA0003608041390000083
and S2, establishing a directed topological graph among the surface ships.
The directed topology graph is G ═ v, ∈, A }, where ν { [ 1,2, … N }, ε { (i, j) | i, j ∈ i ≠ j }, ∈ ν × ν, and,
Figure GDA0003608041390000084
Respectively representing a surface ship set consisting of N surface ships and a weight adjacency matrix, wherein aijRepresenting the weight between the surface vessel i and the surface vessel j; the edge (i, j) is epsilon, which indicates that the jth surface vessel is a neighbor of the ith surface vessel, and the ith surface vessel can directly receive information from the jth surface vessel, then aij> 0, otherwise aij＝0；NiDefining the [ j belongs to nu (i, j) belongs to epsilon ] as a neighbor set of the ith surface ship; determining a Laplace matrix L of the directed topological graph according to the weighted adjacency matrix A, wherein the Laplace matrix L is defined as
Figure GDA0003608041390000085
lijFor elements in the matrix L, when i ≠ j ∈ v, Lij＝-aij(ii) a When i ∈ v,
Figure GDA0003608041390000086
j is NiA node in (b); BETA ═ diag { b1,b2,...,bNDenotes a diagonal weight matrix of the directed topology graph illustrating the interaction of the surface vessel with the virtual leader, where biN is an element in the B matrix, B if the ith surface vessel can directly receive information from the virtual leaderiIs greater than 0; otherwise, for
Figure GDA0003608041390000087
bi＝0。
Referring to fig. 3, which is a topological diagram of a networked surface vessel, node 0 represents a virtual leader and nodes 1-6 represent followers.
S3, designing a sliding mode surface and a control algorithm under a layered control framework according to the dynamics and kinematics model and the directed topological graph, wherein the control algorithm comprises the following steps: a control algorithm of a distributed estimation layer and a control algorithm of a local control layer.
The slip form face under the layered control frame comprises: the sliding mode surface of the distributed estimation layer and the sliding mode surface under the local control layer are respectively as follows:
Figure GDA0003608041390000091
Figure GDA0003608041390000092
wherein,
Figure GDA0003608041390000093
for the sliding-mode faces of the distributed estimation layer,
Figure GDA0003608041390000094
for the sliding surface of the local control layer, first the definition
Figure GDA0003608041390000095
Is Xi,Yi,Ψi,θXi,θYi,ωiIs determined by the estimated value of (c),
Figure GDA0003608041390000096
Figure GDA0003608041390000097
are each ηi,
Figure GDA0003608041390000098
υiAn estimated value of (d); then define
Figure GDA0003608041390000099
Figure GDA00036080413900000910
Figure GDA00036080413900000911
hiRepresenting formation offset, γs1,Υs2> 0 is the predefined time for the distributed estimation layer and the local control layer; gamma is more than 01，γ2< 1 is a normal number.
The control algorithm of the distributed estimation layer is as follows:
Figure GDA00036080413900000912
wherein 0 < xi1< 1 is a normal number, γc1> 0 is the predefined time of the distributed estimation layer in the algorithm.
The control algorithm of the local control layer is as follows:
Figure GDA0003608041390000101
ρeq,idenotes the equivalent control term, ps,iRepresenting a sliding mode cancellation term; 1nRepresenting an n-dimensional vector with all elements 1, 13A 3-dimensional vector representing all elements as 1; degree is a value according to Hadamard's theorem if x is ═ x1,x2,…xn]T，y＝[y1,y2,…yn]TThen, then
Figure GDA0003608041390000102
sig(x)mIs defined as sig (x)m＝[sgn(x1)|x1|m,sgn(x2)|x2|m,…,sgn(xn)|xn|m]TWhere | x | ═ x [ | x |)1|,|x2|,…,|xn|]TSgn (x) is a sign function, and m is a normal number.
Figure GDA0003608041390000103
Figure GDA0003608041390000104
Qi(ηi,υi)＝-Ci(υi)υi-Di(υi)υi，0＜ξ2< 1 is a normal number, γc2The more than 0 is the predefined time of a local control layer in the algorithm;
Figure GDA0003608041390000105
is a diagonal positive definite gain matrix.
S4, estimating the state of the virtual leader according to the control algorithm of the distributed estimation layer, and enabling followers to reach a formation form on the distributed estimation layer to realize formation control; and driving each surface vessel to track to the virtual leader within a predefined time according to a control algorithm of the local control layer.
Based on the predefined time stability, y, if there was a predefined time in the controller designfIf the following formula is established, the predefined time formation tracking of the networked surface ships is realized:
Figure GDA0003608041390000106
wherein the kinematic error eηi＝ηi-η0-hi、eυi＝υi-υoRespectively, a position tracking error in a fixed coordinate of the earth, a velocity tracking error in a fixed coordinate system, hiIndicating a formation offset.
