CN111650948B - Quick tracking control method for horizontal plane track of benthonic AUV - Google Patents

Quick tracking control method for horizontal plane track of benthonic AUV Download PDF

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CN111650948B
CN111650948B CN202010523598.8A CN202010523598A CN111650948B CN 111650948 B CN111650948 B CN 111650948B CN 202010523598 A CN202010523598 A CN 202010523598A CN 111650948 B CN111650948 B CN 111650948B
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CN111650948A (en
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曹禹
孙延超
秦洪德
万磊
张宇昂
景锐洁
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Harbin Engineering University
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Abstract

A method for quickly tracking and controlling a horizontal plane track of a benthonic AUV belongs to the technical field of track tracking and controlling of autonomous underwater robots. The invention solves the problems of limited control precision and slow adjustment speed when the existing control method is applied to the benthonic AUV. The invention combines ocean current disturbance and model uncertainty into a disturbance lumped term, uses a finite time disturbance observer to approach the disturbance lumped term value, and introduces a neural network estimation observation error. And further provides a self-adaptive neural network backstepping controller based on a finite time disturbance observer to realize the finite time high-precision trajectory tracking control of the bentable AUV. The method can be applied to track tracking control of the benthonic AUV.

Description

Quick tracking control method for horizontal plane track of benthonic AUV
Technical Field
The invention belongs to the technical field of trajectory tracking control of autonomous underwater robots, and particularly relates to a method for quickly tracking and controlling a horizontal trajectory of a benthonic AUV.
Background
Autonomous underwater robots (AUVs) have great development prospects in both military and civilian fields as important tools for human exploration and development of oceans. At present, the AUV can be classified into a cruise AUV for a large-scale survey and a hover AUV for a small-scale observation according to its operation characteristics. Although both types of AUV have great utility, the corresponding drawbacks are also evident, such as: the cruise AUV has poor fixed-point observation capability and the hovering AUV has poor large-range investigation capability. Therefore, in order to realize further observation of the ocean, it is very meaningful to develop a novel AUV which is highly autonomous and has the characteristics of a cruise AUV and a hovering AUV. Therefore, the concept of the benthonic AUV is also provided, the benthonic AUV is a novel underwater vehicle combining the characteristics of a seabed observation node and the AUV, can be used for seabed information acquisition, and can meet the requirement for micro target identification while completing a seabed coordinate high-precision detection task. Meanwhile, the modified AUV is a typical nonlinear strong coupling system, and has the research obstacles of AUV commonality such as complex working environment and difficulty in accurately solving hydrodynamic parameters, and has the influence factors such as hydrodynamic coefficient perturbation and easy collision of carriers under the operation requirements of large-scale deployment and accurate sitting and sinking on the sea bottom.
In order to complete submarine oil and gas seismic exploration in a designated area completely and efficiently, the benthonic AUV needs to have good navigation capacity and anti-interference capacity at a certain height from the sea bottom surface and high-precision path tracking performance, namely an effective motion control law is designed, so that the benthonic AUV can track a set track from an initial state and complete a specified task, the global consistency and gradual stability of a tracking position error are ensured in a short time, and the requirement of high-precision rapid deployment operation in the designated area is further met. The current common AUV control method is usually to design a robust controller for external disturbance or to approximate the total interference of the system with a neural network. However, the method has limited control precision and slow adjustment speed, and is difficult to realize high-precision trajectory tracking control within a limited time when applied to an Autonomous Underwater Vehicle (AUV) which has severe working environment and high requirement on trajectory tracking precision and needs to quickly react to external interference.
