CN115291522A - Self-adaptive fuzzy AUV stable tracking control method and device and electronic equipment - Google Patents
Self-adaptive fuzzy AUV stable tracking control method and device and electronic equipment Download PDFInfo
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Abstract
The invention discloses a self-adaptive fuzzy AUV stable tracking control method and device and electronic equipment, wherein the method comprises the following steps: establishing a first dynamic model of the AUV under the condition of no water flow disturbance and a second dynamic model under the condition of water flow disturbance, wherein the first dynamic model comprises the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, designing a first controller and a second controller according to the first dynamic model and the second dynamic model, wherein the second controller contains an unknown item, selecting a fuzzy membership function according to the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, calculating to obtain a fuzzy basis function and replacing the unknown item, finally setting a tracking path of the AUV, and tracking the path by using the second controller. The invention provides a control method for path tracking by using a self-adaptive fuzzy algorithm aiming at an AUV (autonomous underwater vehicle) with partially unknown parameters, and the method controls the fluctuation of a tracking error in a small range, thereby laying a key foundation for the fields of deep sea archaeology, ocean monitoring, seabed surveying and mapping and the like.
Description
Technical Field
The application relates to the field of AUV path tracking control, in particular to a self-adaptive fuzzy AUV stable tracking control method and device and electronic equipment.
Background
Autonomous Underwater Vehicles (AUVs) are underwater unmanned platforms that combine artificial intelligence with other advanced technologies, and are now widely used in many fields such as deep-sea archaeology, seafloor surveying and mapping, and ocean monitoring.
The current methods for controlling the AUV include:
(1) And outputting feedback control in a limited time. In order to solve the problem of trajectory tracking of the AUV, the nonlinear decoupling AUV is used as an object for implementation, and finally satisfactory trajectory tracking performance is obtained. However, the application is limited to the nonlinear AUV of the known dynamic model, and the precise AUV model is difficult to obtain in practical application.
(2) Adaptive neural network control. The neural network is a general approximator of an unknown nonlinear function of an uncertain dynamic system, can be used for an uncertain nonlinear AUV of a dynamic model, estimates the unknown nonlinear function by using a Radial Basis Function Neural Network (RBFNN), ensures the convergence of tracking errors and widens the application field of the neural network. However, the design parameters are more, which will increase the computational burden of the computer, and the problem of the sharp increase of complexity in the inversion process is to be further solved.
Disclosure of Invention
The embodiment of the application aims to provide a method and a device for controlling stable tracking of an adaptive fuzzy AUV (autonomous Underwater vehicle) and electronic equipment, so as to solve the problems of heavy calculation burden and increased complexity in the related technology.
According to a first aspect of the embodiments of the present application, there is provided an adaptive fuzzy AUV stable tracking control method, including:
establishing a first dynamic model of the AUV under no water flow disturbance and a second dynamic model under water flow disturbance, wherein three unknown state variables exist in the first dynamic model and the second dynamic model and respectively represent the longitudinal speed, the transverse speed and the yaw rate of the AUV;
under the condition of no water flow disturbance, designing a first controller according to the first dynamic model so that the controller has stability;
adding water flow interference, and re-deducing the first controller according to the second dynamic model to obtain a second controller, wherein the second controller contains an unknown item;
selecting a fuzzy membership function according to the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, and calculating to obtain a fuzzy basis function by utilizing a fuzzy basis function calculation rule according to the fuzzy membership function;
replacing the unknown item with the fuzzy basis function;
and setting a reference path as a tracking path of the AUV, and performing path tracking by using the second controller after the unknown item is replaced.
Further, establishing a first dynamic model of the AUV under no water flow disturbance and a second dynamic model under water flow disturbance, comprising:
selecting the horizontal and vertical coordinates and the yaw angle of the AUV as three degrees of freedom of AUV plane motion;
constructing a differential equation of a horizontal coordinate, a vertical coordinate and a yaw angle of the AUV by using the longitudinal speed, the transverse speed and the yaw angle speed of the AUV;
constructing a relational expression of longitudinal velocity, transverse velocity and yaw angular velocity of a controller and the AUV by using an inertia matrix, a damping matrix, a Coriolis matrix and a centripetal acceleration matrix;
according to the differential equation and the relational expression, a first dynamic model under the condition of no water flow disturbance is constructed;
and adding the relation into a water flow interference vector, and constructing a second dynamic model under the water flow disturbance together with the differential equation.
