CN115167484B - 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 path tracking control by adopting a model prediction controller MPC, an RBF neural network is trained on line by utilizing real-time measurement data, the uncertainty of an AUV model is compensated, the interference of the model uncertainty on the model prediction controller is restrained, and the overshoot and tracking error of a system are reduced. Simulation results in MATLAB environment show that the RBF-MPC-based path tracking control algorithm has better transient state, steady state performance and better energy-saving effect compared with the classical MPC algorithm.
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 (Autonomous Underwater Vehicles, AUV) are widely used in recent years due to their long range, high operation accuracy, reusability, etc., which are indispensable tools for people to recognize and explore the ocean field. The underwater recovery technology greatly improves the AUV endurance, and accurate path tracking is a key for realizing underwater recovery.
At present, algorithms which are 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 on parameters of a control object and environment, and once the outside is slightly changed, path tracking cannot be well continued in a new state; in addition, the above algorithm is also difficult to handle with respect to the kinematic constraints and actuator constraints that the AUV is subject to during motion. The model predictive control is an algorithm for obtaining the optimal solution under various constraint conditions, and has the advantages of simple parameter selection, strong constraint processing capability, realization of multi-objective optimization, satisfaction of the optimal calculation result and the like. In addition, the predictive ability of model predictive control on future paths is prominent, which also makes it increasingly a research hotspot.
The AUV model has the characteristics of multiple degrees of freedom, nonlinearity and strong coupling, and the part of hydrodynamic additional mass, inertia moment and damping coefficient in the AUV motion mathematical model are difficult to accurately determine. In addition, during the navigation process, the AUV is often interfered by the outside, such as unknown ocean currents, so that uncertainty is added to the AUV path tracking. The radial basis (Radial Basis Function, RBF) neural network can quickly approximate the system dynamics model, has simpler structure, and has certain advantages in solving the problem of optimal values 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 proposal
The autonomous underwater vehicle model prediction path tracking method based on the neural network is characterized by comprising the following steps of:
Step 1: establishing an AUV model, wherein the AUV model comprises a dynamics equation and a kinematics equation;
the AUV kinematics equation:
the AUV dynamics equation:
Wherein x represents forward displacement, y represents lateral displacement, ψ represents course angles, v x and v y are respectively forward speed and lateral speed, r is the course angular velocity ,m11＝M11,m22＝M22,m33＝M33,d11＝D11,d22＝D22,d33＝D33, of the AUV, and is an element in an inertial matrix M and a damping matrix D of additional mass; n is the operating force generated by the operating surface;
Step 2: constructing an AUV path tracking controller based on MPC;
According to the AUV path tracking performance index requirement, an MPC control algorithm is adopted, an AUV model in the step 1 is used as a controlled 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 that the AUV tracking state error is minimum and the control input is minimum, and finally the 1 st element of the control sequence obtained by solving is selected as the input quantity of the AUV model, the state of the AUV is obtained again at the next sampling time after the time is over, and the rolling optimization of the next period is continued; the AUV path tracking target may be expressed as the following roll optimization control problem:
constraint conditions:
x(k+1)＝f(xk,uk) (6)
yk＝g(xk) (7)
umin≤uk≤umax,k＝1,...,Nc (8)
x0＝x(k) (9)
In the formula (5), R and Q represent weight matrices of control output and control input, respectively, N p represents a prediction range, N c represents a control range, y k is AUV system state output y= [ v x x vy y r ψ]T,vx and v y are forward speed and lateral speed, respectively; r (k) is the desired instruction, i.e. the reference state to be tracked; u is a control input u= [ X0N ] T, namely a thrust force X generated by the propeller and an operating force N generated by the operating surface; equations (6) and (7) in the constraint represent the AUV model in step 1, x k＝[vx vy r]T representing 3 states; equation (9) represents system current state feedback;
step 3: approximation of AUV model uncertainty term using RBF neural network
The RBF neural network structure comprises three different layers, 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 predicted output y of the network by linearly combining hidden layers, namely:
Wherein h is a Gaussian activation function, w jq is a weight vector from a j-th hidden layer node to a q-th output layer node, and m represents the number of hidden layer neurons;
The input layer x= [ v x vy r X N]T ] of the RBF neural network outputs an uncertainty term deltaf (x k,uk) of the AUV model, and according to the RBF neural network output expression (10), the uncertainty term of the AUV model can be obtained as follows:
Δf(xk,uk)＝WTH(xk)+ε (11)
wherein W is a weight matrix from a hidden layer to an output layer, H is a vector composed of Gaussian activation functions H, and epsilon is a deviation term