The hierarchical control algorithm can solve the problem of pre-defined time formation tracking control of networked surface ships under different conditions, so that the system can obtain the origin in the pre-defined time. In contrast to existing fixed time results, in control designs the setup time using the proposed scheme is capped by some predefined time parameter and can therefore be easily defined by the user.
Referring to fig. 5, fig. 5 shows a networked surface vessel η according to an embodiment of the inventioni-hiTime evolution diagram; it can be seen that the formation tracking problem of the networked surface warship can be upsilon at predetermined timefThe system reaches an equilibrium state for the 6-point solution.
Referring to fig. 6, fig. 6 is a graph showing the evolution of the error of the networked surface vessel over time according to the embodiment of the present invention, wherein the graphs (a) - (c) show the error eηiThe graphs (d) to (f) show the error eviIt can be seen that the systematic error can converge to 0 within a predetermined time as time goes by.
In addition, the specific embodiment of the invention also provides a networked surface vessel tracking control device, which comprises the following modules:
the model building module is used for carrying out dynamic and kinematic modeling on the N surface vessels to obtain dynamic and kinematic models, setting a virtual leader from the N surface vessels, and setting the rest as followers;
the directed graph building module is used for building a directed topological graph among the surface ships;
the algorithm design module is used for designing a sliding mode surface and a control algorithm under a layered control frame according to the dynamics and kinematics model and the directed topological graph, and the control algorithm comprises a control algorithm of a distributed estimation layer and a control algorithm of a local control layer;
the tracking control module is used for estimating the state of the virtual leader according to a control algorithm of the distributed estimation layer, and the followers reach a formation form in the distributed estimation layer to realize formation control; and driving each surface vessel to track the virtual leader within a predefined time according to a control algorithm of the local control layer.
In addition, the specific embodiment of the present invention further provides a networked surface vessel tracking control device, where the networked surface vessel tracking control device includes a memory, a processor, and a networked surface vessel tracking control program stored in the memory and operable on the processor, and the networked surface vessel tracking control program is executed by the processor to implement the steps of the networked surface vessel tracking method.
In addition, the specific embodiment of the invention also provides a storage medium, wherein the storage medium is stored with a networked surface vessel tracking control program, and the networked surface vessel tracking control program is executed by a processor to realize the steps of the networked surface vessel tracking control method.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (8)

1. A networked surface vessel tracking control method is characterized by comprising the following steps:
performing dynamics and kinematics modeling on N surface vessels to obtain dynamics and kinematics models, setting a virtual leader from the N surface vessels, and setting the rest as followers;
the expression of the dynamics and kinematics model is:
Figure FDA0003608041380000011
wherein i e {1,2, …, N } represents the surface vesselThe serial number of the serial number,
Figure FDA0003608041380000012
indicating the location of the earth's fixed point (X)i,Yi) (viii), (Ψ)i) Is the angle of the course of the vehicle,
Figure FDA0003608041380000013
represents a set of real numbers and is,
Figure FDA0003608041380000014
representing an n-dimensional euclidean space;
Figure FDA0003608041380000015
representing a velocity vector (v) of the objectxi,υyi) (ω) of (c)i) Is the angular velocity;
Figure FDA0003608041380000016
representing the velocity/angular velocity vector in earth fixed coordinates;
Figure FDA0003608041380000017
is a control input;
Figure FDA0003608041380000018
is a perturbation vector in which, among other things,
Figure FDA0003608041380000019
Mi，Ci(υi) And Di(υi) Respectively an inertia matrix, a Coriolis and centripetal matrix and a hydrodynamic damping matrix;
Figure FDA00036080413800000110
is a transformation matrix;
the expression of the reference track of the virtual leader in the earth fixed coordinate is as follows:
Figure FDA00036080413800000111
wherein,
Figure FDA00036080413800000112
respectively the position/attitude vector, the velocity/angle vector and the acceleration vector of the virtual leader in earth fixed coordinates;
establishing a directed topological graph among the surface ships;
designing a sliding mode surface and a control algorithm under a layered control frame according to the dynamics and kinematics model and the directed topological graph, wherein the control algorithm comprises the following steps: a control algorithm of a distributed estimation layer and a control algorithm of a local control layer;
the slip form face under the layered control frame comprises: the sliding mode surface of the distributed estimation layer and the sliding mode surface under the local control layer are respectively as follows:
Figure FDA0003608041380000021
Figure FDA0003608041380000022
wherein,
Figure FDA0003608041380000023
for the sliding-mode faces of the distributed estimation layer,
Figure FDA0003608041380000024
for the sliding surface of the local control layer, first the definition
Figure FDA0003608041380000025
Is Xi,Yi,Ψi,θXi,θYi,ωiIs determined by the estimated value of (c),
Figure FDA0003608041380000026
Figure FDA0003608041380000027
are respectively
Figure FDA0003608041380000028
An estimated value of (d); then define
Figure FDA0003608041380000029
Figure FDA00036080413800000210
Figure FDA00036080413800000211
hiRepresenting formation offset, γs1,Υs2Respectively, the pre-defined times of the distributed estimation layer and the local control layer, and ys1＞0,Υs2＞0；γ1，γ2Is a normal number, and 0 < gamma1＜1，0＜γ2＜1；
Figure FDA00036080413800000212
A value representing Hadamard's theorem if x ═ x1,x2,…xn]T，y＝[y1,y2,…yn]TThen, then
Figure FDA00036080413800000213
sig(x)mIs defined as sig (x)m＝[sgn(x1)|x1|m,sgn(x2)|x2|m,…,sgn(xn)|xn|m]TWhere | x | ═ x [ | x |)1|,|x2|,…,|xn|]TSgn (x) is a sign function, m is a normal number;
estimating the state of the virtual leader according to a control algorithm of the distributed estimation layer, wherein a follower reaches a formation form in the distributed estimation layer to realize formation control; and driving each surface vessel to track to the virtual leader within a predefined time according to a control algorithm of the local control layer.
