CN115390564A - Formation control method, medium and equipment for under-actuated unmanned surface vessel - Google Patents
Formation control method, medium and equipment for under-actuated unmanned surface vessel Download PDFInfo
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Abstract
The application relates to the technical field of ships, in particular to a formation control method, medium and equipment for an under-actuated unmanned ship on the water surface. The formation control method disclosed by the application integrates a self-adaptive control law, a dynamic surface control technology, a neural network technology, a high-gain observer and a minimum parameter learning algorithm, only depends on the sight distance, sight angle, position and bow and roll angle information of a following ship, and a formation controller only needs to adjust two learning parameters on line, so that the preset formation layout relative to a pilot ship can be realized. The conditions that the speed information of the under-actuated pilot ship and the speed information of the following ship are unknown, the uncertainty of the model and the unknown external disturbance are considered, the fault tolerance of the multi-ship formation system for inhibiting the uncertain model and the external disturbance is enhanced, and the robustness of the unmanned ship formation system is enhanced by reducing the calculated amount.
Description
Technical Field
The application relates to the technical field of ships, in particular to a formation control method, medium and equipment for an under-actuated unmanned ship on the water surface.
Background
The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
In recent years, with the rapid development of unmanned technology in the field of intelligent ships, unmanned ships on water surface are more and more widely applied. Unmanned ships on water have become important tools for various kinds of work such as water rescue, environmental monitoring, pollution cleaning, scientific research and the like in inland rivers and near and far seas. Compared with single unmanned ship water surface operation, a plurality of unmanned ships can effectively improve the operation efficiency and the fault tolerance of the system by forming a dynamic cooperative operation network in the sailing process.
Different from the existing formation of the first-order, second-order and general linear system individuals, the unmanned ship is inevitably subjected to environmental disturbance such as wind, wave, flow and the like under the actual working environment, and has the characteristics of nonlinearity, strong coupling and uncertain model. On one hand, external disturbance can affect a dynamic model of the unmanned ship and bring uncertain dynamics, and at the moment, if the model-based unmanned ship formation control method is adopted, the formation control performance is reduced due to model mismatch; on the other hand, the original control action is interfered, and the formation tracking precision of the unmanned ship cluster is influenced. The existing formation method needs to be further improved in the aspects of processing uncertain dynamics and external disturbance of unmanned ships, a more effective formation controller needs to be designed, and the formation controller can meet formation constraint and has fault tolerance in the formation process of the unmanned ships, so that robustness can be guaranteed, and calculated amount can be reduced. The actual control input of the under-actuated unmanned ship on the water surface is less than the system degree of freedom, so that the control problem faces more complex challenges, and meanwhile, the high nonlinearity and the strong coupling property exist in a dynamic model, so that the design of a controller is more complex, and a simple control method cannot be directly applied. In summary, uncertain dynamics of each ship, external disturbance and various formation constraints bring great challenges to the development of unmanned ship formation control methods.
The current mature formation control methods include the following methods: the method is based on a virtual structure method, a behavior method, a following navigator method, an artificial potential field method, a path following method, an information consistency method and the like. The following pilot method is a common formation control method. In the leader structure formation, one or more individuals are selected as pilots, the rest individuals are set as followers, and the followers are driven to track the positions and the directions of the pilots with preset offsets. Although formation control based on the leading structure has the advantages of simple structure, easiness in implementation and the like, because the whole formation is built by a plurality of leading dual-autonomous systems, the failure or fault of a pilot in each leading dual-autonomous system can affect the whole formation, and meanwhile, formation errors can be continuously accumulated along with the gradual superposition of the leading dual-autonomous systems, so that the fault tolerance is poor.
Disclosure of Invention
The embodiment of the application aims to provide a formation control method for an under-actuated unmanned water surface ship, under the conditions that speed information of an under-actuated pilot ship and a following ship is unknown, and an uncertain model and unknown external disturbance exist, a control law is designed for the following ship, so that a preset formation layout relative to a leader ship can be realized for the following ship, and the fault tolerance of a multi-ship formation system for inhibiting the uncertain model and the external disturbance is enhanced.
It is still another object of an embodiment of the present application to provide a computer storage medium implementing the above-described formation control method for an under-actuated surface unmanned ship.
