CN115167484A - Autonomous underwater vehicle model prediction path tracking method based on neural network - Google Patents
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Abstract
The invention relates to an autonomous underwater vehicle model prediction path tracking method based on a neural network, which is characterized in that on the basis of adopting a model prediction controller MPC to carry out path tracking control, an RBF neural network is trained on line by using real-time measurement data to compensate the uncertainty of an AUV model, the interference of the uncertainty of the model on the model prediction controller is inhibited, and the overshoot and tracking error of a system are reduced. Simulation results in MATLAB environment show that compared with a classical MPC algorithm, the RBF-MPC-based path tracking control algorithm has better transient and steady-state performance and better energy-saving effect.
Description
Technical Field
The invention relates to an autonomous underwater vehicle path tracking method, in particular to an autonomous underwater vehicle model prediction path tracking method based on a neural network.
Background
Autonomous Underwater Vehicles (AUV) are indispensable tools for people to know and explore the ocean field due to the characteristics of long range, high operation accuracy, reusability and the like, and are gradually and widely applied in recent years. The underwater recovery technology greatly improves the endurance of the AUV, and the accurate path tracking is the key for realizing the underwater recovery.
At present, algorithms widely applied in the field of path tracking control comprise a PID control algorithm, a sliding mode control algorithm, an optimal control algorithm and the like, but the algorithms have higher dependence degree on parameters and environment of a control object, and once the outside is slightly changed, path tracking cannot be well continued in a new state; in addition, the above algorithm is difficult to handle for kinematic constraints and actuator constraints on the AUV during motion. The model predictive control is an algorithm for obtaining an optimal solution under various constraint conditions, and has the advantages of simple parameter selection, strong processing constraint capability, realization of multi-objective optimization, calculation result satisfaction of optimality and the like. In addition, the predictive capability of the model predictive control on the future path is outstanding, which makes it gradually become a research hotspot.
The AUV model has the characteristics of multiple degrees of freedom, nonlinearity and strong coupling, and the additional mass, the inertia moment and the damping coefficient of partial water power in the AUV motion mathematical model are difficult to accurately determine. In addition, the AUV is often interfered by external factors such as unknown ocean currents during the course of navigation, and uncertainty is added to the AUV path tracking. The Radial Basis Function (RBF) neural network can quickly approach a system dynamics model, has a simpler structure, and has certain advantages in solving an optimal value problem compared with other neural network algorithms.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides an autonomous underwater vehicle model prediction path tracking method based on a neural network.
Technical scheme
An autonomous underwater vehicle model prediction path tracking method based on a neural network is characterized by comprising the following steps:
step 1: establishing an AUV model comprising a kinetic equation and a kinematic equation;
the AUV kinematic equation:
the AUV kinetic equation:
wherein x represents the forward displacement, y represents the lateral displacement, ψ represents the heading angle, v x And v y Forward and lateral speed, respectively, r course angular velocity of AUV, m 11 ＝M 11 ，m 22 ＝M 22 ，m 33 ＝M 33 ，d 11 ＝D 11 ，d 22 ＝D 22 ，d 33 ＝D 33 The elements in the inertia matrix M and the damping matrix D of the additional mass; n is the operating force generated by the operating surface;
step 2: an AUV path tracking controller based on MPC is constructed;
according to the requirement of AUV path tracking performance index, adopting MPC control algorithm, taking the AUV model in step 1 as a controlled object, obtaining the latest measurement state of the AUV at each sampling time k, predicting a control sequence in a time domain according to the requirement of minimum AUV tracking state error and minimum control input, finally selecting the 1 st element of the control sequence obtained by solving as the input quantity of the AUV model, re-obtaining the state of the AUV at the next sampling time after the time is over, and continuing the rolling optimization of the next period; the AUV path tracking objective may be represented as the following rolling optimization control problem:
constraint conditions are as follows:
x(k+1)＝f(x k ,u k ) (6)
y k ＝g(x k ) (7)
u min ≤u k ≤u max ,k＝1,...,N c (8)
x 0 ＝x(k) (9)
in the formula (5), R and Q represent weight matrices of control outputs and control inputs, respectively, and N p Indicates the prediction horizon, N c Denotes the control Range, y k Is AUV System status output y = [ v ] x x v y y r ψ] T ，v x And v y Forward and lateral speeds, respectively; r (k) is the desired instruction, i.e., the reference state to track; u is control input u = [ X0N ]] T Thrust X generated by the propeller and steering force N generated by the steering surface; the expressions (6) and (7) in the constraint represent the AUV model in step 1, x k ＝[v x v y r] T Represents 3 states; equation (9) represents the current state feedback of the system;
and step 3: approximation of AUV model uncertainty by RBF neural network
The RBF neural network structure comprises three different layers, wherein 5 nodes of an input layer, 7 nodes of a hidden layer and 3 nodes of an output layer are arranged; the RBF neural network calculates the prediction output y of the network by linearly combining the hidden layers, namely:
wherein h is a Gaussian activation function, w jq Is the weight vector from the jth hidden layer node to the qth output layer node, and m represents the number of hidden layer neurons;
input layer x = [ v ] of RBF neural network x v y r X N] T Output as a function of AUV modelDetermining the term Δ f (x) k ,u k ) According to the RBF neural network output expression (10), the AUV model uncertainty term can be obtained as follows:
Δf(x k ,u k )＝W T H(x k )+ε (11)
wherein W is a weight matrix from the hidden layer to the output layer, H is a vector formed by a Gaussian activation function H, and epsilon is a deviation term
And 4, step 4: an AUV path tracking controller based on RBF-MPC is constructed;
combining the AUV model in the step 1 and the AUV model uncertainty item described by the RBF in the step 3 to determine a real model of the AUV; on the basis of the real model, an MPC controller in the step 2 is adopted, a target function is constructed according to the requirements of minimum AUV tracking state error and minimum control input, and a control sequence in a prediction time domain is solved in an optimization mode by combining constraint conditions; finally, selecting the 1 st element of the control sequence obtained by solving as the input quantity of the system; after the moment is finished, the state of the AUV is obtained again at the next sampling moment, and the rolling optimization of the next period is continued; let vector x represent the state of the AUV and u represent the control input, the state update equation for the AUV can be described as:
x k+1 ＝f(x k ,u k ) (12)
then the true AUV model f true (x k ,u k ) Expressed as:
x k+1 ＝f nom (x k ,u k )+Δf(x k ,u k )＝f true (x k ,u k ) (13)
wherein, Δ f (x) k ,u k ) Representing the uncertainty in the AUV model using RBF approximation in step 3, f nom (x k ,u k ) The AUV model in step 1 is shown;
the path-tracing control problem of the AUV is therefore described as the following constrained dynamic optimization problem:
constraint conditions are as follows:
x k+1 ＝f nom (x k ,u k )+Δf(x k ,u k ) (15)
e(k+1)＝x k+1 -x ref (16)
u min ≤u k ≤u max ,k＝1,...,N c (17)
x 0 ＝x(k) (18)
in equation (14), R and Q are a weight matrix of a path tracking state deviation and a control input weight matrix, respectively, and equation (15) represents a real AUV system, x k ＝[v x v y r] T Represents 3 states, i.e. v x And v y Respectively the forward speed and the lateral speed, and r is the course angular speed of AUV; equation (16) represents a deviation value between the actual state and the reference state; equation (17) represents the control input u = [ X0N ] when solving the optimization problem] T The constraint range of (1); equation (18) represents the AUV current state feedback.
In the AUV path tracking control process, the model prediction controller obtains the AUV state value at the current moment through the sensor when the AUV performs path tracking; then predicting the state value of the AUV in the prediction time domain according to a prediction model, and optimally solving a control sequence in the prediction time domain through a constructed target function formula (14) in combination with constraint condition formulas (15), (16) and (17); finally, selecting the 1 st element of the control sequence obtained by solving as the input quantity of the system; and after the moment is finished, the state of the AUV is acquired again at the next sampling moment, and the rolling optimization of the next period is continued.
Preferably: m =7 in step 3.
Preferably: adjusting the weight w by gradient descent method jq 。
A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the above-described method.