2. The networked surface vessel tracking control method according to claim 1, wherein the directed topology graph is G ═ { ν, epsilon, a }, where ν { (1, 2,. N }, epsilon { (i, j) | i, j ∈ i ≠ j }, e ν × ν, a ≠ and b ≠ j }, where v ═ v, and b ═ N { (i, j) | i, and j ≠ j }
Figure FDA00036080413800000214
Respectively representing a surface ship set consisting of N surface ships, a set of edges and a weight adjacency matrix, wherein aijRepresenting the weight between the surface vessel i and the surface vessel j; the edge (i, j) belongs to epsilon and indicates that the jth surface vessel is a neighbor of the ith surface vessel; the ith surface vessel can directly receive information from the jth surface vessel, then aij> 0, otherwise aij＝0；
NiThe method comprises the following steps that (j belongs to nu (i, j) belongs to epsilon) and is defined as a neighbor set of the ith surface vessel; determining a Laplace matrix L of the directed topological graph according to the weighted adjacency matrix A, wherein the Laplace matrix L is defined as
Figure FDA00036080413800000215
lijFor elements in the matrix L, when i ≠ j ∈ v, Lij＝-aij(ii) a When i ∈ v,
Figure FDA0003608041380000031
j is NiA node in (1);
Β＝diag{b1,b2,...,bNdenotes a diagonal weight matrix of the directed topology graph illustrating the interaction of the surface vessel with the virtual leader, where biN is an element in the B matrix, B if the ith surface vessel can directly receive information from the virtual leaderiIs greater than 0; otherwise, for
Figure FDA0003608041380000032
3. The networked surface vessel tracking control method according to claim 1, further comprising, after the step of modeling dynamics and kinematics of the N surface vessels to obtain dynamics and kinematics models:
defining the error function as:
Figure FDA0003608041380000033
wherein eηiAnd eυiRespectively, a position tracking error and a speed tracking error in earth fixed coordinates; eta0＝[X0,Y0,Ψ0]TAnd upsilon0＝[υx0,υy0,ω0]TRespectively representing the position and velocity states of the virtual leader; etai＝[Xi,Yi,Ψi]TAnd upsiloni＝[υxi,υyi,ωi]TRespectively representing the position and speed state of each follower; h isiRepresenting a formation offset;
according to the error function, the dynamics and kinematics model is converted into:
Figure FDA0003608041380000034
wherein Qi(ηi,υi)＝-Ci(υi)υi-Di(υi)υi，
Figure FDA0003608041380000035
Is the transformation matrix of the virtual leader.
4. The networked surface vessel tracking control method of claim 1, wherein the control algorithm of the distributed estimation layer is:
Figure FDA0003608041380000041
wherein 0 < xi1< 1 is a normal number, γc1> 0 is the predefined time of the distributed estimation layer in the algorithm.
5. The networked surface vessel tracking control method of claim 1, wherein the control algorithm of the local control layer is:
Figure FDA0003608041380000042
ρeq,idenotes the equivalent control term, ps,iRepresenting a sliding mode cancellation term; 1nRepresenting an n-dimensional vector with all elements 1, 13A 3-dimensional vector representing all elements as 1; degree is a value according to Hadamard's theorem if x is ═ x1,x2,…xn]T，y＝[y1,y2,…yn]TThen x omicron y ═ x1y1,x2y2,…xnyn]T；sig(x)mIs defined as sig (x)m＝[sgn(x1)|x1|m,sgn(x2)|x2|m,…,sgn(xn)|xn|m]TWhere | x | ═ x [ | x |)1|,|x2|,…,|xn|]TSgn (x) is a sign function, m is a normal number;
Figure FDA0003608041380000043
Figure FDA0003608041380000051
Qi(ηi,υi)＝-Ci(υi)υi-Di(υi)υi，0＜ξ2< 1 is a normal number, γc2The more than 0 is the predefined time of a local control layer in the algorithm;
Figure FDA0003608041380000052
is a diagonal positive definite gain matrix.