It is still another object of an embodiment of the present application to provide a computer apparatus for implementing the above formation control method for an under-actuated surface unmanned ship.
In a first aspect, a formation control method for an under-actuated surface unmanned ship is provided, which is characterized by comprising the following steps:
1) Designing a following ship kinematics virtual control law based on an improved self-adaptive control law to stabilize a sight distance and a sight angle tracking error so as to construct a following ship advancing direction virtual control law;
2) Stabilizing the yaw angle tracking error of the following ship by utilizing the following ship kinematics virtual control law and the following ship advancing direction virtual control law in the step 1) and adopting a dynamic surface control technology, and further constructing a following ship yaw direction virtual control law;
3) Constructing a high-gain observer to estimate the speed of the following ship;
4) Stabilizing the forward speed error u under the condition of an uncertain model of a following ship and external disturbance e And yaw rate error r e And combining the high-gain observer, the following ship advancing direction virtual control law and the following ship bow rolling direction virtual control law, and constructing a self-adaptive output feedback formation control law for the following ship based on an RBF neural network and a minimum parameter learning algorithm.
In one possible implementation, step 1) includes the step of constructing a mathematical model of the unmanned ship:
the degree of freedom motion of the ship adopts a geodetic coordinate system and a ship body coordinate system, and the kinematics equation of each unmanned ship is as follows:
wherein eta = [ x, y, ψ ]] T The position vector of the unmanned ship in a geodetic coordinate system is indicated, (x, y) the position of the unmanned ship, psi the yawing angle of the unmanned ship, and v = [ u, v, r ]] T The velocity vector of the unmanned ship under a ship body coordinate system is indicated, u, v and R respectively indicate the advancing speed, the transverse drift speed and the heading angle speed of the unmanned ship, R (psi) indicates a rotation matrix related to the heading angle of the unmanned ship, and the rotation matrix is as follows:
the kinetic equation for each unmanned vessel is:
wherein the content of the first and second substances,
d wu 、d wv 、d wr respectively representing the forces or moments m of external disturbance acting on three channels of advancing, rolling and yawing of the unmanned ship u 、m v 、m r Is the inertial force coefficient in the unmanned ship model, c 13 、c 23 、c 31 、c 32 Is the centripetal and Coriolis force coefficient in the unmanned ship model, d 11 、 d 22 、d 23 、d 32 、d 33 Is the hydrodynamic damping coefficient, g, in the unmanned ship model u 、g v 、g r Representing unmodeled dynamics of unmanned vessels,. Tau u 、τ r Denotes the actuator input of the unmanned ship, wherein u Thrust in the forward direction of the unmanned ship, τ r The moment in the direction of the bow angular velocity of the unmanned ship; because the unmanned ship is under-actuated, no actuator is input in the transverse drift direction of the unmanned ship model;
defining the apparent distance rho of a following ship to a leading ship L And the viewing angle lambda L (ii) a Setting the position vectors of the leading ship and the following ship as eta respectively L And η, their velocity vectors are respectively denoted as v L V, apparent distance ρ L And line of sight angle λ L Are respectively defined as:
and
wherein, tan -1 Is the inverse of the tangent functionThe function, the desired apparent distance and the angle of sight respectively, of the following ship is rho Ld And λ Ld (ii) a The formation tracking error is defined as ρ Le ＝ρ L -ρ Ld ，λ Le ＝λ L -λ Ld Where ρ is Le To follow the line-of-sight error of the ship, λ Le To follow the line-of-sight angle error of the ship.
In a possible implementation, in step 1), the adaptive control law uses the position and the yaw angle of the pilot ship so that the apparent distance ρ of the following ship to the pilot ship L And the viewing angle lambda L Tracking a desired p Ld And λ Ld Firstly, calculating a relative kinematic equation between a pilot ship and a following ship, and according to a sight distance error rho of the following ship Le And line-of-sight angle error λ Le Designing a following ship kinematics virtual control law:
and
wherein k is ρ And k λ Is a control gain, e 1 And e 2 Is a normal number, and p is a normal number.