A computer-readable storage medium having stored thereon computer-executable instructions for use in the above-described method when executed.
A computer program comprising computer executable instructions which when executed perform the method described above.
Advantageous effects
The invention provides an autonomous underwater vehicle Model Prediction path tracking method based on a neural network, which adopts a Model Prediction Controller (MPC) to carry out path tracking Control, utilizes real-time measurement data to train an RBF neural network on line, compensates the uncertainty of an AUV Model, inhibits the interference of the uncertainty of the Model on the Model Prediction controller, and reduces the overshoot and the tracking error of a system. Simulation results in MATLAB environment show that compared with a classical MPC algorithm, the RBF-MPC-based path tracking control algorithm has better transient and steady-state performance and better energy-saving effect.
Compared with the prior art, the method has the following beneficial effects:
1. due to strong nonlinearity and strong coupling of an underwater vehicle system, an AUV is difficult to establish an accurate system model in practice, and the model is compensated by adopting an RBF neural network, so that the model is closer to an AUV real model;
2. the RBF neural network and the MPC algorithm are combined and applied to the AUV path tracking control algorithm, so that the interference of model uncertainty on a model prediction controller is inhibited, and the overshoot and the tracking error of the system are reduced. Compared with a classical MPC algorithm, the method has better transient state and steady state performance and better energy-saving effect.
Drawings
The drawings, in which like reference numerals refer to like parts throughout, are for the purpose of illustrating particular embodiments only and are not to be considered limiting of the invention.
FIG. 1 AUV model;
FIG. 2 is a schematic view of an RBF neural network;
FIG. 3 is a schematic view of a RBF-MPC;
FIG. 4 path tracking control results;
FIG. 5 x orientation tracking bias comparison;
FIG. 6 y contrast in direction tracking bias;
FIG. 7 is a graph of control input force;
fig. 8 shows a control curve of the input torque.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention has the following implementation steps:
step 1: aiming at the research object AUV, a dynamics and kinematics model is established;
in order to facilitate subsequent research and analysis, coupling influence caused by horizontal plane motion and vertical plane motion of the under-actuated AUV is ignored, a nonlinear secondary damping term in a dynamic model is ignored, and dynamics and a motion equation of 3 degrees of freedom of the under-actuated AUV in a horizontal plane are established.
Step 2: constructing an MPC-based AUV path tracking controller: and (4) adopting an MPC control algorithm according to the AUV path tracking performance index requirement. The AUV model in the step 1 is a research object, the latest measurement state of the AUV is obtained at each sampling time k, a control sequence in a time domain is predicted according to the requirement of minimum error of the AUV tracking state and minimum control input, finally, the 1 st element of the control sequence obtained by solving is selected as the input quantity of the AUV model, the AUV state is obtained again at the next sampling time after the time is over, and the rolling optimization of the next period is continued.
And step 3: and describing uncertainty items of the model by using the RBF neural network: mass of AUV, water during actual voyageThe dynamic additional mass, moment of inertia, damping coefficient, etc. typically vary with operating conditions, including mission and environment. In addition, the strong non-linearity and the strong coupling of the underwater vehicle system make it difficult to build an accurate AUV model, thereby affecting the performance of its path tracking. Therefore, an RBF neural network is adopted to approximate the model uncertainty. The RBF neural network part is in a form of 5-7-3, namely 5 nodes of an input layer, 7 nodes of a hidden layer, 3 nodes of an output layer and an output are model uncertainty items delta f (x) of AUV k ,u k )。
And 4, step 4: an AUV path tracking controller based on RBF-MPC is constructed: and combining the AUV nominal model in the step 1 and the model uncertainty item described by the RBF in the step 3 to determine a real model of the AUV. On the basis of the real model, the MPC controller in the step 2 is adopted, an objective function is constructed according to the requirement of minimum AUV tracking state error and minimum control input, and a control sequence in a prediction time domain is solved in an optimization mode by combining constraint conditions; and finally, selecting the 1 st element of the control sequence obtained by solving as the input quantity of the system. And after the moment is finished, the state of the AUV is acquired again at the next sampling moment, and the rolling optimization of the next period is continued.