Step 4: constructing an AUV path tracking controller based on RBF-MPC;
Combining the AUV model in the step 1 and the AUV model uncertainty item described by the RBF in the step 3, thereby determining a real model of the AUV; on the basis of a real model, an MPC controller in the step 2 is adopted, an objective function is constructed according to the minimum AUV tracking state error and the minimum control input requirement, and a control sequence in a prediction time domain is optimized and solved 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 over, the state of the AUV is re-acquired at the next sampling moment, and the rolling optimization of the next period is continued; let the vector x denote the state of the AUV and u denote the control input, the state update equation of the AUV can be described as:
xk+1＝f(xk,uk) (12)
The true AUV model f true(xk,uk) is expressed as:
xk+1＝fnom(xk,uk)+Δf(xk,uk)＝ftrue(xk,uk) (13)
Wherein Δf (x k,uk) represents an uncertainty term in the AUV model using RBF approximation in step 3, and f nom(xk,uk represents the AUV model in step 1;
the path tracking control problem of the AUV is thus described as the following constrained dynamic optimization problem:
constraint conditions:
xk+1＝fnom(xk,uk)+Δf(xk,uk) (15)
e(k+1)＝xk+1-xref (16)
umin≤uk≤umax,k＝1,...,Nc (17)
x0＝x(k) (18)
In the formula (14), R and Q are respectively a weight matrix and a control input weight matrix of path tracking state deviation, the formula (15) represents a real AUV system, x k＝[vx vy r]T represents 3 states, namely v x and v y are respectively a forward speed and a lateral speed, and R is the heading angular speed of the AUV; equation (16) represents a deviation value between the actual state and the reference state; equation (17) represents the constraint range of the control input u= [ X0N ] T when solving the optimization problem; equation (18) represents AUV current state feedback.
In the AUV path tracking control process, a model prediction controller obtains an AUV state value at the current moment through a sensor when the AUV performs path tracking; then predicting the state value of the AUV in the prediction time domain according to the prediction model, and optimally solving the control sequence in the prediction time domain by combining the constructed target function formula (14) with the constraint condition formulas (15), the formulas (16) and the formulas (17); finally, selecting the 1 st element of the control sequence obtained by solving as the input quantity of the system; and after the time is over, the state of the AUV is re-acquired at the next sampling time, and the rolling optimization of the next period is continued.
Preferably: m=7 in step 3.
Preferably: the weight w jq is adjusted by a gradient descent method.
A computer system, comprising: one or more processors, a computer-readable storage medium 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 methods described above.
A computer readable storage medium, characterized by storing computer executable instructions that, when executed, are used in the method described above.
A computer program comprising computer executable instructions which when executed are adapted to implement the method described above.
Advantageous effects
According to the autonomous underwater vehicle model prediction path tracking method based on the neural network, on the basis of path tracking control by adopting a model prediction controller (Model Prediction Control, MPC), the RBF neural network is trained on line by using real-time measurement data, the uncertainty of an AUV model is compensated, the interference of the model uncertainty on the model prediction controller is restrained, and the overshoot and tracking error of the system are reduced. Simulation results in MATLAB environment show that the RBF-MPC-based path tracking control algorithm has better transient state, steady state performance and better energy-saving effect compared with the classical MPC algorithm.
Compared with the prior art, the method has the following beneficial effects:
1. because of strong nonlinearity and strong coupling of an underwater vehicle system, an AUV is difficult to establish an accurate system model in practice, and an RBF neural network is adopted to compensate the model, so that the model is more approximate 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 tracking error of the system are reduced. Compared with the classical MPC algorithm, the method has better transient state and steady state performance and better energy-saving effect.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to refer to like parts throughout the several views.
FIG. 1 AUV model;
FIG. 2 RBF is a schematic diagram of a neural network;
FIG. 3 RBF-MPC schematic;
FIG. 4 path trace control results;
FIG. 5 x direction tracking bias contrast;
FIG. 6 y direction tracking bias contrast;
FIG. 7 is a graph of the change in control input force;
Fig. 8 controls the variation curve of the input torque.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The implementation steps of the invention are as follows:
Step 1: aiming at an AUV (autonomous Underwater vehicle) of the research object, a dynamics and kinematics model is established;
in order to facilitate subsequent research and analysis, coupling influence caused by the horizontal plane motion and the vertical plane motion of the underactuated AUV is ignored, a nonlinear secondary damping item in a dynamics model is ignored, and dynamics and a motion equation of 3 degrees of freedom of the horizontal plane of the underactuated AUV are established.