In a possible implementation scheme, in step 1), the adaptive control law is
The virtual control law of the advancing direction of the following ship is based on the relative kinematics between the pilot ship and the following ship and the sight distance error rho of the following ship Le And line-of-sight angle error lambda following the ship Le The relative kinematic equation between the leading vessel and the following vessel is:
wherein Δ ρ ＝u L cos(ψ L -λ L )-v L sin(ψ L -λ L )+v sin(ψ-λ L )，Δ λ ＝ u L sin(ψ L -λ L )+v L cos(ψ L -λ L )-v cos(ψ-λ L )，Δ ρ And Δ λ Having a common upper bound p 0 Namely: delta of ρ ≤p 0 ,Δ λ ≤p 0 ,p 0 ＝|u L |+|v L I + v i, assuming that the speed of the drift of the unmanned ship is passive and bounded and the speed of the lead ship is bounded, there is a normal number p, such that p 0 ≤p；
Apparent distance error rho following ship Le And line-of-sight angle error λ Le The derivative of (c) is:
wherein w ρ ＝u cos(ψ-λ L )，w λ ＝u sin(ψ-λ L )，
Designing the following ship kinematics virtual control law according to a relative kinematics equation and an error derivative equation:
in one possible implementation, the control law for the virtual kinematics in step 1)
And
is processed to make
Wherein alpha is u And alpha ψ Virtual control laws for u and ψ, respectively:
α u and alpha ψ Namely the following ship advancing direction virtual control law.
In a possible implementation scheme, in the step 2), the following ship advancing direction is made to virtually control the law alpha u And alpha ψ Respectively through two time constants of T u And T ψ Of the first order filter of, generating a signal beta u And beta ψ Then the following relationship exists:
β u (0)＝α u (0)
β ψ (0)＝α ψ (0)
then define the error u e ,z u ,ψ e ,z ψ The following relationship is satisfied: u. of e ＝u-β u ,z u ＝β u -α u ，ψ e ＝ ψ-β ψ ,z ψ ＝β ψ -α ψ ；
For psi e And (5) obtaining a derivative:
design of virtual control law alpha following bow rolling direction r ：
Wherein k is ψ Is the control gain.
In a possible implementation scheme, in the step 3), the following ship heading direction in the step 2) is made to be a virtual control law alpha r With a transit time constant of T r To obtain beta r Namely:
β r (0)＝α r (0)
definition error r e And z r Satisfy r e ＝r-β r ,z r ＝β r -α r ；
The following linear system was used:
wherein pi 1 ∈R 3 And pi 2 ∈R 3 Is a state vector, δ is a normal number, λ 1 >0; estimation of η can be obtained
According to the kinematics equation of the unmanned ship, the following equations are provided:
since | | | R T (·) | =1, resulting in a high-gain observer:
wherein B is v Is a normal number.
In a possible implementation scheme, in step 4), the RBF neural network has the following theorem:
for the Gaussian base function, if
Wherein constant beta>0 and
is a bounded variable, then:
wherein G is t Is a bounded function vector;
according to the high gain observer in step 3)
Comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other,
is a bounded function vector, the kinetic equation f of the unmanned ship i +d wi /m i Expressed as:
wherein
And
is defined as:
designing advancing thrust tau of under-actuated following ship u And steering torque tau r Control law of i|i＝u,r Satisfies the following conditions:
the corresponding adaptive law based on minimum parameter learning is as follows:
wherein
b i 、Γ i And delta i Are all positive control parameters that are to be controlled,
is that
Is selected to be close to λ i True value of (c).
In a possible implementation scheme, formation control is realized by adopting the visual distance and the visual angle information of the following ship, and the visual distance and the visual angle information are directly acquired by equipping a navigation radar on the following ship.
In a second aspect, there is also provided a computer storage medium storing a computer program which, when executed by a processor, implements the formation control method for an under-actuated surface unmanned vessel as set forth in any one of the possible embodiments of the first aspect.
In a third aspect, there is also provided a computer device, including:
a memory storing a computer program that when executed by the processor implements the formation control method for an under-actuated surface unmanned vessel as set forth in any one of the possible embodiments of the first aspect.