Two coordinate systems are typically used in step 1 to describe the motion of the AUV: a ground coordinate system and a vehicle coordinate system. The origin O of the ground coordinate system is fixed at one place on the earth, and OX is defined as positive to east and OY is defined as positive to north. Origin O of the vehicle coordinate system B Selecting the floating center of AUV, and defining O B X B Along the longitudinal axis of the AUV and pointing in the heading, O B Y B Perpendicular thereto, positive to the right. As shown in FIG. 1, the forward displacement is represented by x, y Indicating lateral displacement, # indicating heading angle, v x And v y Defining a generalized coordinate vector eta = [ x y ψ ] for forward and lateral velocities, respectively, r is the heading angular velocity of the AUV] T Generalized velocity vector v = [ v ] x v y r] T The equation of motion of the AUV on the horizontal plane is obtained as follows:
where M is an inertial matrix with additional mass, C (v) is a matrix of Copenforces and centripetal forces, D (v) is a damping matrix, and τ is the forces and moments generated in the three degrees of freedom, under-actuation is studied in the present invention and therefore represents the thrust generated by the propeller and the steering forces generated by the steering surfaces.
If the AUV is symmetric in front and back and left and right, the following are provided:
τ＝[X Y N] T ＝[X 0 N] (7)
from this, the kinematic equation and the kinetic equation of the underactuated AUV on the horizontal plane are respectively expressed as:
and
in the formula, m 11 ＝M 11 ,m 22 ＝M 22 ,m 33 ＝M 33 ,d 11 ＝D 11 ,d 22 ＝D 22 ,d 33 ＝D 33 The partial elements in the matrix D are damped for the inertial matrix M of the additional mass.
The AUV path tracking target in step 2 can be represented as the following rolling optimization control problem:
constraint conditions are as follows:
x(k+1)＝f(x k ,u k ) (11)
y k ＝g(x k ) (12)
u min ≤u k ≤u max ,k＝1,...,N c (13)
x 0 ＝x(k) (14)
in the formula (10), R and Q represent weight matrices of control outputs and control inputs, respectively, and N p Indicates the prediction horizon, N c Denotes the control range, y k Is AUV System State output v x x v y y r ψ] T ，v x And v y Respectively a forward speed and a lateral speed, r is a course angular velocity of AUV, x represents a forward displacement, y Lateral displacement is represented, and psi is a heading angle; r (k) is the desired instruction, the reference state to track; equations (11) and (12) in the constraint represent the system prediction model, x k ＝[v x v y r] T Representing 3 states, constraint (13) is input of control amount u = [ X0N ]] T The amplitude of (a), namely the thrust X generated by the propeller and the steering force N generated by the steering surface; equation (14) represents the system current state feedback.
The RBF network structure in step 3 is shown in fig. 2, and the structure includes three different layers, where n is the number of nodes of the input layer, m is the number of nodes of the hidden layer, and l is the number of nodes of the hidden layer. For the present invention, 5 nodes of an input layer, i.e., n =5, 7 nodes of a hidden layer, i.e., m =7, and 3 nodes of an output layer, i.e., l =3 are set.
The application of the Gaussian function as the activation function in the RBF neural network is very wide, and as the most commonly used base function, the Gaussian function selects the weight according to the distance between the central points of the input layer and the hidden layer, so that the calculation precision of the Gaussian function is higher, and the model can be more effectively approximated j The calculation method is as follows:
wherein, | | x-c j I means x and c j Euclidean distance between them, the RBF neural network takes the center (c) j ) And width (σ) j ) Is a gaussian basis function of the parameter.
Center value c j For the Gaussian base function center point vector value of the j hidden layer neural node:
c j ＝[c 1j …c nj ] T (16)
width sigma j Width of Gaussian basis function, σ, representing hidden layer j ＝[σ 1 ,σ 2 ,…,σ l ] T The sigma value is larger, the Gaussian function is wider, and the network has stronger mapping capability to the input.