Further, designing a first controller according to the first dynamic model in the absence of water flow disturbance includes:
s21: forming a position vector of the AUV by using a horizontal coordinate and a vertical coordinate of the AUV and a yaw angle, forming a speed vector of the AUV by using a longitudinal speed, a horizontal speed and a yaw angle of the AUV, using a difference between the position vector and a reference position vector as a first error tracking vector, using a difference between the speed vector and the output of a command filter as a second error tracking vector, and obtaining the output of the command filter according to an equation of a command filtering technology;
s22: introducing a first error compensation vector and a second error compensation vector, taking the difference between the first error tracking vector and the first error compensation vector as a first error vector, and taking the difference between the second error tracking vector and the second error compensation vector as a second error vector;
s23: combining the first error compensation vector, the second error compensation vector, and the first kinetic model into the first error vector and the second error vector to obtain a first controller, the first controller having stability.
Further, adding a water flow disturbance, and re-deriving the first controller according to the second dynamic model to obtain a second controller, including:
and replacing the first dynamic model in the S23 with the second dynamic model by utilizing the second dynamic model, and executing S21-S23 to obtain a second controller.
Further, selecting a fuzzy membership function according to the longitudinal speed, the transverse speed and the yaw rate of the AUV, and calculating to obtain a fuzzy basis function according to the fuzzy membership function and by using a fuzzy basis function calculation rule, wherein the fuzzy basis function comprises the following steps:
selecting the domains of longitudinal speed, transverse speed and yaw rate of the AUV;
selecting fuzzy membership functions, wherein the independent variables of the fuzzy membership functions are respectively the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, the central point is an odd number of points which are uniformly distributed in the discourse domain of the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, and the width is a determined normal number, so that three groups of fuzzy membership functions are obtained;
and substituting the fuzzy membership function into a fuzzy basis function calculation rule to obtain a fuzzy basis function.
Further, replacing the unknown term with the fuzzy basis function includes:
arranging the fuzzy basis functions in sequence to form a fuzzy basis function column vector, wherein the dimensionality of the fuzzy basis function column vector is the number of the central points of the fuzzy membership function;
multiplying the fuzzy basis function column vector by the transpose of a weight vector in a neural network to obtain an estimated value of the unknown item; according to the RBFNN, obtaining an updating rule of each element in the weight vector by using a gradient descent algorithm, thereby obtaining the weight vector;
and bringing the estimated value into the second controller to replace the unknown item.
Further, setting a reference path as a tracking path of the AUV, and performing path tracking by using the second controller after replacing the unknown item, including:
setting a reference horizontal and vertical coordinate as a bounded function of time, solving an arctangent value of a derivative ratio related to the time by the bounded function of the horizontal and vertical coordinate to obtain a reference yaw angle, and forming a reference signal by the reference horizontal and vertical coordinate and the reference yaw angle as a reference path;
selecting water flow interference according to the reference signal, and ensuring that the water flow interference is smaller than the reference signal and has boundedness;
and substituting the second controller after the unknown item is replaced into the second dynamic model, and performing path tracking on the reference signal.
According to a second aspect of embodiments of the present application, there is provided an adaptive fuzzy AUV stable tracking control apparatus, including:
the system comprises an establishing module, a judging module and a judging module, wherein the establishing module is used for establishing a first dynamic model of the AUV under no water flow disturbance and a second dynamic model under water flow disturbance, and three unknown state variables exist in the first dynamic model and the second dynamic model and respectively represent the longitudinal speed, the transverse speed and the yaw rate of the AUV;
the design module is used for designing a first controller according to the first dynamic model under the condition of no water flow disturbance, so that the controller has stability;
the derivation module is used for adding water flow interference, and re-deriving the first controller according to the second dynamic model to obtain a second controller, wherein the second controller contains an unknown item;
the calculation module is used for selecting a fuzzy membership function according to the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, and calculating to obtain a fuzzy basis function by utilizing a fuzzy basis function calculation rule according to the fuzzy membership function;
a replacement module for replacing the unknown item with the fuzzy basis function;
and the tracking module is used for setting a reference path as a tracking path of the AUV and carrying out path tracking by using the second controller after the unknown item is replaced.
According to a third aspect of embodiments herein, there is provided an electronic device comprising:
one or more processors;
a memory for storing one or more programs;
when executed by the one or more processors, cause the one or more processors to implement a method as described in the first aspect.
According to a fourth aspect of embodiments herein, there is provided a computer-readable storage medium having stored thereon computer instructions, characterized in that the instructions, when executed by a processor, implement the steps of the method according to the first aspect.