Step 2: constructing an AUV path tracking controller based on MPC: and adopting an MPC control algorithm according to AUV path tracking performance index requirements. And (3) taking the AUV model in the step (1) as a research object, acquiring the latest measurement state of the AUV at each sampling moment (k), predicting a control sequence in a time domain according to the minimum error of the AUV tracking state and the minimum requirement of control input, and finally selecting the 1 st element of the control sequence obtained by solving as the input quantity of the AUV model, acquiring the state of the AUV again at the next sampling moment after the moment is finished, and continuing the rolling optimization of the next period.
Step 3: uncertainty term of RBF neural network description model is adopted: during actual sailing, the mass, hydrodynamic additional mass, moment of inertia, damping coefficient, etc. of the AUV typically vary with changes in operating conditions (including tasks and environments). In addition, the strong nonlinearity and strong coupling of the underwater vehicle system makes it difficult to build an accurate AUV model, thereby affecting its path tracking performance. The RBF neural network is used to approximate the model uncertainty term. The RBF neural network part is in the form of 5-7-3, namely 5 nodes of an input layer, 7 nodes of a hidden layer and 3 nodes of an output layer, and the output is a model uncertainty term delta f (x k,uk) of the AUV.
Step 4: constructing an AUV path tracking controller based on RBF-MPC: combining the nominal model of the AUV in step 1 and the model uncertainty term described by the RBF in step 3, thereby determining the true model of the AUV. On the basis of a real model, an MPC controller in the step 2 is adopted, an objective function is constructed according to the minimum AUV tracking state error and the minimum control input requirement, and a control sequence in a prediction time domain is optimized and solved 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 time is over, the state of the AUV is re-acquired at the next sampling time, and the rolling optimization of the next period is continued.
Two coordinate systems are typically used in step 1 to describe the movement of the AUV: a ground coordinate system and a carrier coordinate system. The origin O of the ground coordinate system is fixed at one place on the earth, and it is specified that OX is positive to the east and OY is positive to the north. The origin O B of the vehicle coordinate system is selected at the center of buoyancy of the AUV, with O BXB defined along the longitudinal axis of the AUV and pointing in the heading, O BYB perpendicular thereto, and positive to the right. As shown in fig. 1, x represents forward displacement, y represents lateral displacement, ψ represents heading angle, v x and v y are respectively forward speed and lateral speed, r is heading angular speed of AUV, and a generalized coordinate vector η= [ x y ψ ] T and a generalized speed vector v= [ v x vy r]T are defined, so as to obtain a motion equation of AUV on a horizontal plane, which is:
Where M is the inertial matrix with additional mass, C (v) is the Golgi force and centripetal force matrix, D (v) is the damping matrix, τ is the force and moment generated in three degrees of freedom, underactuation is studied in the present invention so it represents the thrust generated by the propeller and the steering force generated by the steering surface.
Assuming that the AUV is symmetrical in front-back and left-right directions, there are:
τ＝[X Y N]T＝[X 0 N] (7)
from this, the kinematic and kinetic equations of the underactuated AUV in the horizontal plane are expressed as:
And
Wherein ,m11＝M11,m22＝M22,m33＝M33,d11＝D11,d22＝D22,d33＝D33, is an inertial matrix M of additional mass, and a part of elements in a damping matrix D.
The AUV path tracking target in step 2 may be expressed as the following scroll optimization control problem:
constraint conditions:
x(k+1)＝f(xk,uk) (11)
yk＝g(xk) (12)
umin≤uk≤umax,k＝1,...,Nc (13)
x0＝x(k) (14)
In the formula (10), R and Q respectively represent a weight matrix of a control output and a control input, N p represents a prediction range, N c represents a control range, y k is AUV system state output [ v x x vy y r ψ]T,vx and v y are respectively a forward speed and a lateral speed, R is a heading angle speed of the AUV, x represents forward displacement, y represents lateral displacement, and ψ represents a heading angle; r (k) is the desired instruction, i.e. the reference state to be tracked; the formula (11) and the formula (12) in the constraint represent a system prediction model, X k＝[vx vy r]T represents 3 states, and the constraint formula (13) is the amplitude of the input u= [ X0N ] T of the control quantity, namely the thrust X generated by the propeller and the control force N generated by the control surface; equation (14) represents the system current state feedback.
