Formation control method, medium and device for underactuated unmanned surface ships

Abstract

The present application relates to the field of ship technology, and more specifically, to a formation control method, medium and equipment for underactuated unmanned surface ships. The formation control method of the present application integrates adaptive control law, dynamic surface control technology, neural network technology, high-gain observer and minimum parameter learning algorithm, and only relies on the line of sight, line of sight angle, position and bow angle information of the following ship. The formation controller only needs to adjust two learning parameters online to achieve the preset formation layout relative to the pilot ship. Considering that the speed information of the underactuated pilot ship and the following ship is unknown, as well as the uncertainty of the model and unknown external disturbances, it not only enhances the fault tolerance of the multi-ship formation system to suppress uncertain models and external disturbances, but also enhances the robustness of the unmanned ship formation system by reducing the amount of calculation.

Description

Technical Field

[0001] The present application relates to the field of ship technology, and in particular to a formation control method, medium and equipment for under-actuated unmanned surface ships. Background Art

[0002] The descriptions in this section merely provide background information related to the present disclosure and may not constitute prior art.

[0003] In recent years, with the rapid development of unmanned technology in the field of intelligent ships, the application of surface unmanned ships has become more and more extensive. Surface unmanned ships have become an important tool for various tasks such as water rescue, environmental monitoring of inland rivers and near and far seas, pollution cleanup, scientific research, etc. Compared with the surface operation of a single unmanned ship, multiple unmanned ships can effectively improve the operation efficiency and system fault tolerance by forming a dynamic collaborative operation network during navigation.

[0004] Different from the existing first-order, second-order and general linear system formations, in actual working environments, unmanned ships will inevitably be subject to environmental disturbances such as wind, waves, and currents, and have the characteristics of "nonlinearity, strong coupling, and model uncertainty". On the one hand, external disturbances will affect the dynamic model of unmanned ships and bring about uncertain dynamics. At this time, if the model-based unmanned ship formation control method is adopted, the formation control performance will be reduced due to model mismatch; on the other hand, it will also interfere with the original control function and affect the formation tracking accuracy of the unmanned ship cluster. The existing formation methods need to be further improved in dealing with the uncertain dynamics and external disturbances of unmanned ships. It is necessary to design a more effective formation controller that can meet the formation constraints and have fault tolerance in the process of unmanned ship formation, ensure robustness, and reduce the amount of calculation. Because the actual control input of underactuated surface unmanned ships is less than the system's degrees of freedom, the control problem faces more complex challenges. At the same time, the high nonlinearity and strong coupling in the dynamic model make the controller design more complicated, and simple control methods cannot be directly applied. In summary, the uncertain dynamics of each ship, the external disturbances it is subject to, and various formation constraints pose great challenges to the development of unmanned ship formation control methods.

[0005] At present, there are several relatively mature formation control methods: based on virtual structure method, based on behavior method, based on following leader method, based on artificial potential field method, based on path following method and based on information consistency method. Among them, following leader method is a commonly used formation control method. In the leading-following structure formation, one or more individuals are selected as leaders, and the remaining individuals are set as followers, and the followers are driven to track the position and direction of the leader with a preset offset. Although the formation control based on the leading-following structure has the advantages of simple structure and easy implementation, since the entire formation is built by multiple leading-following dual-autonomous systems, the failure or failure of the leader in each leading-following dual-autonomous system will affect the entire formation. At the same time, the formation error will continue to accumulate with the step-by-step superposition of the leading-following dual-autonomous system, and the fault tolerance is poor. Summary of the invention

[0006] The purpose of the embodiments of the present application is to provide a formation control method for under-actuated unmanned surface ships. When the speed information of the under-actuated lead ship and the follower ship is unknown, and there are uncertain models and unknown external disturbances, a control law is designed for the follower ship so that the follower ship can achieve a preset formation layout relative to the lead ship, thereby enhancing the fault tolerance of the multi-ship formation system in suppressing uncertain models and external disturbances.

[0007] Another object of an embodiment of the present application is to provide a computer storage medium for implementing the above-mentioned formation control method for under-actuated unmanned surface vessels.

[0008] Another object of an embodiment of the present application is to provide a computer device for implementing the above-mentioned formation control method for under-actuated unmanned surface vessels.