The technical scheme provided by the embodiment of the application can have the following beneficial effects:
according to the embodiment, the unknown items in the second controller are estimated by adopting the fuzzy control method and calculating the fuzzy basis function, so that the parameters of the second controller become known, and the method can be directly used for path tracking and can ensure the boundedness of the tracking error. In addition, a fuzzy basis function calculation rule is adopted, a group of fuzzy basis functions are directly obtained for calculation, calculation burden is reduced, and complexity of the control method is reduced.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and together with the description, serve to explain the principles of the application.
Fig. 1 is a flow diagram illustrating a method of adaptive fuzzy AUV stable tracking control in accordance with an exemplary embodiment.
FIG. 2 is a schematic illustration of the position abscissa and its reference signal time response of an embodiment of the present invention.
FIG. 3 is a schematic diagram of a position ordinate and its reference signal time response of an embodiment of the present invention.
FIG. 4 is a schematic diagram of yaw angle and its reference signal time response according to an embodiment of the present invention.
FIG. 5 is a schematic of three speeds of an embodiment of the present invention.
Fig. 6 is a schematic diagram of a tracking error time response of an embodiment of the present invention.
Fig. 7 is a block diagram illustrating an adaptive fuzzy AUV settling tracking control apparatus in accordance with an exemplary embodiment.
Detailed Description
Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the application, as detailed in the appended claims.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used in this application and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.
It is to be understood that although the terms first, second, third, etc. may be used herein to describe various information, such information should not be limited to these terms. These terms are only used to distinguish one type of information from another. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of the present application. The word "if," as used herein, may be interpreted as "at … …" or "at … …" or "in response to a determination," depending on the context.
Fig. 1 is a flow diagram illustrating a method of adaptive fuzzy AUV stability tracking control, which may include the steps of, as shown in fig. 1:
s1: establishing a first dynamic model of the AUV under the condition of no water flow disturbance and a second dynamic model under the condition of water flow disturbance, wherein three unknown state variables exist in the first dynamic model and the second dynamic model and respectively represent the longitudinal speed, the transverse speed and the yaw rate of the AUV;
s2: under the condition of no water flow disturbance, designing a first controller according to the first dynamic model so that the controller has stability;
s3: adding water flow interference, and re-deducing the first controller according to the second dynamic model to obtain a second controller, wherein the second controller contains an unknown item;
s4: selecting a fuzzy membership function according to the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, and calculating to obtain a fuzzy basis function by utilizing a fuzzy basis function calculation rule according to the fuzzy membership function;
s5: replacing the unknown item with the fuzzy basis function;
s6: and setting a reference path as a tracking path of the AUV, and performing path tracking by using the second controller after the unknown item is replaced.
According to the embodiment, the unknown items in the second controller are estimated by adopting the fuzzy control method and calculating the fuzzy basis function, so that the parameters of the second controller become known, and the method can be directly used for path tracking and can ensure the boundedness of the tracking error. In addition, a fuzzy basis function calculation rule is adopted, a group of fuzzy basis functions are directly obtained for calculation, calculation burden is reduced, and complexity of the control method is reduced.
In the specific implementation of S1: establishing a first dynamic model of the AUV under no water flow disturbance and a second dynamic model under water flow disturbance, wherein three unknown state variables exist in the first dynamic model and the second dynamic model and respectively represent the longitudinal speed, the transverse speed and the yaw rate of the AUV; the step comprises the following substeps:
s11: selecting the horizontal and vertical coordinates and the yaw angle of the AUV as three degrees of freedom of AUV plane motion;
specifically, η = [ x, y, ψ is selected] T ∈R 3 The position vector of the AUV is x and y respectively correspond to the abscissa and ordinate of the AUV in the world reference system, and psi represents the yaw angle of the AUV.
S12: constructing a differential equation of a horizontal coordinate, a vertical coordinate and a yaw angle of the AUV by using the longitudinal speed, the transverse speed and the yaw angle speed of the AUV;
specifically, the velocity vector is represented as V = [ u, V, r =] T Where u and v are the linear velocity of the vehicle relative to the vehicle, u represents the longitudinal velocity of the vehicle, v represents the lateral velocity of the vehicle, and r represents the yaw rate of the vehicle relative to the vehicle. The differential equation of the position vector η and the velocity vector V is as follows:
where J (η) is defined as the Jacobian matrix transformation matrix, which is of the form:
s13: constructing a relational expression of a controller and the longitudinal speed, the transverse speed and the yaw rate of the AUV by using an inertia matrix, a damping matrix, a Coriolis matrix and a centripetal acceleration matrix;
specifically, M ∈ R 3×3 For the inertia matrix, C (V) represents the coriolis matrix and the centripetal acceleration matrix, and D (V) represents the damping matrix. The matrix M, C (V) is given belowAnd forms of D (V):
and (3) constructing a relational expression of the controller rho and the speed vector V by using the matrix:
where ρ is the vector of the controller.