Disclosure of Invention
The invention aims to solve the problems of limited control precision and low adjustment speed when the conventional control method is applied to an underwater AUV (autonomous underwater vehicle), and provides a method for quickly tracking and controlling a horizontal locus of the underwater AUV.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for quickly tracking and controlling a horizontal track of a benthonic AUV (autonomous Underwater vehicle) specifically comprises the following steps:
step one, considering model uncertainty and ocean current disturbance asOne disturbance lumped term τ' d Establishing a kinematics and dynamics equation of the benthonic AUV considering the disturbance lumped term;
step two, based on the kinematics and the kinetic equation established in the step one, establishing an error system of the track tracking by using a backstepping control method;
step three, designing a sliding mode disturbance observer according to the track tracking error system established in the step two, and utilizing the designed sliding mode disturbance observer to disturb the lumped term tau' d Performing approximation to obtain a disturbance lumped term tau' d The observed value of (a);
step four, adopting radial basis function neural network to observe errors of disturbance lumped items
Figure BDA0002533010510000021
Estimating to obtain observation error
Figure BDA0002533010510000022
An estimated value of (d);
step five, according to the disturbance lumped term tau' d Observed value and observation error of
Figure BDA0002533010510000023
The controller is designed according to the estimated value of the model AUV, so that the pose of the benthonic AUV tracks the expected value in a limited time, and the tracking error converges in the limited time.
The invention has the beneficial effects that: the invention provides a method for quickly tracking and controlling a horizontal plane track of a benthonic AUV (autonomous underwater vehicle). And further provides a self-adaptive neural network backstepping controller based on a finite time disturbance observer to realize the finite time high-precision trajectory tracking control of the bentable AUV.
By adopting the method, the pose quantity eta of the benthonic AUV motion control system can still track the expected value eta in a limited time under the condition that external interference exists d And is andtracking error e 1 ＝η-η d Convergence within a limited time. The control input quantity can be ensured to be a finite value, and the method is more close to the actual engineering.
Drawings
FIG. 1 is a graph of surging tracking of a bentable AUV;
FIG. 2 is a graph of the sway tracking of a benthonic AUV;
FIG. 3 is a graph of yaw tracking of a benthonic AUV;
FIG. 4 is a graph of an observation of longitudinal disturbances by a disturbance observer;
in the figure, H1 represents the longitudinal interference value, d1 represents the longitudinal interference observation value;
FIG. 5 is a graph of the observation of cross-talk by a disturbance observer;
in the figure, H2 represents the cross-interference value, d2 represents the cross-interference observation value;
FIG. 6 is a graph of the observation of yaw interference by the disturbance observer;
in the figure, H3 represents a yawing interference value, and d3 represents a yawing interference observation value;
FIG. 7 is a graph of actuator longitudinal control force output;
FIG. 8 is a graph of actuator lateral control force output;
FIG. 9 is a graph of actuator yaw control torque output.
Detailed Description
In a first specific embodiment, a method for quickly tracking and controlling a horizontal trajectory of a bentable AUV according to this embodiment specifically includes the following steps:
step one, considering model uncertainty and ocean current disturbance as a disturbance lumped term tau' d Establishing a kinematics and dynamics equation of the benthonic AUV considering the disturbance lumped term;
step two, based on the kinematics and the kinetic equation established in the step one, establishing an error system of the track tracking by using a backstepping control method;
step three, designing a sliding mode disturbance observer according to the track tracking error system established in the step two, and utilizing the designed sliding mode disturbanceObserver lumped term τ to disturbance' d Performing approximation to obtain a disturbance lumped term tau' d The observed value of (a);
step four, adopting the radial basis function neural network to observe the error of the disturbance lumped term
Figure BDA0002533010510000032
Estimating to obtain observation error
Figure BDA0002533010510000033
An estimated value of (d);
step five, according to the disturbance lumped term tau' d Observed value and observation error of
Figure BDA0002533010510000034
The controller is designed according to the estimated value of the model AUV, so that the pose of the benthonic AUV tracks the expected value in a limited time, and the tracking error converges in the limited time.
The kinematics and kinetic equations of the benthonic AUV are expressed by Newton-Euler equation based on the motion of rigid bodies in the fluid:
Figure BDA0002533010510000031
where M is the mass inertia matrix, η ═ x, y, ψ] T The three-freedom-degree position and the three-freedom-degree attitude of the benthonic AUV in the horizontal plane under a fixed coordinate system are shown, and v is [ u, v, r [ ]] T Representing the velocity and angular velocity in the horizontal plane in the carrier coordinate system, J ∈ R 3×3 Representing a coordinate transformation matrix between the fixed coordinate system and the carrier coordinate system; c (v) ε R 3x3 Is a coriolis centripetal force matrix containing additional mass terms; d (v) ε R 3x3 Is a fluid damping matrix; g (eta) epsilon R 3 Restoring force and restoring moment vectors generated by the action of gravity and buoyancy on the boat body; tau epsilon to R 3 The control force and moment vectors generated when the actuator operates; tau is d ∈R 3 The disturbance vector caused by the external interference.