In step 3, the RBF network structure is shown in fig. 2, and the structure includes three different layers, where n is the number of input layer nodes, m is the number of hidden layer nodes, and l is the number of hidden layer nodes. For the present invention, 5 nodes of the input layer, i.e., n=5, 7 nodes of the hidden layer, i.e., m=7, and 3 nodes of the output layer, i.e., l=3 are set.
The gaussian function is widely applied as an activation function in the RBF neural network, and is used as the most common basis function, and the calculation accuracy is higher by selecting the weight through the distance between the center points of the input layer and the hidden layer, so that the model can be approximated more effectively, and in the RBF neural network application, the calculation mode of the hidden layer h j is as follows:
Where, ||x-c j || represents the Euclidean distance between x and c j, and the RBF neural network uses Gaussian basis functions with center (c j) and width (σ j) as parameters.
The center value c j is the Gaussian basis function center point vector value of the j-th hidden layer neural node:
cj＝[c1j…cnj]T (16)
The width sigma j represents the width of the Gaussian basis function of the hidden layer, sigma j＝[σ1,σ2,…,σl]T is a positive number, influences the mapping range of the neural network, and the larger the sigma value is, the wider the Gaussian basis function is, which shows that the mapping capability of the network to the input is stronger.
The RBF network structure diagram is shown in fig. 3, and the RBF calculates the predicted output y of the network by linearly combining hidden layers, namely:
In the formula, h is a Gaussian activation function, w jq is a weight vector from a j hidden layer node to a q output layer node, and the weight w jq is adjusted by adopting a gradient descent method.
In the invention, the RBF neural network part is in the form of 5-7-3, namely 5 nodes of an input layer, the input layer x= [ v x vy r X N]T ], 7 hidden layer nodes, 3 nodes of an output layer and model uncertainty term deltaf (x k,uk) of AUV are output.
Based on the RBF neural network output expression (17), the AUV model uncertainty term is obtained as:
Δf(xk,uk)＝WTH(xk)+ε (18)
Where W is the weight matrix of the hidden layer to the output layer, H is the vector of gaussian activation functions H, i.e. h= [ H 1h2…hm]T, ∈is the bias term.
The parameter learning rate η=0.10, the momentum factor α=0.05, the base width parameter b=50, and the central vector value of the RBF neural network:
Weight matrix:
Step 4: constructing an AUV path tracking controller based on RBF-MPC: let the vector x denote the state of the AUV and u denote the control input, the state update equation of the AUV can be described as:
xk+1＝f(xk,uk) (21)
Δf (x k,uk) represents the uncertainty term in the AUV model approximated by RBF in step 3, f nom(xk,uk) represents the nominal model of AUV in step 1, then the true AUV model f true(xk,uk) is expressed as:
xk+1＝fnom(xk,uk)+Δf(xk,uk)＝ftrue(xk,uk) (22)
the path-tracking control problem of an AUV can thus be described as the following constrained dynamic optimization problem:
constraint conditions:
xk+1＝fnom(xk,uk)+Δf(xk,uk) (24)
e(k+1)＝xk+1-xref (25)
umin≤uk≤umax,k＝1,...,Nc (26)
x0＝x(k) (27)
In the formula (23), R and Q are respectively a weight matrix and a control input weight matrix of path tracking state deviation, the formula (24) represents a real AUV system, x k＝[vx vy r]T represents 3 states, namely v x and v y are respectively a forward speed and a lateral speed, and R is the heading angular speed of the AUV; equation (25) represents a deviation value between the actual state and the reference state; equation (26) represents the constraint range of the control input u= [ X0N ] T when solving the optimization problem; equation (27) represents AUV current state feedback.
In the AUV path tracking control process, a model prediction controller obtains an AUV state value at the current moment through a sensor when the AUV performs path tracking; then predicting the state value of the AUV in the prediction time domain according to the prediction model, and optimally solving the control sequence in the prediction time domain by combining the constructed target function formula (23) with the constraint condition formulas (24), the formulas (25) and the formulas (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 time is over, the state of the AUV is re-acquired at the next sampling time, and the rolling optimization of the next period is continued.