The application has the following beneficial effects: the formation control method integrates a self-adaptive control law, a dynamic surface control technology, a neural network technology, a high-gain observer and a minimum parameter learning algorithm, only depends on the sight distance, sight angle, position and bow angle information of a following ship, and a formation controller only needs to adjust two learning parameters tau on line u And τ r Thus, a pre-set formation layout relative to the pilot vessel can be achieved. The conditions that the speed information of the under-actuated pilot ship and the speed information of the following ship are unknown, and the uncertainty of the model and the unknown external disturbance are considered, so that the fault tolerance of the multi-ship formation system for inhibiting the uncertainty model and the external disturbance is enhanced, and the robustness of the unmanned ship formation system is enhanced by reducing the calculated amount.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that for a person skilled in the art, other related drawings can be obtained from these drawings without inventive effort.
Fig. 1 is a schematic diagram of a formation structure according to an embodiment of the present application;
fig. 2 is a schematic frame diagram of a formation control scheme according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without making any creative effort belong to the protection scope of the present application.
In the description of the present application, it is to be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present application can be understood by those of ordinary skill in the art according to the specific circumstances.
According to a first aspect of the present application, there is first provided a formation control method for an under-actuated surface unmanned ship. The aim of the application is: under the conditions that speed information of an under-actuated pilot ship and speed information of a following ship are unknown, uncertain models and unknown external disturbance exist, a control law tau is designed for the following ship u And τ r So that the following ship can realize a preset formation layout (rho) relative to the leading ship Ld ,λ Ld )。
The method comprises the following steps of firstly, carrying out mathematical models of the unmanned ship, including a kinematic model and a dynamic model. When studying 6-degree-of-freedom motions of a ship, two coordinate systems are often adopted, one is a geodetic coordinate system and the other is a hull coordinate system.
The kinematic equation for each unmanned vessel is:
wherein eta = [ x, y, ψ ]] T The position vector of the unmanned ship in a geodetic coordinate system is indicated, (x, y) the position of the unmanned ship, psi the yawing angle of the unmanned ship, and v = [ u, v, r ]] T The speed vector of the unmanned ship under a ship body coordinate system is indicated, u, v and R respectively indicate the advancing speed, the transverse drift speed and the heading angle speed of the unmanned ship, R (psi) indicates a rotation matrix related to the heading angle of the unmanned ship, and the speed vector comprises the following components:
the nonlinear dynamical equation of the horizontal plane of each unmanned ship is as follows:
wherein M is j Is a matrix of inertia coefficients, C j Is a matrix of Coriolis and centripetal forces, D j Are damping coefficient matrices, which are respectively defined as:
the kinetic equation for each unmanned vessel is:
wherein the content of the first and second substances,
d wu ,、d wv ,、d wr respectively representing the force or moment of external disturbance (such as wind, wave, flow and the like) acting on three channels of advancing, rolling and yawing of the unmanned ship, m u 、 m v 、m r Is the coefficient of inertia force in the unmanned ship model, c 13 、c 23 、c 31 、c 32 Is the centripetal and Coriolis force coefficient in the unmanned ship model, d 11 、d 22 、d 23 、d 32 、d 33 Is the hydrodynamic damping coefficient, g, in the unmanned ship model u 、g v 、g r Representing unmodeled dynamics of unmanned vessels,. Tau u 、τ r Denotes the actuator input of the unmanned ship, wherein u Thrust in the advancing direction of the unmanned ship, tau r The moment in the direction of the bow angular velocity of the unmanned ship. Because the unmanned ship is under-actuated, no actuator input exists in the transverse drift direction of the unmanned ship model.
Further, taking the case of a pilot ship and a follower ship as an example, the position vectors of the pilot ship and the follower ship are η L And η, their velocity vectors are respectively denoted as v L And v. Apparent distance rho of following ship to piloted ship L And line of sight angle λ L Are respectively defined as
And
wherein, tan -1 Is the inverse function of the tangent function, and the apparent distance and the apparent line angle which are expected to follow the ship are respectively rho Ld And λ Ld . The platooning tracking error may be defined as ρ Le ＝ρ L -ρ Ld ，λ Le ＝λ L -λ Ld Where ρ is Le To follow the line of sight error of the ship, λ Le To follow the line angle error of the ship, as shown in fig. 1.
The schematic diagram of the formation control method of the application is shown in FIG. 2, and the specific steps are given as follows:
1) Based on an improved self-adaptive control law, a following ship kinematics virtual control law is designed to stabilize a visual distance and a visual angle tracking error, so that a following ship advancing direction virtual control law is constructed.