The structure diagram of the RBF network is shown in fig. 3, and the RBF calculates the prediction output y of the network by linearly combining hidden layers, that is:
where h is the Gaussian activation function, w jq Is the jth hidden layer node to the jthThe weight vector of q output layer nodes is adjusted by adopting a gradient descent method jq 。
Specifically, in the present invention, the RBF neural network portion is in the form of 5-7-3, that is, there are 5 nodes in the input layer, and the input layer x = [ v ] x v y r X N] T The number of hidden layer nodes is 7, the number of output layer nodes is 3, and the output is the model uncertainty item delta f (x) of AUV k ,u k )。
According to the RBF neural network output expression (17), the AUV model uncertainty term can be obtained as follows:
Δf(x k ,u k )＝W T H(x k )+ε (18)
wherein W is a weight matrix from the hidden layer to the output layer, and H is a vector formed by Gaussian activation function H, i.e. H = [ H ] 1 h 2 …h m ] T And ε is a bias term.
The parameter learning rate eta of the RBF neural network =0.10, the momentum factor alpha =0.05, the base width parameter b =50, and the central vector value:
the weight matrix is:
and 4, step 4: an AUV path tracking controller based on RBF-MPC is constructed: let vector x represent the state of the AUV and u represent the control input, the state update equation for the AUV can be described as:
x k+1 ＝f(x k ,u k ) (21)
Δf(x k ,u k ) Representing the uncertainty in the AUV model using RBF approximation in step 3, f nom (x k ,u k ) Representing the nominal AUV model in step 1, the true AUV model f true (x k ,u k ) Expressed as:
x k+1 ＝f nom (x k ,u k )+Δf(x k ,u k )＝f true (x k ,u k ) (22)
the path-tracing control problem of an AUV can thus be described as the following constrained dynamic optimization problem:
constraint conditions are as follows:
x k+1 ＝f nom (x k ,u k )+Δf(x k ,u k ) (24)
e(k+1)＝x k+1 -x ref (25)
u min ≤u k ≤u max ,k＝1,...,N c (26)
x 0 ＝x(k) (27)
in the formula (23), R and Q are a weight matrix of the path tracking state deviation and a control input weight matrix, respectively, and the formula (24) represents a real AUV system, x k ＝[v x v y r] T Represents 3 states, i.e. v x And v y Respectively the forward speed and the lateral speed, and r is the course angular speed of AUV; equation (25) represents a deviation value between the actual state and the reference state; equation (26) represents the control input u = [ X0N ] when solving the optimization problem] T The constraint range of (1); equation (27) represents the AUV current state feedback.
In the AUV path tracking control process, the model prediction controller obtains the AUV state value at the current moment through the sensor when the AUV performs path tracking; then predicting the state value of the AUV in the prediction time domain according to a prediction model, and optimally solving a control sequence in the prediction time domain through a constructed target function formula (23) in combination with constraint condition formulas (24), (25) and (26); and finally, selecting the 1 st element of the control sequence obtained by solving as the input quantity of the system. And after the moment is finished, the state of the AUV is acquired again at the next sampling moment, and the rolling optimization of the next period is continued.
Based on the theory, under an MATLAB simulation environment, a reference path is given, a classical MPC control method and a RBF-MPC control method are respectively adopted, and tracking effects of the two methods on the reference path are compared by observing various state parameters of AUV under the two controllers. With the REMUS AUV model, the actual mass of the AUV was 30.5kg, and the mass of the AUV in the controller was set to 23.5kg in the simulation experiment. The initial position of the AUV is (10 m, -10 m), the sequentially reached target position is (17 m, -56 m), (187 m, -146 m), (208 m, -234 m), (334m, 414m), (488 m, -488 m), (980 m, -980 m), the initial heading angle is 0, the sampling interval T =0.1 of the controller, the predicted step length N =50, and the simulation time is 360s.
As can be seen from FIG. 4, both controllers can better complete the tracking task, and as can be seen from the enlarged partial view, both controllers can generate smooth motion tracks, but the difference between the two controllers is very obvious at the turning point. Whether the path-tracing segment is the first corner path-tracing segment with the abscissa of 30-80m or the path-tracing segment is the second corner path-tracing segment with the abscissa of 350-400m, the RBF-MPC controller has smaller overshoot than the MPC controller, can reduce the error between the reference path and the expected path more rapidly and has better tracing performance.