S14: according to the differential equation and the relational expression, a first dynamic model under the condition of no water flow disturbance is constructed;
specifically, equations (1) and (2) are combined to construct a first kinetic equation under no water flow disturbance:
s15: and adding the relation into a water flow interference vector, and constructing a second dynamic model under the water flow disturbance together with the differential equation.
Specifically, let h = [ h = 1 ,h 2 ,h 3 ] T And (3) constructing a second dynamic model under the water flow disturbance according to the formula (3) as a water flow disturbance vector:
it is noted that the interference signal vector h can be divided into two types, i.e. related to the position vector η and the velocity vector V, and independent of both. Since the interference associated with η and V is complex and would render the present invention unsuitable, the present invention only considers the case of independence of the two, thereby simplifying the effect of water flow disturbance.
In the specific implementation of S2: under the condition of no water flow disturbance, designing a first controller according to the first dynamic model, so that the controller has stability; the step comprises the following substeps:
s21: forming a position vector of the AUV by using a horizontal coordinate and a vertical coordinate of the AUV and a yaw angle, forming a speed vector of the AUV by using a longitudinal speed, a transverse speed and a yaw angle of the AUV, using a difference between the position vector and a reference position vector as a first error tracking vector, using a difference between the speed vector and the output of a command filter as a second error tracking vector, and obtaining the output of the command filter according to an equation of a command filtering technology;
in particular, the first error tracking vector σ is used 1 And a second error tracking vector sigma 2 The definition is as follows:
where eta = [ x, y, ψ ]] T ∈R 3 Is a position vector, η t ＝[x t ,y t ,ψ t ] T Is a reference position vector, V = [ u, V, r =] T Is the velocity vector, χ = [ ] 1,1 ,χ 2,1 ,χ 3,1 ] T For the output of the command filter, the solution is the following equation for the command filtering technique:
wherein, beta i ＞0，0＜γ i 1 or less is a known parameter, alpha 1 ＝[α 1，1 ,α 2，1 ,α 3，1 ] T For the dummy control signal, it is designed in the following stepsThe formula thereof. To ensure that the vector dimensions at both ends of equation (3) are equal, the error tracking vector is written as σ 1 ＝[σ 1,1 ,σ 1,2 ,σ 1,3 ] T ，σ 2 ＝[σ 2,1 ,σ 2,2 ,σ 2,3 ] T . This step introduces command filtering technique to reduce the computational burden in the control design process, but at the command filter output χ and the virtual control signal α 1 Errors are generated between the two, and the tracking performance is influenced.
S22: introducing a first error compensation vector and a second error compensation vector, taking the difference between the first error tracking vector and the first error compensation vector as a first error vector, and taking the difference between the second error tracking vector and the second error compensation vector as a second error vector;
specifically, a first error compensation vector ζ is introduced 1 And a second error compensation vector ζ 2 Defining a first error vector e 1 And a second error vector e 2 Comprises the following steps:
s23: combining the first error compensation vector, the second error compensation vector, and the first kinetic model into the first error vector and the second error vector to obtain a first controller, the first controller having stability.
In particular, for the first error vector e 1 Is derived by
Error compensation vector zeta based on Lyapunov function 1 And ζ 2 Virtual control signal alpha 1 Selection is performed. Firstly, the Lyapunov function W is carried out 1 Is selected as
According to (7), W 1 Is a derivative of
Designing a first error compensation vector ζ from (10) 1 Is composed of
Wherein Δ 1 ＝diag(Δ 1,1 ,Δ 1,2 ,Δ 1,3 ) Are known.
Then, the virtual control signal alpha is designed according to (10) and (11) 1 Is composed of
Substituting the related variables in the formula (10) with the formulas (11) and (12) to obtain
Tracking the vector sigma by taking into account the second error 2 And a second error vector e 2 A relationship of (e) 2 Is a derivative of
Wherein f (V) = [ f = [) 1 (V),f 2 (V),f 3 (V)] T ＝-M -1 C(V)V-M -1 D (V) V is an unknown term representing a non-linear function, which needs to be estimated by
Representing an estimate of an unknown item.