Based on the theory, under MATLAB simulation environment, a reference path is given, a classical MPC control method and an RBF-MPC control method are adopted respectively, and tracking effects of the two methods on the reference path are compared by observing various state parameters of the AUV under the two controllers. The mass of the AUV in the controller was set to 23.5kg in a simulation experiment using REMUS AUV model, which was actually 30.5kg of AUV. The initial position of the AUV is (10 m, -10 m), the target point position is (17 m, -56 m), (187 m, -146 m), (208 m, -234 m), (334 m,414 m), (488 m, -488 m), (980 m, -980 m), the initial heading angle is 0, the sampling interval T of the controller is=0.1, the prediction step N is=50, and the simulation time is 360s.
As can be seen from fig. 4, both controllers can well complete the tracking task, and from the partial enlarged view, both controllers can generate smooth motion trajectories, but at the turning points, the difference between the two controllers is very obvious. The RBF-MPC controller has smaller overshoot than the MPC controller, can reduce the error with the expected reference path more quickly and has better tracking performance, whether in the first corner path tracking section with the horizontal coordinate of 30-80m or the second corner path tracking section with the horizontal coordinate of 350-400 m.
In order to further clearly see the difference in tracking effect between the MPC controller and the RBF-MPC controller, the tracking deviation of the transverse and longitudinal positions and the course angle deviation result are shown in FIGS. 5 and 6. The maximum position deviation of the MPC controller in the x direction can reach 21.5m, 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 on the position error in the y-direction is also significant, especially between 18s and 75 s; also, the deviation of the heading angle is more pronounced at the peak. Therefore, the model uncertainty can be seen to cause the MPC controller to have larger steady-state error, and after the neural network compensation is added, the overshoot is obviously reduced, and the steady state is reached more quickly. Fig. 8 shows the control input force and torque curves of the AUV when two controllers are used. From a trend, both controllers remained essentially identical, but the fluctuations generated by the MPC controller were more pronounced. The result shows that the MPC controller simplifies the underwater vehicle model, has larger modeling error, and therefore, has larger path tracking control error, and has better tracking effect compared with the MPC controller which does not use RBF neural network to perform model approximation training.
It follows that RBF-MPC controllers provide better performance than typical MPC controllers in the presence of modeling errors or significant uncertainties, and that the performance of the control system is significantly improved upon the identification of the neural network model.
The variation of control input force and torque using the MPC controller and the RBF-MPC controller is illustrated in FIGS. 7 and 8. From the aspect of variation trend, the RBF-MPC controller generates smaller input fluctuation, particularly the difference between the peak values of 10s, 59s and 66s is obvious, and in the steady-state stage, the RBF-MPC controller obtains more stable control input, consumes less energy and is more beneficial to long-time underwater operation of the AUV.
In summary, the RBF-MPC has smaller path tracking overshoot and smaller steady state error in terms of control effect in the presence of model uncertainty and disturbance; in terms of control input, the input amplitude is smaller, and the energy is saved. The overall advantage is evident compared to conventional MPC controllers.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made without departing from the spirit and scope of the invention.