Firstly, according to the kinematic equation and apparent distance rho of the unmanned ship L Angle of sight λ L And defining the formation tracking error, and deducing a relative kinematic equation between the pilot ship and the following ship:
wherein Δ ρ ＝u L cos(ψ L -λ L )-v L sin(ψ L -λ L )+v sin(ψ-λ L )，Δ λ ＝ u L sin(ψ L -λ L )+v L cos(ψ L -λ L )-v cos(ψ-λ L )。Δ ρ And Δ λ Having a common upper bound p 0 Namely: delta ρ ≤p 0 ,Δ λ ≤p 0 ,p 0 ＝|u L |+|v L L + | v |. Assuming that the speed of the drift of the unmanned ship is passive and bounded and the forward speed of the lead ship is bounded, there is a normal number p, such that p 0 ≤p。
Second, apparent distance error ρ for following ship Le And line-of-sight angle error λ Le The derivation is as follows:
wherein w ρ ＝u cos(ψ-λ L )，w λ ＝u sin(ψ-λ L )。
Next, a virtual control law following the ship kinematics is designed according to the relative kinematics equation and the error derivation equation as follows:
wherein k is ρ And k λ Is a control gain, e 1 And e 2 Is a normal number, the modified adaptive control law is
k p Is a control gain. The self-adaptive control law can still ensure formation tracking under the condition of speed loss of a pilot ship and a following ship, and only one self-adaptive parameter needs to be updated, so that the parameter adjusting process is simplified, and the engineering practicability is improved.
Control law for virtual kinematics
And
is processed to make
Wherein alpha is u And alpha ψ Virtual control laws for u and ψ, respectively:
α u and alpha ψ Namely the following ship advancing direction virtual control law.
And 2) stabilizing the bow roll angle tracking error of the following ship by adopting a dynamic surface control technology, and further constructing a virtual control law of the bow roll direction of the following ship.
Law of virtual control of advancing direction of following ship u And alpha ψ Respectively by two time constants of T u And T ψ Of the first order filter, generating a signal beta u And beta ψ Then the following relationship exists:
β u (0)＝α u (0)
β ψ (0)＝α ψ (0)
then define the error u e ,z u ,ψ e ,z ψ The following relationship is satisfied: u. of e ＝u-β u ,z u ＝β u -α u ，ψ e ＝ ψ-β ψ ,z ψ ＝β ψ -α ψ 。
For psi e And (5) obtaining a derivative:
virtual control law alpha designed to follow ship bow rolling direction r ：
Wherein k is ψ Is the control gain.
And step 3): a high gain observer is constructed to estimate the velocity of the following vessel. The high-gain observer is used for designing a self-adaptive output feedback formation control law for the following ship by combining a virtual control law, a neural network approximation technology and a minimum parameter learning algorithm.
Firstly, the virtual control law alpha of the bow rolling direction of the following ship in the step 2) r With a transit time constant of T r To a first order filter of to obtain beta r Namely:
β r (0)＝α r (0)
defining an error r e And z r Satisfy r e ＝r-β r ,z r ＝β r -α r 。
Secondly, the high-gain observer can be used for estimating the speed information of the unmanned ship under the conditions that the unmanned ship has uncertain dynamics and is disturbed by the outside, and the high-gain observer is very useful in the scene that formation is realized only by the position and the heading angle information of the unmanned ship. To construct an efficient high gain amplifier, we consider the following linear system:
wherein pi 1 And pi 2 ∈R 3 Is a state vector, δ is a normal number, λ 1 >0. Estimation of η can be obtained
According to the kinematics equation of the unmanned ship, the following equations are provided:
further, there are:
since | | | R T (·) | =1, further we can get a high gain observer:
wherein B is v Is a normal number.
Step 4) stabilizing the forward speed error u under the conditions of uncertain model of the following ship and external disturbance e And yaw rate error r e And constructing a self-adaptive output feedback formation control law based on the RBF neural network and a minimum parameter learning algorithm.
For the RBF neural network, the following theorem holds:
for the Gaussian base function, if
Wherein constant beta>0 and
is a bounded variable, then:
wherein G is t Is a bounded function vector.