The second error compensation vector ζ 2 Is designed as
Wherein Δ 2 ＝diag(Δ 2,1 ,Δ 2,2 ,Δ 2,3 ) Are known.
Finally, a first controller rho is obtained 1 Is composed of
In the specific implementation of S3: adding water flow interference, and re-deducing the first controller according to the second dynamic model to obtain a second controller, wherein the second controller contains an unknown item;
specifically, the second dynamic model is used, the first dynamic model in the step S23 is replaced by the second dynamic model, and then the steps S21 to S23 are executed to obtain the second controller.
Replacing the formula (3) with the formula (4), namely replacing the first dynamic model with the second dynamic model, and re-executing S21-S23 to obtain the second controller rho 2 The following:
it is easy to see that ρ 2 ＝ρ 1 Namely, after the water flow disturbance vector is added, the expression of the controller is not changed, and the water flow disturbance is reduced. Meanwhile, the unknown items are replaced by the estimated values of the unknown items, and the estimated values can be obtained through calculation, so that on one hand, the controllability of the controller design is improved, the influence of the unknown items is reduced, and on the other hand, required parameters are reduced to a certain extent.
In the specific implementation of S4: selecting a fuzzy membership function according to the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, and calculating to obtain a fuzzy basis function by utilizing a fuzzy basis function calculation rule according to the fuzzy membership function; the step comprises the following substeps:
s41: selecting the domains of longitudinal speed, transverse speed and yaw rate of the AUV;
specifically, the domains of longitudinal velocity, transverse velocity and yaw rate of the AUV are limited in small intervals symmetrical about the origin, the specific length of the intervals can be selected according to the final path tracking effect, and the domains are selected as [ -3,3].
S42: selecting fuzzy membership functions, wherein the independent variables of the fuzzy membership functions are respectively the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, the central point is an odd number of points which are uniformly distributed in the discourse domain of the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, and the width is a determined normal number, so that three groups of fuzzy membership functions are obtained;
specifically, for the selection of the fuzzy membership function, the following rule should be satisfied:
1) Each pair of
All need to be overlapped;
2) Whole fuzzy membership function sequence
The domain of discourse that needs to cover the argument x;
3) The number of fuzzy membership function is odd number, usually 5, 7, 9, 11, the central point is distributed uniformly in the domain, the width is non-negative number, and it can be selected by oneself.
The method selects a Gaussian basis function as a fuzzy membership function, respectively takes the longitudinal speed u, the transverse speed v and the yaw rate r of the AUV as independent variables, uniformly sets the width as 2, and can obtain three groups of fuzzy membership functions, wherein each group comprises 7. The method comprises the following specific steps:
a fuzzy membership function of the longitudinal velocity u of
A fuzzy membership function of the transverse velocity v of
The fuzzy membership function of the yaw rate r is
S43: and substituting the fuzzy membership function into a fuzzy basis function calculation rule to obtain a fuzzy basis function.
Specifically, the fuzzy basis function calculation rule is as follows:
and (3) respectively substituting the 7 pairs of fuzzy membership functions into a formula (18) to obtain 7 fuzzy basis functions. Compared with the existing neural network base functions, the fuzzy base functions need fewer numbers, a single fuzzy base function can contain all independent variables, and the same effect as the neural network base functions can be achieved.
In the specific implementation of S5: replacing the unknown item with the fuzzy basis function; the step comprises the following substeps:
s51: arranging the fuzzy basis functions in sequence to form a fuzzy basis function column vector, wherein the dimensionality of the fuzzy basis function column vector is the number of the central points of the fuzzy membership function;
specifically, the fuzzy basis function column vector φ = [ ] 1 ,φ 2 ,φ 3 ,φ 4 ,φ 5 ,φ 6 ,φ 7 ] T The 7 fuzzy basis functions included in the column vector are calculated by equation (18) of S43.
S52: multiplying the fuzzy basis function column vector by the transpose of a weight vector in a neural network to obtain an estimated value of the unknown item; according to the RBFNN, obtaining an updating rule of each element in the weight vector by using a gradient descent algorithm, thereby obtaining the weight vector;
specifically, for an unknown nonlinear AUV, consider a general approximation method of an unknown nonlinear function: radial basis functionA digital neural network (RBFNN) to estimate the second controller ρ 2 The unknown item f (V).