In order to further clearly see the difference of the tracking effect of the MPC controller and the RBF-MPC controller, the tracking deviation of the horizontal and vertical positions and the heading angle deviation results are shown in FIGS. 5 and 6. The position deviation of the MPC controller in the x direction can reach 21.5m at most, and the RBF-MPC controller can reduce the error to 11.9m, and the error is reduced by nearly 50%; the effect of the RBF-MPC controller is also significant in the y-direction position error, especially between 18s and 75 s; also, the deviation of the heading angle is more obvious at the peak. Therefore, it can be seen that the model uncertainty causes a large steady-state error to exist in the MPC controller, and after the MPC controller is added into the neural network compensation, the overshoot is obviously reduced, and the MPC controller can reach a steady state more quickly. Fig. 8 shows the control input force and torque curves of the AUV using two controllers. From a trend point of view, the two controllers remain substantially the same, but the fluctuations produced by the MPC controller are more pronounced. The results show that the MPC controller simplifies the model of the underwater vehicle, has larger modeling error, so the path tracking control error is larger, and compared with the MPC controller which does not use the RBF neural network for model approximation training, the RBF-MPC controller designed by the invention has better tracking effect.
It can be concluded from this that the RBF-MPC controller can provide better performance than a general MPC controller in the presence of modeling errors or significant uncertainties, and the performance of the control system is significantly improved after the neural network model is identified.
The changes in control input force and torque using the MPC controller and the RBF-MPC controller are shown in FIGS. 7 and 8. From the aspect of the change trend, the RBF-MPC controller generates smaller input fluctuation, the difference is obvious particularly at the peak values of 10s, 59s and 66s, and in the steady state stage, the RBF-MPC controller obtains a smoother control input, consumes less energy and is more beneficial to long-time underwater operation of the AUV.
In conclusion, under the condition that model uncertainty and disturbance exist, the RBF-MPC has smaller path tracking overshoot and smaller steady-state error in the aspect of control effect; in the aspect of control input, the input amplitude is smaller, and the energy is saved. Compared with the traditional MPC controller, the comprehensive advantages are obvious.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.
Claims (6)
1. An autonomous underwater vehicle model prediction path tracking method based on a neural network is characterized by comprising the following steps:
step 1: establishing an AUV model comprising a kinetic equation and a kinematic equation;
the AUV kinematic equation:
the AUV kinetic equation:
wherein x represents the forward displacement, y represents the lateral displacement, ψ represents the heading angle, v x And v y Forward and lateral speed, respectively, r course angular velocity of AUV, m 11 ＝M 11 ，m 22 ＝M 22 ，m 33 ＝M 33 ，d 11 ＝D 11 ，d 22 ＝D 22 ，d 33 ＝D 33 The elements in the inertia matrix M and the damping matrix D of the additional mass; n is the operating force generated by the operating surface;
step 2: an AUV path tracking controller based on MPC is constructed;
according to the AUV path tracking performance index requirement, adopting an MPC control algorithm, taking the AUV model in the step 1 as a controlled object, acquiring the latest measurement state of the AUV at each sampling time k, predicting a control sequence in a time domain according to the requirements of minimum AUV tracking state error and minimum control input, finally selecting the 1 st element of the control sequence obtained by solving as the input quantity of the AUV model, re-acquiring the state of the AUV at the next sampling time after the time is ended, and continuing the rolling optimization of the next period; the AUV path tracking objective may be represented as the following rolling optimization control problem:
constraint conditions are as follows:
x(k+1)＝f(x k ,u k ) (6)
y k ＝g(x k ) (7)
u min ≤u k ≤u max ,k＝1,...,N c (8)
x 0 ＝x(k) (9)
in the formula (5), R and Q represent weight matrices of control outputs and control inputs, respectively, and N p Indicates the prediction horizon, N c Denotes the control Range, y k Is AUV System status output y = [ v ] x x v y y r ψ] T ，v x And v y Forward and lateral speeds, respectively; r (k) is the desired instruction, i.e., the reference state to track; u is control input u = [ X0N =] T Thrust X generated by the propeller and steering force N generated by the steering surface; the expressions (6) and (7) in the constraint represent the AUV model in step 1, x k ＝[v x v y r] T Represents 3 states; equation (9) represents the current state feedback of the system;