[0009] In a first aspect, a formation control method for an underactuated unmanned surface vessel is provided, characterized in that it comprises the following steps:

[0010] 1) Based on the improved adaptive control law, a virtual control law of the following ship's kinematics is designed to stabilize the tracking errors of the sight range and sight angle, thereby constructing a virtual control law of the following ship's forward direction;

[0011] 2) Using the virtual control law of the kinematics of the following ship and the virtual control law of the following ship's forward direction in step 1), the dynamic surface control technology is adopted to stabilize the bow angle tracking error of the following ship, and then the virtual control law of the bow direction of the following ship is constructed;

[0012] 3) Build a high-gain observer to estimate the speed of the following ship;

[0013] 4) Stabilize the forward speed error u under the uncertain model of the following ship and under external disturbance e and the yaw angular velocity error r eCombining the high-gain observer, the virtual control law of the following ship's forward direction and the virtual control law of the following ship's bow pitch direction, an adaptive output feedback formation control law is constructed for the following ship based on the RBF neural network and the minimum parameter learning algorithm.

[0014] In one possible implementation, step 1) includes the step of constructing a mathematical model of the unmanned ship:

[0015] The ship's freedom of motion uses the earth coordinate system and the hull coordinate system. The kinematic equation of each unmanned ship is: where η = [x, y, ψ] T refers to the position vector of the unmanned ship in the geodetic coordinate system, (x, y) refers to the position of the unmanned ship, ψ refers to the bowing angle of the unmanned ship, v = [u, v, r] T It refers to the velocity vector of the unmanned ship in the hull coordinate system, u, v, and r refer to the forward speed, drift speed, and bow angular velocity of the unmanned ship respectively, and R(ψ) refers to the rotation matrix related to the bow angular velocity of the unmanned ship, which is:

[0016]

[0017] The dynamic equation of each unmanned ship is:

[0018]

[0019]

[0020]

[0021] in, d wu d wv d wr They represent the force or moment of external disturbance on the three channels of unmanned ship forward, side drift and bow pitch, m u 、m v 、m r is the inertia coefficient in the unmanned ship model, c 13 、c 23 、c 31 、c 32 are the centripetal force and Coriolis force coefficients in the unmanned ship model, d 11 , d 22 d 23 d 32 d 33 is the hydrodynamic damping coefficient in the unmanned ship model, g u , g v , g r represents the unmodeled dynamics of the unmanned ship, τu , τ r represents the actuator input of the unmanned ship, where τ u is the thrust of the unmanned ship in the forward direction, τ r is the torque in the direction of the unmanned ship’s bow angular velocity; since the unmanned ship is under-driven, there is no actuator input in the lateral drift direction of the unmanned ship model;

[0022] Define the sight distance ρ of the following ship to the pilot ship L and the sight angle λ L ; Assume that the position vectors of the pilot ship and the following ship are η L and η, their velocity vectors are denoted by ν L and ν, then the line of sight ρ L and the sight angle λ L They are defined as: and Among them, tan -1 is the inverse function of the tangent function. The desired sight distance and sight angle of the following ship are ρ Ld and λ Ld ; The formation tracking error is defined as ρ Le =ρ L -ρ Ld ,λ Le =λ L -λ Ld , where ρ Le is the sight range error of the following ship, λ Le is the line of sight angle error of the following ship.

[0023] In a possible implementation, in step 1), the adaptive control law uses the position and the bow angle of the pilot ship so that the sight distance ρ of the following ship to the pilot ship is L and the sight angle λ L Tracking the expected ρ Ld and λ Ld First, the relative kinematic equation between the pilot ship and the following ship is calculated, and the line of sight error ρ of the following ship is calculated. Le and the line of sight angle error λ Le , design the virtual control law of the following ship kinematics: and Among them, k ρ and k λ is the control gain, ∈1 and ∈2 are positive constants, and p is a positive constant.