The method considers model uncertainty and ocean current disturbance, considers the model uncertainty and the ocean current disturbance as a disturbance lumped term, and considers feasible mathematical expression forms of the disturbance lumped term.
The second embodiment is as follows: the difference between this embodiment and the first embodiment is that, in the first step, a kinematic and kinetic equation of the bentable AUV considering the disturbance lumped term is established, which specifically includes:
Figure BDA0002533010510000041
wherein v ═ u, v 0 ,r] T V represents the velocity and angular velocity vector of the benthonic AUV in the horizontal plane under the carrier coordinate system, u represents the surging velocity, v represents the surging velocity 0 Representing the yaw velocity, and r representing the yaw angular velocity; superscript T represents transpose; eta ═ x, y, psi] T Representing three-degree-of-freedom pose vectors of the benthonic AUV in a horizontal plane under a fixed coordinate system, x and y respectively representing longitudinal and transverse position coordinates of the benthonic AUV under the fixed coordinate system, and psi representing a heading angle; j (η) represents a coordinate transformation matrix between the fixed coordinate system and the carrier coordinate system, J (η) being equal to R 3×3 R represents a real number; tau' d A perturbed lumped term representing the system; tau represents a control input vector, which can also be called a control force and moment vector generated when the actuator runs;
Figure BDA0002533010510000042
is the first derivative of η and is,
Figure BDA0002533010510000043
representing the velocity and angular velocity vectors of the benthonic AUV under a fixed coordinate system;
Figure BDA0002533010510000045
is the first derivative of v and is,
Figure BDA0002533010510000044
representing the acceleration and angular acceleration vectors of the benthonic AUV under a carrier coordinate system; m 0 A nominal value representing a mass inertia matrix; upper corner mark generation-1Inverse of the table matrix, C 0 (v) A nominal value representing a coriolis centripetal force matrix; d 0 (v) A nominal value representing a fluid damping matrix; g 0 Nominal values representing the restoring force and restoring moment vectors;
the fixed coordinate system O-XYZ is: taking any point on the sea surface or in the sea as an origin O, wherein the X axis is positioned on the horizontal plane, and the specified north direction is taken as the positive direction; the Y axis is positioned on the horizontal plane, and the specified east-righting direction is taken as the positive direction, namely, the Y axis is obtained by rotating the OX axis by 90 degrees clockwise according to the right-hand rule; the Z axis is vertical to the XOY coordinate plane and takes the geocentric direction as positive;
the carrier coordinate system O 0 -X 0 Y 0 Z 0 Comprises the following steps: the position of the center of gravity of the bentable AUV is taken as an origin O 0 ，X 0 The shaft is arranged in the longitudinal section of the benthonic AUV, is parallel to the waterline plane of the benthonic AUV and takes the heading direction of the boat as the positive direction; y is 0 The shaft is vertical to the longitudinal section of the bentable AUV, is parallel to the horizontal plane and takes the starboard direction as the positive direction; z 0 The shaft is arranged in the longitudinal section of the benthonic AUV, is vertical to the water line plane of the benthonic AUV and takes the submarine bottom direction as the positive direction;
Figure BDA0002533010510000046
in the formula, Δ M represents an uncertainty value of the mass inertia matrix; Δ c (v) represents the uncertainty value of the coriolis centripetal force matrix; Δ d (v) represents the uncertainty value of the fluid damping matrix; Δ g represents the uncertainty values of the restoring force and restoring moment vectors; tau is d Representing an uncertainty value of the perturbation vector caused by the external disturbance.