It is known that for any given continuous non-linear function g i (x) And any normal number
There is one RBFNN
The following inequality holds:
where x represents the input vector to RBFNN,
is a weight vector, phi i (x)＝[φ i,1 (x),...,φ i,H (x)] T Is a neural network basis function. H represents the number of neural network nodes. The invention needs to replace the neural network basis function with the fuzzy basis function because of using the fuzzy method.
Defining an optimal weight vector
Is composed of
Wherein
Is the output of RBFNN.
The minimum approximation error can be expressed as
And satisfy
The invention deals with the unknown item f (V) in the second controller, namely, f (V) is replaced by the estimated value of the unknown item
Obtained according to the formula (21)
f(V)＝θ *T φ+δ (22)
Where φ is the fuzzy basis function column vector, δ = [ d ] 1 ,δ 2 ,δ 3 ] T For the minimum approximation error column vector, θ * The optimal weight matrix is a matrix with the dimension of phi as the row number and the dimension of f (V) as the column number. For ease of analysis, f (V) is rewritten to
Wherein
i =1,2,3 is the column vector of the optimal weight matrix.
Given the uncertainty of the unknown term f (V), the subsequent process cannot directly use equation (14), which can be rewritten to author
Wherein (. DELTA.e) 2 )/(Δt)＝(e 2 (t)-e 2 (t-l))/l is e 2 Wherein step l > 0.
The following error vectors are defined:
by substituting (15), (17) and (23) into (14),
can be re-expressed as
Substituting (24) and (26) into (25) to obtain
Minimizing an error cost function R i ＝0.5E i 2 I =1,2,3, and according to the gradient descent algorithm, the weight update rule can be obtained as follows:
μ i i =1,2,3 is a known parameter,
namely, the weight vector is a 7-dimensional column vector and a weight matrix
A matrix of 7 rows and 3 columns.
S53: and bringing the estimated value into the second controller to replace the unknown item.
Specifically, the estimated value of the unknown item
Replacing the unknown f (V) to get the final form of the second controller:
the subsequent steps involving the second controller are all using equation (29).
In the specific implementation of S6: setting a reference path as a tracking path of the AUV, and performing path tracking by using the second controller after replacing the unknown item; the method comprises the following substeps:
s61: setting a reference horizontal and vertical coordinate as a bounded function of time, solving an arctangent value of a derivative ratio related to the time by the bounded function of the horizontal and vertical coordinate to obtain a reference yaw angle, and forming a reference signal by the reference horizontal and vertical coordinate and the reference yaw angle to be used as a reference path;
specifically, in order to ensure the stability of path tracking, it is necessary to refer to the abscissa x t And ordinate y t Selected as a bounded function, the invention selects (x) t ,y t ) = (1.2 sin (t), -1.2cos (t)), reference yaw angle ψ t The calculation is as follows:
final reference path η t ＝[x t ,y t ,ψ t ] T ＝[1.2sin(t),-1.2cos(t),0.5π-t] T And so on.
S62: selecting water flow interference according to the reference signal, and ensuring that the water flow interference is smaller than the reference signal and has boundedness;
specifically, since in practical applications the magnitude of the water flow disturbance should be smaller than the reference path, according to the reference path, the water flow vector h = [0.14sin (π t + 0.3), 0.1sin (3t + 0.2), 0.2sin (4 t-0.5)] T The boundedness of the water flow interference also ensures the stability of path tracking.
S63: and substituting the second controller after the unknown item is replaced into the second dynamic model, and performing path tracking on the reference signal.
Specifically, equation (29) is substituted into equation set (4), and combined with (6), (11), (15), (28), a simultaneous differential equation set is obtained. By solving the system of differential equations, the reference abscissa x is observed separately t Ordinate y t Yaw angle psi t Tracking effect ofAnd if the three speeds and the change trend of the first error tracking vector exist, the effect can be observed by drawing a path tracking graph.
To illustrate the effectiveness of the method of the invention more effectively, all the parameters and parameter matrices are initialized as shown in table 1, and the inertia matrix M, coriolis matrix and centripetal acceleration C (V), damping matrix D (V) are as follows:
d 11 (V)＝0.7225+1.3274|u|+5.8664u 2
d 22 (V)＝0.8612+36.2823|v|+8.05|r|
d 23 (V)＝-0.1079+0.845|v|+3.45|r|
d 32 (V)＝-0.1052-5.0437|v|-0.13|r|
d 33 (V)＝1.9-0.08|v|+0.75|r|
TABLE 1 parameters and parameter initialization
Example (b): AUV adaptive fuzzy control with water flow interference
The unknown non-linear AUV model simulation with the water flow disturbance is shown in FIGS. 2-6, and the tracking performance of the position and the heading is satisfactory, as can be seen from FIGS. 2-4. Fig. 5 shows that the three types of speeds, namely the longitudinal speed u, the transverse speed v and the yaw rate r, are bounded and approximately show a periodic variation trend. As can be seen from fig. 6, the larger deviation of the tracking error from the initial moment gradually tends to be bounded and stable over time, and although the effect is slightly worse than the case of no water flow disturbance, the overall situation is satisfactory.