[0024] In one possible implementation, in step 1), the adaptive control law is The virtual control law of the following ship's forward direction is based on the relative kinematics between the pilot ship and the following ship, the line of sight error ρ of the following ship Le and the line of sight angle error λ of the following ship Le , the relative kinematic equation between the lead ship and the following ship is:

[0025]

[0026]

[0027] Where 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 have a common upper bound p0, namely: Δ ρ ≤p0,Δ λ ≤p0,p0=|u L |+|v L |+|v|, assuming that the drift speed of the unmanned ship is passively bounded, and the forward speed of the pilot ship is bounded, there exists a positive constant p such that p0≤p;

[0028] The line-of-sight error of the following ship ρ Le and the line of sight angle error λ Le The derivative of is:

[0029]

[0030]

[0031] where w ρ =u cos(ψ-λ L ), w λ =u sin(ψ-λ L ),

[0032] The virtual control law of the following ship kinematics is designed according to the relative kinematics equation and the error derivative equation:

[0033]

[0034] In one possible implementation, the virtual kinematic control law in step 1) is and To process, where α u and α ψ The virtual control laws for u and ψ are: α u and α ψ That is the virtual control law of the following ship's forward direction.

[0035] In a possible implementation, in step 2), let the virtual control law α of the following ship's forward direction be u and α ψ Through two time constants T u and T ψ A first-order filter generates a signal β u and β ψ , then the following relationship exists:

[0036]

[0037] β u (0) = α u (0)

[0038]

[0039] β ψ (0) = α ψ (0)

[0040] Next, define the error u e ,z u ,ψ e ,z ψ , satisfying the following relationship: e =u-β u ,z u =β u -α u , ψ e = ψ-β ψ ,z ψ =β ψ -α ψ ;

[0041] P e The derivative is:

[0042]

[0043] Design of virtual control law to follow the bow rolling direction r : where kψ is the control gain.

[0044] In a possible implementation, in step 3), let the virtual control law α following the bow rolling direction in step 2) be r The time constant is T r The first-order filter of r ,Right now:

[0045]

[0046] β r (0) = α r (0)

[0047] Definition error r e and z r , satisfying r e = r - β r ,z r =β r -α r ;

[0048] The following linear system is used:

[0049]

[0050] where π1∈R 3 and π2∈R 3 is the state vector, δ is a positive constant, λ1>0; the estimate of η is obtained

[0051] According to the kinematic equation of the unmanned ship, we have:

[0052]

[0053]

[0054] Since ||R T (·)||=1, and we get a high gain observer:

[0055]

[0056] Among them B v is a normal number.

[0057] In one possible implementation, in step 4), the RBF neural network has the following theorem:

[0058] For the Gaussian basis function, if where the constant β>0 and is a bounded variable, then: Among them G tis a bounded function vector;

[0059] According to the high gain observer in step 3) have:

[0060]

[0061] in, is a bounded function vector, then the dynamic equation of the unmanned ship is i +d wi / m i It is expressed as:

[0062]

[0063] in and Defined as:

[0064]

[0065]

[0066] Design the forward thrust τ of the underactuated follower ship u and steering torque τ r The control law τ i|i＝u,r satisfy:

[0067]

[0068] The corresponding adaptive law based on minimum parameter learning is:

[0069]

[0070] in b i , Γ i and δ i are all positive control parameters, yes The initial value of i The truth value of .

[0071] In a possible implementation scheme, formation control is achieved by using the line of sight and sight angle information of the following ship, and the line of sight and sight angle information is directly obtained by equipping the following ship with a navigation radar.

[0072] In a second aspect, a computer storage medium is also provided, which stores a computer program, and when the program is executed by a processor, the formation control method for under-actuated unmanned surface vessels described in any possible implementation scheme of the first aspect is implemented.

[0073] In a third aspect, a computer device is also provided, including:

[0074] A memory and a processor, wherein the memory stores a computer program, and when the program is executed by the processor, the formation control method for under-actuated unmanned surface ships described in any possible implementation scheme of the first aspect is implemented.

[0075] The application has the beneficial effects that: the formation control method of the application integrates adaptive control law, dynamic surface control technology, neural network technology, high gain observer and minimum parameter learning algorithm, and only depends on the sight range, sight angle, position and bow angle information of the following ship. The formation controller only needs to adjust two learning parameters τ online. u and τ r , the preset formation layout relative to the pilot ship can be realized. Considering the unknown speed information of the underactuated pilot ship and the following ship, as well as the uncertainty of the model and unknown external disturbances, it not only enhances the fault tolerance of the multi-ship formation system to suppress uncertain models and external disturbances, but also enhances the robustness of the unmanned ship formation system by reducing the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0077] Figure 1 A schematic diagram of a formation structure according to an embodiment of the present application is shown;

[0078] Figure 2 It is a principle framework diagram of a formation control scheme according to an embodiment of the present application. DETAILED DESCRIPTION

[0079] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations.