According to the high gain observer in step 3)
Comprises the following steps:
wherein the content of the first and second substances,
is a bounded function vector, the kinetic equation f of the unmanned ship i +d wi /m i Can be expressed as:
wherein
And
is defined as follows:
designing advancing thrust tau of under-actuated following ship u And steering torque tau r Control law of i|i = u, r satisfying:
the corresponding adaptive law based on minimum parameter learning is as follows:
wherein
b i 、Γ i And delta i Are all positive control parameters that are to be controlled,
is that
Is usually chosen close to lambda i True value of (1).
In the embodiment, the formation control is realized by adopting the sight distance and sight angle information of the following ship, the sight distance and sight angle information are directly acquired by equipping a navigation radar on the following ship, the following ship does not adopt bow roll angle information of a pilot ship in the scheme, communication is not needed between the following ship and the pilot ship in the whole formation process, the communication cost is greatly saved, and the realization mode is convenient.
Aiming at the problems of maintaining and controlling translational motion of the formation of the under-actuated unmanned ship following structure in the presence of model uncertainty and external environment disturbance, the self-adaptive output feedback formation control method for the under-actuated unmanned ship on the water surface provided by the application has the following characteristics compared with the existing formation control method of the following structure:
the formation control method integrates an adaptive control law, a dynamic surface control technology, a neural network technology, a high gain observer and a minimum parameter learning algorithm.
The formation control method only depends on the sight distance, sight line angle, position and bow and roll angle information of the following ship, and the formation controller in the scheme only needs to adjust two learning parameters tau on line u And τ r Thus, a preset formation layout relative to the pilot ship can be realized。
The formation control method considers the conditions that the speed information of the under-actuated pilot ship and the following ship is unknown, the uncertainty of the model and the unknown external disturbance (wind, wave, current and the like) are unknown, the fault tolerance of the multi-ship formation system for restraining the uncertainty model and the external disturbance is enhanced, and the robustness of the unmanned ship formation system is enhanced by reducing the calculated amount.
According to a second aspect of the present application, there is also provided a computer storage medium storing a computer program which, when executed by a processor, implements the formation control method for an under-actuated surface unmanned ship described in the embodiment of the first aspect.
Preferably, the storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic disk, U-disk, memory card, or optical disk.
According to a third aspect of the present application, there is also provided a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the program is executed by the processor to implement the formation control method for an under-actuated surface unmanned ship described in the embodiment of the first aspect.
The memory includes: various media that can store program codes, such as ROM, RAM, magnetic disk, U-disk, memory card, or optical disk. A processor is coupled to the memory for executing the computer programs stored by the memory.
Preferably, the Processor may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; the Integrated Circuit may also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic device, or discrete hardware component.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made to the present application by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (10)
1. The formation control method for the under-actuated unmanned surface vessel is characterized by comprising the following steps of:
1) Designing a following ship kinematics virtual control law based on an improved self-adaptive control law to stabilize a sight distance and a sight angle tracking error so as to construct a following ship advancing direction virtual control law;
2) Stabilizing the yaw angle tracking error of the following ship by utilizing the following ship kinematics virtual control law and the following ship advancing direction virtual control law in the step 1) and adopting a dynamic surface control technology, and further constructing a following ship yaw direction virtual control law;
3) Constructing a high-gain observer to estimate the speed of the following vessel;
4) Stabilizing the forward speed error u under the condition of an uncertain model of a following ship and external disturbance e And yaw rate error r e And combining the high-gain observer, the following ship advancing direction virtual control law and the following ship bow rolling direction virtual control law, and constructing a self-adaptive output feedback formation control law for the following ship based on an RBF neural network and a minimum parameter learning algorithm.