Corresponding to the foregoing embodiments of the adaptive fuzzy AUV stable tracking control method, the present application also provides embodiments of an adaptive fuzzy AUV stable tracking control apparatus.
Fig. 7 is a block diagram illustrating an apparatus for adaptive fuzzy AUV stable tracking control, according to an exemplary embodiment. Referring to fig. 7, the apparatus includes:
the establishing module 21 is used for establishing a first dynamic model of the AUV under no water flow disturbance and a second dynamic model under water flow disturbance, wherein three unknown state variables exist in the first dynamic model and the second dynamic model and respectively represent the longitudinal speed, the transverse speed and the yaw rate of the AUV;
a design module 22 configured to design a first controller according to the first dynamic model under no water flow disturbance, so that the controller has stability;
a derivation module 23, configured to add water flow disturbance, and re-derive the first controller according to the second dynamic model to obtain a second controller, where the second controller includes an unknown item;
the calculation module 24 is configured to select a fuzzy membership function according to the longitudinal speed, the transverse speed, and the yaw rate of the AUV, and calculate a fuzzy basis function according to the fuzzy membership function and by using a fuzzy basis function calculation rule;
a replacement module 25, configured to replace the unknown item with the fuzzy basis function;
and the tracking module 26 is used for setting a reference path as a tracking path of the AUV, and performing path tracking by using the second controller after the unknown item is replaced.
With regard to the apparatus in the above-described embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment related to the method, and will not be elaborated here.
For the device embodiments, since they substantially correspond to the method embodiments, reference may be made to the partial description of the method embodiments for relevant points. The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the scheme of the application. One of ordinary skill in the art can understand and implement it without inventive effort.
Correspondingly, the present application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when executed by the one or more processors, cause the one or more processors to implement the adaptive fuzzy AUV stable tracking control method as described above.
Accordingly, the present application also provides a computer readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the adaptive fuzzy AUV stable tracking control method as described above.
Other embodiments of the present application will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the application and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the application being indicated by the following claims.
It will be understood that the present application is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the application is limited only by the appended claims.
Claims (10)
1. A self-adaptive fuzzy AUV stable tracking control method is characterized by comprising the following steps:
establishing a first dynamic model of the AUV under the condition of no water flow disturbance and a second dynamic model under the condition of water flow disturbance, wherein three unknown state variables exist in the first dynamic model and the second dynamic model and respectively represent the longitudinal speed, the transverse speed and the yaw rate of the AUV;
under the condition of no water flow disturbance, designing a first controller according to the first dynamic model, so that the controller has stability;
adding water flow interference, and re-deducing the first controller according to the second dynamic model to obtain a second controller, wherein the second controller contains an unknown item;
selecting a fuzzy membership function according to the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, and calculating to obtain a fuzzy basis function by utilizing a fuzzy basis function calculation rule according to the fuzzy membership function;
replacing the unknown item with the fuzzy basis function;
and setting a reference path as a tracking path of the AUV, and performing path tracking by using the second controller after the unknown item is replaced.
2. The method of claim 1, wherein establishing a first kinetic model of the AUV in the absence of water flow disturbance and a second kinetic model of the AUV in the presence of water flow disturbance comprises:
selecting the horizontal and vertical coordinates and the yaw angle of the AUV as three degrees of freedom of AUV plane motion;
constructing a differential equation of a horizontal coordinate, a vertical coordinate and a yaw angle of the AUV by using the longitudinal speed, the transverse speed and the yaw angle speed of the AUV;
constructing a relational expression of a controller and the longitudinal speed, the transverse speed and the yaw rate of the AUV by using an inertia matrix, a damping matrix, a Coriolis matrix and a centripetal acceleration matrix;
according to the differential equation and the relational expression, a first dynamic model under no water flow disturbance is constructed;
and adding the relation into a water flow interference vector, and constructing with the differential equation to obtain a second dynamic model under water flow disturbance.