[0080] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application for which protection is sought, but merely represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present application.

[0081] In the description of this application, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0082] According to the first aspect of the present application, a formation control method for underactuated unmanned surface ships is first provided. The objective of the present application is to design a control law τ for the following ship when the speed information of the underactuated pilot ship and the following ship is unknown and there are uncertain models and unknown external disturbances. u and τ r , so that the following ship can achieve the preset formation layout relative to the leading ship (ρ Ld ,λ Ld ).

[0083] First of all, the mathematical model of the unmanned ship includes the kinematic model and the dynamic model. When studying the 6-DOF motion of a ship, two coordinate systems are often used, one is the earth coordinate system and the other is the ship coordinate system.

[0084] The kinematic equation of each unmanned ship is: where η = [x, y, ψ] T refers to the position vector of the unmanned ship in the geodetic coordinate system, (x, y) refers to the position of the unmanned ship, ψ refers to the bowing angle of the unmanned ship, v = [u, v, r] T It refers to the velocity vector of the unmanned ship in the hull coordinate system, u, v, and r refer to the forward speed, drift speed, and bow angular velocity of the unmanned ship respectively, and R(ψ) refers to the rotation matrix related to the bow angular velocity of the unmanned ship, which is:

[0085]

[0086] The nonlinear dynamic equation of each unmanned ship on the horizontal plane is:

[0087]

[0088] Among them, M j is the inertia coefficient matrix, C j is the Coriolis force and centripetal force matrix, D j is the damping coefficient matrix, which are defined as:

[0089]

[0090]

[0091]

[0092] The dynamic equation of each unmanned ship is:

[0093]

[0094]

[0095]

[0096] in, d wu ,、d wv ,、d wr They represent the forces or moments of external disturbances (such as wind, waves, currents, etc.) acting on the three channels of unmanned ship forward, drift and bow pitch, respectively. u 、 v 、m r is the inertia coefficient in the unmanned ship model, c 13 、c 23 、c 31 、c 32 are the centripetal force and Coriolis force coefficients in the unmanned ship model, d 11 ,d 22 ,d 23 ,d 32 ,d 33 is the hydrodynamic damping coefficient in the unmanned ship model, g u , g v , g r represents the unmodeled dynamics of the unmanned ship, τ u , τ r represents the actuator input of the unmanned ship, where τ u is the thrust of the unmanned ship in the forward direction, τ r is the torque in the direction of the unmanned ship's bow angular velocity. Since the unmanned ship is under-driven, there is no actuator input in the lateral drift direction of the unmanned ship model.

[0097] Further, taking 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 denoted by ν L and ν. The sight distance of the following ship to the pilot ship ρ L and the sight angle λ L They are defined as and Among them, tan -1 is the inverse function of the tangent function. The desired sight distance and sight angle of the following ship are ρ Ld and λ Ld The formation tracking error can be defined as ρ Le =ρ L -ρ Ld ,λ Le =λ L -λ Ld , where ρ Le is the sight range error of the following ship, λ Le is the line of sight angle error of the following ship, such as Figure 1 shown.

[0098] The principle diagram of the formation control method of this application is as follows Figure 2 As shown, the specific steps are given below:

[0099] 1) Based on an improved adaptive control law, a virtual control law of the following ship's kinematics is designed to stabilize the tracking errors of the sight range and sight angle, thereby constructing a virtual control law of the following ship's forward direction.

[0100] First, according to the kinematic equation of the unmanned ship, the line of sight ρ L , sight angle λ L As well as the definition of formation tracking error, the relative kinematic equation between the lead ship and the following ship is derived:

[0101]

[0102]

[0103] Where 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 have a common upper bound p0, namely: Δ ρ ≤p0,Δ λ ≤p0,p0=|u L|+|v L |+|v|. Assuming that the drift speed of the unmanned ship is passively bounded, and the forward speed of the pilot ship is bounded, there exists a positive constant p such that p0≤p.

[0104] Secondly, the line of sight error ρ of the following ship Le and the line of sight angle error λ Le Derivative, we have:

[0105]

[0106]

[0107] where w ρ =u cos(ψ-λ L ), w λ =u sin(ψ-λ L ).