Claims (6)
1. The autonomous underwater vehicle model prediction path tracking method based on the neural network is characterized by comprising the following steps of:
Step 1: establishing an AUV model, wherein the AUV model comprises a dynamics equation and a kinematics equation;
the AUV kinematics equation:
the AUV dynamics equation:
Wherein x represents forward displacement, y represents lateral displacement, ψ represents course angles, v x and v y are respectively forward speed and lateral speed, r is the course angular velocity ,m11＝M11,m22＝M22,m33＝M33,d11＝D11,d22＝D22,d33＝D33, of the AUV, and is an element in an inertial matrix M and a damping matrix D of additional mass; n is the operating force generated by the operating surface;
Step 2: constructing an AUV path tracking controller based on MPC;
According to the AUV path tracking performance index requirement, an MPC control algorithm is adopted, an AUV model in the step 1 is used as a controlled 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 that the AUV tracking state error is minimum and the control input is minimum, and finally the 1 st element of the control sequence obtained by solving is selected as the input quantity of the AUV model, the state of the AUV is obtained again at the next sampling time after the time is over, and the rolling optimization of the next period is continued; the AUV path tracking target may be expressed as the following roll optimization control problem:
constraint conditions:
x(k+1)＝f(xk,uk) (6)
yk＝g(xk) (7)
umin≤uk≤umax,k＝1,...,Nc (8)
x0＝x(k) (9)
In the formula (5), R and Q represent weight matrices of control output and control input, respectively, N p represents a prediction range, N c represents a control range, y k is AUV system state output y= [ v x x vy y r ψ]T,vx and v y are forward speed and lateral speed, respectively; r (k) is the desired instruction, i.e. the reference state to be tracked; u is a control input u= [ X0N ] T, namely a thrust force X generated by the propeller and an operating force N generated by the operating surface; equations (6) and (7) in the constraint represent the AUV model in step 1, x k＝[vx vy r]T representing 3 states; equation (9) represents system current state feedback;
step 3: approximation of AUV model uncertainty term using RBF neural network
The RBF neural network structure comprises three different layers, 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 predicted output y of the network by linearly combining hidden layers, namely:
Wherein h is a Gaussian activation function, w jq is a weight vector from a j-th hidden layer node to a q-th output layer node, and m represents the number of hidden layer neurons;
The input layer x= [ v x vy r X N]T ] of the RBF neural network outputs an uncertainty term deltaf (x k,uk) of the AUV model, and according to the RBF neural network output expression (10), the uncertainty term of the AUV model can be obtained as follows:
Δf(xk,uk)＝WTH(xk)+ε (11)
wherein W is a weight matrix from a hidden layer to an output layer, H is a vector composed of Gaussian activation functions H, and epsilon is a deviation term
Step 4: constructing an AUV path tracking controller based on RBF-MPC;
Combining the AUV model in the step 1 and the AUV model uncertainty item described by the RBF in the step 3, thereby determining a real model of the AUV; on the basis of a real model, an MPC controller in the step 2 is adopted, an objective function is constructed according to the minimum AUV tracking state error and the minimum control input requirement, and a control sequence in a prediction time domain is optimized and solved 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 over, the state of the AUV is re-acquired at the next sampling moment, and the rolling optimization of the next period is continued; let the vector x denote the state of the AUV and u denote the control input, the state update equation of the AUV can be described as:
xk+1＝f(xk,uk) (12)
The true AUV model f true(xk,uk) is expressed as:
xk+1＝fnom(xk,uk)+Δf(xk,uk)＝ftrue(xk,uk) (13)
Wherein Δf (x k,uk) represents an uncertainty term in the AUV model using RBF approximation in step 3, and f nom(xk,uk represents the AUV model in step 1;
the path tracking control problem of the AUV is thus described as the following constrained dynamic optimization problem:
constraint conditions:
xk+1＝fnom(xk,uk)+Δf(xk,uk) (15)
e(k+1)＝xk+1-xref (16)
umin≤uk≤umax,k＝1,...,Nc (17)
x0＝x(k) (18)
In the formula (14), R and Q are respectively a weight matrix and a control input weight matrix of path tracking state deviation, the formula (15) represents a real AUV system, x k＝[vx vy r]T represents 3 states, namely v x and v y are respectively a forward speed and a lateral speed, and R is the heading angular speed of the AUV; equation (16) represents a deviation value between the actual state and the reference state; equation (17) represents the constraint range of the control input u= [ X0N ] T when solving the optimization problem; equation (18) represents AUV current state feedback;
In the AUV path tracking control process, a model prediction controller obtains an AUV state value at the current moment through a sensor when the AUV performs path tracking; then predicting the state value of the AUV in the prediction time domain according to the prediction model, and optimally solving the control sequence in the prediction time domain by combining the constructed target function formula (14) with the constraint condition formulas (15), the formulas (16) and the formulas (17); finally, selecting the 1 st element of the control sequence obtained by solving as the input quantity of the system; and after the time is over, the state of the AUV is re-acquired at the next sampling time, and the rolling optimization of the next period is continued.
2. The autonomous underwater vehicle model predictive path tracking method based on a neural network according to claim 1, characterized in that m=7 in step 3.
3. The autonomous underwater vehicle model predictive path tracking method based on a neural network according to claim 1, characterized in that the weight w jq is adjusted by a gradient descent method.
4. A computer system, comprising: one or more processors, a computer-readable storage medium 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, characterized by storing computer executable instructions that, when executed, are adapted to implement the method of claim 1.
6. A computer program comprising computer executable instructions which, when executed, are adapted to implement the method of claim 1.
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