2. The formation control method for the under-actuated surface unmanned ship according to claim 1, wherein the step 1) comprises a step of constructing a mathematical model of the unmanned ship:
the freedom degree motion of the ship adopts a geodetic coordinate system and a ship body coordinate system, and the kinematic equation of each unmanned ship is as follows:
wherein eta = [ x, y, ψ ]] T The position vector of the unmanned ship in a geodetic coordinate system is indicated, (x, y) the position of the unmanned ship, psi the yaw angle of the unmanned ship, and v = [ u, v, r ]] T Refers to the unmanned ship sitting on the hullThe velocity vector under the mark system, u, v and R respectively refer to the advancing speed, the drift speed and the heading angle speed of the unmanned ship, R (psi) refers to a rotation matrix related to the heading angle of the unmanned ship, and the rotation matrix is as follows:
the kinetic equation for each unmanned vessel is:
wherein the content of the first and second substances,
d wu 、d wv 、d wr respectively represents the force or moment of external disturbance action on three channels of advancing, rolling and yawing of the unmanned ship, m u 、m v 、m r Is the inertial force coefficient in the unmanned ship model, c 13 、c 23 、c 31 、c 32 Is the centripetal and Coriolis force coefficient in the unmanned ship model, d 11 、d 22 、d 23 、d 32 、d 33 Is the hydrodynamic damping coefficient, g, in the unmanned ship model u 、g v 、g r Representing unmodeled dynamics of unmanned vessels,. Tau u 、τ r Representing unmanned vesselsAn actuator input of wherein u Thrust in the advancing direction of the unmanned ship, tau r The moment in the bow angular velocity direction of the unmanned ship; because the unmanned ship is under-actuated, no actuator is input in the transverse drift direction of the unmanned ship model;
defining the apparent distance rho of a following ship to a pilot ship L And the viewing angle lambda L (ii) a Setting the position vectors of the leading ship and the following ship as eta respectively L And η, their velocity vectors are respectively expressed as v L And v, then apparent distance ρ L And the viewing angle lambda L Are respectively defined as:
and
wherein, tan -1 Is the inverse function of the tangent function, and the apparent distance and the apparent line angle which are expected to follow the ship are respectively rho Ld And λ Ld (ii) a The formation tracking error is defined as ρ Le ＝ρ L -ρ Ld ，λ Le ＝λ L -λ Ld Where ρ is Le To follow the line of sight error of the ship, λ Le To follow the line angle error of the ship.
3. The formation control method for the under-actuated surface unmanned ship of claim 2, wherein in step 1), the adaptive control law utilizes the position and the yawing angle of the pilot ship so that the apparent distance ρ of the following ship to the pilot ship L And the viewing angle lambda L Tracking a desired p Ld And λ Ld Firstly, calculating a relative kinematic equation between a pilot ship and a following ship, and according to a sight distance error rho of the following ship Le And line-of-sight angle error λ Le Designing a following ship kinematics virtual control law:
and
wherein k is ρ And k λ Is a control gain, e 1 And e 2 Is a normal number, and p is a normal number.
4. The formation control method for the under-actuated surface unmanned ship according to claim 3, wherein in step 1), the adaptive control law is
The virtual control law of the advancing direction of the following ship is based on the relative kinematics between the pilot ship and the following ship and the sight distance error rho of the following ship Le And line-of-sight angle error lambda following the ship Le The relative kinematic equation between the leading vessel and the following vessel is:
wherein Δ ρ ＝u L cos(ψ L -λ L )-v L sin(ψ L -λ L )+v sin(ψ-λ L )，Δ λ ＝u L sin(ψ L -λ L )+v L cos(ψ L -λ L )-v cos(ψ-λ L )，Δ ρ And Δ λ Having a common upper bound p 0 Namely: delta of ρ ≤p 0 ,Δ λ ≤p 0 ,p 0 ＝|u L |+|v L I + v i, assuming that the speed of the drift of the unmanned vessel is passively bounded and the speed of the forward speed of the pilot vessel is bounded, there is a normal number p, such that p 0 ≤p；
Apparent distance error rho following ship Le And line-of-sight angle error λ Le The derivative of (c) is:
wherein w ρ ＝u cos(ψ-λ L )，w λ ＝u sin(ψ-λ L )，
Designing the following ship kinematics virtual control law according to a relative kinematics equation and an error derivative equation:
5. the formation control method for the under-actuated surface unmanned ship according to claim 4, wherein the virtual kinematics control law in the step 1) is applied
And
is processed to make
Wherein alpha is u And alpha ψ Virtual control laws for u and ψ, respectively:
α u and alpha ψ Namely the following ship advancing direction virtual control law.