[0108] Next, the following virtual control law of the following ship kinematics is designed based on the relative kinematics equation and the error derivative equation:

[0109]

[0110] Among them, k ρ and k λ is the control gain, ∈1 and ∈2 are positive constants, and the improved adaptive control law is k p is a control gain. The adaptive control law can still ensure formation tracking when the speed of the lead ship and the following ship is missing, and only one adaptive parameter needs to be updated, which simplifies the parameter adjustment process and improves engineering practicability.

[0111] Virtual kinematics control law and To process, where α u and α ψ The virtual control laws for u and ψ are: α u and α ψ That is the virtual control law of the following ship's forward direction.

[0112] Step 2) Dynamic surface control technology is used to stabilize the bow angle tracking error of the following ship, and then a virtual control law for the bow direction of the following ship is constructed.

[0113] Let the virtual control law α follow the ship's forward direction u and α ψ Through two time constants Tu and T ψ A first-order filter generates a signal β u and β ψ , then the following relationship exists:

[0114]

[0115] β u (0) = α u (0)

[0116]

[0117] β ψ (0) = α ψ (0)

[0118] Next, define the error u e ,z u ,ψ e ,z ψ , satisfying the following relationship: e =u-β u ,z u =β u -α u , ψ e = ψ-β ψ ,z ψ =β ψ -α ψ .

[0119] P e The derivative is:

[0120]

[0121] Design of virtual control law to follow the bow rolling direction r : where k ψ is the control gain.

[0122] Step 3): Construct a high-gain observer to estimate the speed of the following ship. The high-gain observer is used to design an adaptive output feedback formation control law for the following ship by combining the virtual control law, neural network approximation technology and minimum parameter learning algorithm.

[0123] First, let the virtual control law α in step 2) follow the bow rolling direction r The time constant is T r The first-order filter of r ,Right now:

[0124]

[0125] β r (0) = αr (0)

[0126] Definition error r e and z r , satisfying r e = r - β r ,z r =β r -α r .

[0127] Secondly, the high-gain observer can be used to estimate the speed information of the unmanned ship when the unmanned ship has uncertain dynamics and is subject to external disturbances. This is very useful in the scenario where only the position and bow angle information of the unmanned ship are used to form a formation. To construct an effective high-gain observer, we consider the following linear system:

[0128]

[0129] where π1 and π2∈R 3 is the state vector, δ is a positive constant, λ1>0. The estimate of η is

[0130] According to the kinematic equation of the unmanned ship, we have:

[0131]

[0132] Further, there are:

[0133]

[0134] Since ||R T (·)||=1, and we can further get a high gain observer:

[0135]

[0136] Among them B v is a normal number.

[0137] Step 4) Stabilize the forward speed error u under the uncertain model of the following ship and external disturbances e and the yaw angular velocity error r e , and constructed an adaptive output feedback formation control law based on RBF neural network and minimum parameter learning algorithm.

[0138] For RBF neural network, there is the following theorem:

[0139] For the Gaussian basis function, if where the constant β>0 and is a bounded variable, then: Among them G tis a bounded function vector.

[0140] According to the high gain observer in step 3) have:

[0141]

[0142] in, is a bounded function vector, then the dynamic equation of the unmanned ship is i +d wi / m i It can be expressed as:

[0143]

[0144] in and Defined as:

[0145]

[0146]

[0147] Design the forward thrust τ of the underactuated follower ship u and steering torque τ r The control law τ i|i =u,r satisfies:

[0148]

[0149] The corresponding adaptive law based on minimum parameter learning is:

[0150]

[0151] in b i , Γ i and δ i are all positive control parameters, yes The initial value of i The truth value of .

[0152] In this embodiment, the line of sight and sight angle information of the following ship are used to realize formation control. The line of sight and sight angle information are directly obtained by equipping the following ship with a navigation radar. In this scheme, the following ship does not use the bow angle information of the pilot ship. During the entire formation process, there is no need for communication between the following ship and the pilot ship, which greatly saves communication costs and is relatively convenient to implement.

[0153] Aiming at the formation maintenance and translation motion control problems of the leading-following structure of underactuated unmanned ships in the presence of model uncertainty and external environmental disturbances, this application proposes an adaptive output feedback formation control method for underactuated surface unmanned ships. Compared with the existing formation control method of the leading-following structure, it has the following characteristics:

[0154] The formation control method combines adaptive control law, dynamic surface control technology, neural network technology, high gain observer and minimum parameter learning algorithm.