and 3, step 3: approximation of AUV model uncertainty by RBF neural network
The RBF neural network structure comprises three different layers, wherein 5 nodes of an input layer, 7 nodes of a hidden layer and 3 nodes of an output layer are arranged; the RBF neural network computes the predicted output y of the network by linearly combining the hidden layers, namely:
where h is the Gaussian activation function, w jq Is the weight vector from the jth hidden layer node to the qth output layer node, and m represents the number of hidden layer neurons;
input layer x = [ v ] of RBF neural network x v y r X N] T The output is the uncertainty term delta f (x) of the AUV model k ,u k ) According to the RBF neural network output expression (10), the AUV model uncertainty term can be obtained as follows:
Δf(x k ,u k )＝W T H(x k )+ε (11)
wherein W is a weight matrix from the hidden layer to the output layer, H is a vector formed by a Gaussian activation function H, and epsilon is a deviation term
And 4, step 4: an AUV path tracking controller based on RBF-MPC is constructed;
combining the AUV model in the step 1 and the AUV model uncertainty item described by the RBF in the step 3 to determine a real model of the AUV; on the basis of the real model, an MPC controller in the step 2 is adopted, a target function is constructed according to the requirements of minimum AUV tracking state error and minimum control input, and a control sequence in a prediction time domain is solved in an optimization mode by combining constraint conditions; finally, selecting the 1 st element of the control sequence obtained by solving as the input quantity of the system; after the moment is finished, the state of the AUV is obtained again at the next sampling moment, and the rolling optimization of the next period is continued; let vector x represent the state of the AUV and u represent the control input, the state update equation for the AUV can be described as:
x k+1 ＝f(x k ,u k ) (12)
then the true AUV model f true (x k ,u k ) Expressed as:
x k+1 ＝f nom (x k ,u k )+Δf(x k ,u k )＝f true (x k ,u k ) (13)
wherein, Δ f (x) k ,u k ) Representing the uncertainty in the AUV model using RBF approximation in step 3, f nom (x k ,u k ) The AUV model in step 1 is shown;
the path-tracing control problem of the AUV is therefore described as the following constrained dynamic optimization problem:
constraint conditions are as follows:
x k+1 ＝f nom (x k ,u k )+Δf(x k ,u k ) (15)
e(k+1)＝x k+1 -x ref (16)
u min ≤u k ≤u max ,k＝1,...,N c (17)
x 0 ＝x(k) (18)
in equation (14), R and Q are a weight matrix of a path tracking state deviation and a control input weight matrix, respectively, and equation (15) represents a real AUV system, x k ＝[v x v y r] T Represents 3 states, i.e. v x And v y Respectively the forward speed and the lateral speed, and r is the course angular speed of AUV; equation (16) represents a deviation value between the actual state and the reference state; equation (17) represents the control input u = [ X0N ] when solving the optimization problem] T The constraint range of (1); equation (18) represents the AUV current state feedback.
In the AUV path tracking control process, the model prediction controller obtains the AUV state value at the current moment through the sensor when the AUV performs path tracking; then predicting the state value of the AUV in the prediction time domain according to a prediction model, and optimally solving a control sequence in the prediction time domain through a constructed target function formula (14) in combination with constraint condition formulas (15), (16) and (17); finally, selecting the 1 st element of the control sequence obtained by solving as the input quantity of the system; and after the moment is finished, the state of the AUV is acquired again at the next sampling moment, and the rolling optimization of the next period is continued.
2. The neural network based autonomous underwater vehicle model predictive path tracking method as claimed in claim 1, characterized in that m =7 in step 3.
3. The neural network-based autonomous underwater vehicle model predicted path tracking method of claim 1, characterized in that the weight w is adjusted by gradient descent method jq 。
4. A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of claim 1.
5. A computer-readable storage medium having stored thereon computer-executable instructions, which when executed, perform the method of claim 1.
6. A computer program comprising computer executable instructions which when executed perform the method of claim 1.
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