6. A networked surface vessel tracking control device is characterized by comprising the following modules:
the model building module is used for carrying out dynamic and kinematic modeling on the N surface vessels to obtain dynamic and kinematic models, setting a virtual leader from the N surface vessels, and setting the rest as followers;
the expression of the dynamics and kinematics model is:
Figure FDA0003608041380000053
wherein i belongs to {1, 2.., N } represents the serial number of the surface warship,
Figure FDA0003608041380000054
indicating the location of the earth's fixed point (X)i,Yi) (viii), (Ψ)i) Is the angle of the course direction and is,
Figure FDA0003608041380000055
represents a set of real numbers and is,
Figure FDA0003608041380000056
representing an n-dimensional euclidean space;
Figure FDA0003608041380000057
indicating the speed of an objectDegree vector ([ nu ])xi,υyi) (ω) of (C)i) Is the angular velocity;
Figure FDA0003608041380000058
representing the velocity/angular velocity vector in earth fixed coordinates;
Figure FDA0003608041380000059
is a control input;
Figure FDA00036080413800000510
is a perturbation vector in which, among other things,
Figure FDA00036080413800000511
Mi，Ci(υi) And Di(υi) Respectively an inertia matrix, a Coriolis and centripetal matrix and a hydrodynamic damping matrix;
Figure FDA00036080413800000512
is a transformation matrix;
the expression of the reference trajectory of the virtual leader in the earth fixed coordinates is as follows:
Figure FDA00036080413800000513
wherein,
Figure FDA00036080413800000514
respectively the position/attitude vector, the velocity/angle vector and the acceleration vector of the virtual leader in earth fixed coordinates;
the directed graph building module is used for building a directed topological graph among the surface ships;
the algorithm design module is used for designing a sliding mode surface and a control algorithm under a layered control frame according to the dynamics and kinematics model and the directed topological graph, and the control algorithm comprises a control algorithm of a distributed estimation layer and a control algorithm of a local control layer;
the slip form face under the layered control frame comprises: the sliding mode surface of the distributed estimation layer and the sliding mode surface under the local control layer are respectively as follows:
Figure FDA0003608041380000061
Figure FDA0003608041380000062
wherein,
Figure FDA0003608041380000063
for the sliding-mode faces of the distributed estimation layer,
Figure FDA0003608041380000064
for the sliding surface of the local control layer, first the definition
Figure FDA0003608041380000065
Is Xi,Yi,Ψi,θXi,θYi,ωiIs determined by the estimated value of (c),
Figure FDA0003608041380000066
Figure FDA0003608041380000067
are respectively
Figure FDA0003608041380000068
An estimated value of (d); then define
Figure FDA0003608041380000069
Figure FDA00036080413800000610
Figure FDA00036080413800000611
hiRepresenting formation offset, γs1,Υs2Predefined time, and y, of the distributed estimation layer and the local control layer, respectivelys1＞0,Υs2＞0；γ1，γ2Is a normal number, and 0 < gamma1＜1，0＜γ2＜1；
Figure FDA00036080413800000612
A value representing Hadamard's theorem if x ═ x1,x2,…xn]T，y＝[y1,y2,…yn]TThen, then
Figure FDA00036080413800000613
sig(x)mIs defined as sig (x)m＝[sgn(x1)|x1|m,sgn(x2)|x2|m,…,sgn(xn)|xn|m]TWhere | x | ═ x [ | x |)1|,|x2|,…,|xn|]TSgn (x) is a sign function, m is a normal number;
the tracking control module is used for estimating the state of the virtual leader according to a control algorithm of the distributed estimation layer, and the followers reach a formation form in the distributed estimation layer to realize formation control; and driving each surface vessel to track to the virtual leader within a predefined time according to a control algorithm of the local control layer.
7. A networked surface vessel tracking control device, characterized in that the networked surface vessel tracking control device comprises a memory, a processor and a networked surface vessel tracking control program stored on the memory and operable on the processor, which when executed by the processor implements the steps of the networked surface vessel tracking method according to any one of claims 1 to 5.
8. A storage medium having stored thereon a networked surface vessel tracking control program which, when executed by a processor, performs the steps of the networked surface vessel tracking control method of any one of claims 1 to 5.
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