[0155] The formation control method only depends on the sight range, sight angle, position and bow angle information of the following ship. The formation controller in the scheme only needs to adjust two learning parameters τ online. u and τ r , the preset formation layout relative to the pilot ship can be achieved.

[0156] The formation control method takes into account the fact that the speed information of the under-actuated lead ship and the following ship is unknown, as well as the uncertainty of the model and unknown external disturbances (wind, waves, currents, etc.). It not only enhances the fault tolerance of the multi-ship formation system in suppressing uncertain models and external disturbances, but also enhances the robustness of the unmanned ship formation system by reducing the amount of calculation.

[0157] According to the second aspect of the present application, a computer storage medium is also provided, which stores a computer program, and when the program is executed by a processor, it implements the formation control method for under-actuated unmanned surface ships described in the embodiment of the first aspect.

[0158] Preferably, the storage medium includes: ROM, RAM, disk, USB flash drive, memory card or CD, etc., which can store program codes.

[0159] According to the third aspect of the present application, the present application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, which, when executed by the processor, implements the formation control method for under-actuated surface unmanned vessels described in the embodiment of the first aspect.

[0160] The memory includes: ROM, RAM, disk, USB flash drive, memory card or CD and other media that can store program codes. The processor is connected to the memory and is used to execute the computer program stored in the memory.

[0161] Preferably, the processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components.

[0162] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A formation control method for underactuated unmanned surface ships, characterized in that: The following steps are involved: 1) Based on the improved adaptive control law, a virtual control law of the following ship's kinematics is designed to stabilize the tracking errors of the sight range and sight angle, thereby constructing a virtual control law of the following ship's forward direction; Step 1) includes the steps of constructing a mathematical model of an unmanned ship: The ship's freedom of motion uses the earth coordinate system and the hull coordinate system. The kinematic equation of each unmanned ship is: where η = [x, y, ψ] T refers to the position vector of the unmanned ship in the geodetic coordinate system, (x, y) refers to the position of the unmanned ship, ψ refers to the bowing angle of the unmanned ship, v = [u, v, r] T It refers to the velocity vector of the unmanned ship in the hull coordinate system, u, v, and r refer to the forward speed, drift speed, and bow angular velocity of the unmanned ship respectively, and R(ψ) refers to the rotation matrix related to the bow angular velocity of the unmanned ship, which is: The dynamic equation of each unmanned ship is: in, d wu ,d wv ,d wr They represent the force or moment of external disturbance on the three channels of unmanned ship forward, side drift and bow pitch, m u 、m v 、m r is the inertia coefficient in the unmanned ship model, c 13 、c 23 、c 31 、c 32 are the centripetal force and Coriolis force coefficients in the unmanned ship model, d 11 ,d 22 ,d 23 ,d 32 ,d 33 is the hydrodynamic damping coefficient in the unmanned ship model, g u , g v , g r represents the unmodeled dynamics of the unmanned ship, τ u , τ r represents the actuator input of the unmanned ship, where τ u is the thrust of the unmanned ship in the forward direction, τ r is the torque in the direction of the unmanned ship’s bow angular velocity; since the unmanned ship is under-driven, there is no actuator input in the lateral drift direction of the unmanned ship model; Define the sight distance ρ of the following ship to the pilot ship L and the sight angle λ L ; Assume that the position vectors of the pilot ship and the following ship are η L and η, their velocity vectors are denoted by ν L and ν, then the line of sight ρ L and the sight angle λ L They are defined as: and Among them, tan -1 is the inverse function of the tangent function. The desired sight distance and sight angle of the following ship are ρ Ld and λ Ld ; The formation tracking error is defined as ρ Le =ρ L -ρ Ld ,λ Le =λ L -λ Ld , where ρ Le is the sight range error of the following ship, λ Le is the line of sight angle error of the following ship; In step 1), the adaptive control law uses the position and yaw angle of the pilot ship to make the sight distance ρ of the following ship to the pilot ship L and the sight angle λ L Tracking the expected ρ Ld and λ Ld First, the relative kinematic equation between the pilot ship and the following ship is calculated, and the line of sight error ρ of the following ship is calculated. Le and the line of sight angle error λ Le , design the virtual control law of the following ship kinematics: and Among them, k ρ and k λ is the control gain, ∈1 and ∈2 are positive constants, and p is a positive constant; In step 1), the adaptive control law is The virtual control law of the following ship's forward direction is based on the relative kinematics between the pilot ship and the following ship, the line of sight error ρ of the following ship Le and the line of sight angle error λ of the following ship Le , the relative kinematic equation between the lead ship and the following ship is: Where Δ ρ =u L cos(ψ L -λ L )-v L sin(ψ L -λ L )+vsin(ψ-λ L ), Δ λ =u L sin(ψ L -λ L )+v L cos(ψ L -λ L )-vcos(ψ-λ L ), Δ ρ and Δ λ Have a common upper bound p0, namely: Δ ρ ≤p0,Δ λ ≤p0,p0=|u L |+|v L |+|v|, assuming that the drift speed of the unmanned ship is passively bounded, and the forward speed of the pilot ship is bounded, there exists a positive constant p such that p0≤p; The line-of-sight error of the following ship ρ Le and the line of sight angle error λ Le The derivative of is: among themw ρ =u cos(ψ-λ L ),w λ =u sin(ψ-λ L ), The virtual control law of the following ship kinematics is designed according to the relative kinematics equation and the error derivative equation: For the virtual kinematic control law in step 1) and To process, where α u and α ψ The virtual control laws for u and ψ are: α u and α ψ That is the virtual control law for the following ship's forward direction; 2) Using the virtual control law of the kinematics of the following ship and the virtual control law of the following ship's forward direction in step 1), the dynamic surface control technology is adopted to stabilize the bow angle tracking error of the following ship, and then the virtual control law of the bow direction of the following ship is constructed; 3) Build a high-gain observer to estimate the speed of the following ship; 4) Stabilize the forward speed error u under the uncertain model of the following ship and under external disturbance e and the yaw angular velocity error r e Combining the high-gain observer, the virtual control law of the following ship's forward direction and the virtual control law of the following ship's bow pitch direction, an adaptive output feedback formation control law is constructed for the following ship based on the RBF neural network and the minimum parameter learning algorithm.