3. The method of claim 1, wherein designing a first controller from the first kinetic model in the absence of a water flow disturbance comprises:
s21: forming a position vector of the AUV by using a horizontal coordinate and a vertical coordinate of the AUV and a yaw angle, forming a speed vector of the AUV by using a longitudinal speed, a horizontal speed and a yaw angle of the AUV, using a difference between the position vector and a reference position vector as a first error tracking vector, using a difference between the speed vector and the output of a command filter as a second error tracking vector, and obtaining the output of the command filter according to an equation of a command filtering technology;
s22: introducing a first error compensation vector and a second error compensation vector, taking the difference between the first error tracking vector and the first error compensation vector as a first error vector, and taking the difference between the second error tracking vector and the second error compensation vector as a second error vector;
s23: combining the first error compensation vector, the second error compensation vector, and the first kinetic model into the first error vector and the second error vector to obtain a first controller, the first controller having stability.
4. The method of claim 3, wherein adding a flow disturbance and re-deriving the first controller from the second kinetic model to obtain a second controller comprises:
and replacing the first dynamic model in the S23 with the second dynamic model by utilizing the second dynamic model, and executing S21-S23 to obtain a second controller.
5. The method of claim 1, wherein selecting a fuzzy membership function according to the longitudinal velocity, the lateral velocity and the yaw rate of the AUV, and calculating a fuzzy basis function according to the fuzzy membership function and a fuzzy basis function calculation rule, comprising:
selecting the domains of longitudinal speed, transverse speed and yaw rate of the AUV;
selecting fuzzy membership functions, wherein the independent variables of the fuzzy membership functions are respectively the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, the central point is an odd number of points which are uniformly distributed in the discourse domain of the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, and the width is a determined normal number, so that three groups of fuzzy membership functions are obtained;
and substituting the fuzzy membership function into a fuzzy basis function calculation rule to obtain a fuzzy basis function.
6. The method of claim 1, wherein replacing the unknown term with the fuzzy basis function comprises:
arranging the fuzzy basis functions in sequence to form a fuzzy basis function column vector, wherein the dimensionality of the fuzzy basis function column vector is the number of the central points of the fuzzy membership function;
multiplying the fuzzy basis function column vector by the transpose of the weight vector in the neural network to obtain the estimation value of the unknown item; according to the RBFNN, obtaining an updating rule of each element in the weight vector by using a gradient descent algorithm, thereby obtaining the weight vector;
and bringing the estimated value into the second controller to replace the unknown item.
7. The method of claim 1, wherein setting a reference path as a tracking path of the AUV, and performing path tracking by using the second controller after replacing the unknown item comprises:
setting a reference horizontal and vertical coordinate as a bounded function of time, solving an arctangent value of a derivative ratio related to the time by the bounded function of the horizontal and vertical coordinate to obtain a reference yaw angle, and forming a reference signal by the reference horizontal and vertical coordinate and the reference yaw angle to be used as a reference path;
selecting water flow interference according to the reference signal, and ensuring that the water flow interference is smaller than the reference signal and has boundedness;
and substituting the second controller after the unknown item is replaced into the second dynamic model, and performing path tracking on the reference signal.
8. An adaptive fuzzy AUV stable tracking control device, comprising:
the system comprises an establishing module, a judging module and a judging module, wherein the establishing module is used for establishing a first dynamic model of the AUV under no water flow disturbance and a second dynamic model under water flow disturbance, and three unknown state variables exist in the first dynamic model and the second dynamic model and respectively represent the longitudinal speed, the transverse speed and the yaw rate of the AUV;
the design module is used for designing a first controller according to the first dynamic model under the condition of no water flow disturbance, so that the controller has stability;
the derivation module is used for adding water flow interference, and re-deriving the first controller according to the second dynamic model to obtain a second controller, wherein the second controller contains an unknown item;
the calculation module is used for selecting a fuzzy membership function according to the longitudinal speed, the transverse speed and the yaw angular speed of the AUV, and then calculating to obtain a fuzzy basis function by utilizing a fuzzy basis function calculation rule according to the fuzzy membership function;
a replacement module for replacing the unknown item with the fuzzy basis function;
and the tracking module is used for setting a reference path as a tracking path of the AUV and carrying out path tracking by using the second controller after the unknown item is replaced.
9. An electronic device, comprising:
one or more processors;
a memory for storing one or more programs;
when executed by the one or more processors, cause the one or more processors to implement the method of any one of claims 1-7.
10. A computer-readable storage medium having stored thereon computer instructions, which when executed by a processor, perform the steps of the method according to any one of claims 1-7.
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