6. The formation control method for the under-actuated surface unmanned ship according to claim 5, wherein in the step 2), the following ship advancing direction is controlled to be a virtual control law α u And alpha ψ Respectively by two time constants of T u And T ψ Of the first order filter of, generating a signal beta u And beta ψ Then the following relationship exists:
β u (0)＝α u (0)
β ψ (0)＝α ψ (0)
then define the error u e ,z u ,ψ e ,z ψ And satisfies the following relationship: u. u e ＝u-β u ,z u ＝β u -α u ，ψ e ＝ψ-β ψ ,β ψ ＝β ψ -α ψ ；
To psi e Obtaining a derivative:
design of virtual control law alpha following bow rolling direction r ：
Wherein k is ψ Is the control gain.
7. The unmanned ship for under-actuated water surface of claim 6The ship formation control method is characterized in that in the step 3), the virtual control law alpha following the ship bow rolling direction in the step 2) is controlled r With a transit time constant of T r To obtain beta r Namely:
β r (0)＝α r (0)
definition error r e And z r Satisfy r e ＝r-β r ,z r ＝β r -α r ；
The following linear system was used:
wherein pi 1 ∈R 3 And pi 2 ∈R 3 Is a state vector, δ is a normal number, λ 1 >0; estimation of η can be obtained
According to the kinematics equation of the unmanned ship, the following equations are provided:
since | | | R T (·) | =1, resulting in a high-gain observer:
wherein B is v Is a normal number.
8. The formation control method for the under-actuated surface unmanned ship according to claim 7, wherein in the step 4), the RBF neural network has the following theorem:
for the Gaussian base function, if
Wherein constant beta>0 and
is a bounded variable, then:
wherein G is t Is a bounded function vector;
according to the high gain observer in step 3)
Comprises the following steps:
wherein the content of the first and second substances,
is a bounded function vector, the kinetic equation f of the unmanned ship i +d wi /m i Expressed as:
wherein theta is i And
is defined as:
designing the forward thrust τ of an under-actuated following vessel u And steering torque tau r Control law of i|i＝u And r satisfies:
the corresponding adaptive law based on minimum parameter learning is as follows:
wherein
b i 、Γ i And delta i Are all positive control parameters that are to be controlled,
is that
Is selected to be close to λ i True value of (1).
9. A computer storage medium characterized by storing a computer program which, when executed by a processor, implements the formation control method for an under-actuated surface unmanned ship according to any one of claims 1 to 8.
10. A computer device, comprising:
a memory storing a computer program that when executed by the processor implements the formation control method for an under-actuated surface unmanned ship according to any one of claims 1 to 8, and a processor.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117170382A (en) * | 2023-10-11 | 2023-12-05 | 哈尔滨理工大学 | Double unmanned ship cooperative control method suitable for homodromous real-time point location tracking |
| CN117472060A (en) * | 2023-11-15 | 2024-01-30 | 大连海事大学 | Anti-collision dynamic event triggering formation control method for underactuated unmanned ship with preset performance |
| CN117472061A (en) * | 2023-11-15 | 2024-01-30 | 大连海事大学 | Unmanned ship formation control design method with limited time and stable preset performance |
| CN117472060B (en) * | 2023-11-15 | 2024-05-10 | 大连海事大学 | Anti-collision dynamic event triggering formation control method for underactuated unmanned ship with preset performance |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117170382A (en) * | 2023-10-11 | 2023-12-05 | 哈尔滨理工大学 | Double unmanned ship cooperative control method suitable for homodromous real-time point location tracking |
| CN117170382B (en) * | 2023-10-11 | 2024-04-26 | 哈尔滨理工大学 | Double unmanned ship cooperative control method suitable for homodromous real-time point location tracking |
| CN117472060A (en) * | 2023-11-15 | 2024-01-30 | 大连海事大学 | Anti-collision dynamic event triggering formation control method for underactuated unmanned ship with preset performance |
| CN117472061A (en) * | 2023-11-15 | 2024-01-30 | 大连海事大学 | Unmanned ship formation control design method with limited time and stable preset performance |
| CN117472060B (en) * | 2023-11-15 | 2024-05-10 | 大连海事大学 | Anti-collision dynamic event triggering formation control method for underactuated unmanned ship with preset performance |
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