2. The formation control method for underactuated unmanned surface vessels according to claim 1, characterized in that: In step 2), let the virtual control law α of the following ship's forward direction be u and α ψ Through two time constants T u and T ψ A first-order filter generates a signal β u and β ψ , then the following relationship exists: β u (0)＝α u (0) β ψ (0)＝α ψ (0) Next, define the error u e ,z u ,ψ e ,z ψ , satisfying the following relationship: e =u-β u ,z u =β u -α u , ψ e =ψ-β ψ ,z ψ =β ψ -α ψ ; P e The derivative is: Design of virtual control law to follow the bow rolling direction r : where k ψ is the control gain.

3. The formation control method for underactuated unmanned surface vessels according to claim 2, characterized in that: In step 3), let the virtual control law α following the bow rolling direction in step 2) be r The time constant is T r The first-order filter of r ,Right now: β r (0)＝α r (0) Definition error r e and z r , satisfying r e = r - β r ,z r =β r -α r ; The following linear system is used: where π1∈R 3 and π2∈R 3 is the state vector, δ is a positive constant, λ1>0; the estimate of η is obtained According to the kinematic equation of the unmanned ship, we have: Since ‖R T (·)‖=1, and we get a high gain observer: Among them B v is a normal number.

4. The formation control method for underactuated unmanned surface vessels according to claim 3, characterized in that: In step 4), the RBF neural network has the following theorem: For the Gaussian basis function, if where the constant β>0 and is a bounded variable, then: Among them G t is a bounded function vector; According to the high gain observer in step 3) have: in, is a bounded function vector, then the dynamic equation of the unmanned ship is i +d wi / m i It is expressed as: where θ i and Defined as: Design the forward thrust τ of the underactuated follower ship u and steering torque τ r The control law τ i|i＝u , r satisfies: The corresponding adaptive law based on minimum parameter learning is: in b i , Γ i and δ i are all positive control parameters, yes The initial value of i The truth value of .

5. A computer storage medium, characterized in that: It stores a computer program, which, when executed by a processor, implements the formation control method for under-actuated unmanned surface ships described in any one of claims 1 to 4.

6. A computer device, characterized in that: include: A memory and a processor, wherein the memory stores a computer program, and when the program is executed by the processor, the formation control method for under-actuated unmanned surface vessels described in any one of 1 to 4 is implemented.

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