The third concrete implementation mode: the second embodiment is different from the second embodiment in that the specific process of the second step is as follows:
defining a tracking error:
Figure BDA0002533010510000051
in the formula, e 1 Indicating a tracking error; e.g. of the type 2 Representing a velocity tracking error; eta d ＝[x d ,y d ,ψ d ] T Representing the expected value x of the three-degree-of-freedom pose of the benthonic AUV in the horizontal plane under the fixed coordinate system d Is the expected value of x, y d Is the desired value of y,. psi d A desired value of ψ;
Figure BDA0002533010510000052
is eta d The first derivative of (a);
Figure BDA0002533010510000053
is e 1 The first derivative of (a); v. of d Representing the horizontal speed and angular speed expectation vector of the benthonic AUV under a carrier coordinate system;
then the error system for establishing trajectory tracking according to equation (2) is:
Figure BDA0002533010510000054
in the formula,
Figure BDA0002533010510000055
is e 2 The first derivative of (a);
Figure BDA0002533010510000056
is the first derivative of J (η);
Figure BDA0002533010510000057
is v is d The first derivative of (a);
defining a virtual error z:
z＝e 2 -α 1 (6)
in the formula, alpha 1 Is a virtual control law one;
taking the virtual error integral term as epsilon:
Figure BDA0002533010510000058
the error system of the trajectory tracking is changed to:
Figure BDA0002533010510000059
in the formula,
Figure BDA00025330105100000510
is the first derivative of ε;
Figure BDA00025330105100000511
is the first derivative of z;
Figure BDA00025330105100000512
is alpha 1 The first derivative of (a).
There is a disturbance lumped term τ 'in equation (2)' d In order to realize the estimation of the disturbance value in a short time, a sliding mode disturbance observer is adopted for approximation. The basic idea of the backstepping control is feedback control, on the basis, a system is divided into a plurality of subsystems with next-order output as the input of a previous-order subsystem, each-order subsystem is processed by utilizing a Lyapunov function to obtain corresponding virtual input, the input of the next-order subsystem is designed by the method until the actual input is finally obtained, and the design of the backstepping control law can be completed by integrating the processing steps.
The fourth concrete implementation mode: the third embodiment is different from the third embodiment in that the specific process of the third step is as follows:
selecting a sliding mode surface function s as follows:
s＝ρ-v (9)
where ρ is an intermediate variable,
Figure BDA0002533010510000061
is the first derivative of ρ, and
Figure BDA0002533010510000062
form (1) ofComprises the following steps:
Figure BDA0002533010510000063
in the formula, k 7 For positive definite diagonal matrix, k 7 ∈R 3×3 (ii) a L is positive definite diagonal matrix, L is diag 1 ,L 2 ,L 3 ]∈R 3×3 ，L 1 ,L 2 ,L 3 Are all the elements in the L, and the elements in the L,
Figure BDA0002533010510000064
m＝1,2,3，
Figure BDA0002533010510000065
the maximum value of the disturbance in three degrees of freedom; r is more than 0 and less than 1; sign stands for sign function; s ═ s 1 ,s 2 ,s 3 ] T ，s 1 ,s 2 ,s 3 Are all elements in s, with | s r ＝[|s 1 | r ,|s 2 | r ,|s 3 | r ] T - | represents the absolute value;
then the lumped term τ 'is disturbed' d Observed value of
Figure BDA0002533010510000066
In the formula,
Figure BDA0002533010510000067
is a perturbed lumped term τ' d The observed value of (a);
Figure BDA0002533010510000068
is the first derivative of s.
If 0 < a is present 1 < 1 and 0 < a 2 < 2, then for r i (i ═ 1, …, n), the following inequality is satisfied:
Figure BDA0002533010510000069
Figure BDA00025330105100000610
sign stands for sign function, for vectors
ξ＝[ζ 1 …ζ n ] T (14)
The following equation exists
ζ α ＝[|ζ 1 | α sign(ζ 1 )…|ζ n | α sign(ζ n )] T (15)
sign(ζ)＝[sign(ζ 1 )…sign(ζ n )] T (16)
Although the system (11) has obtained an estimate of the disturbance, the value of L is not readily unambiguous, resulting in an observation error in the system
Figure BDA00025330105100000611
The disturbance observer adopts the basic design principle that unknown items such as parameter perturbation items, model uncertainty items, external disturbance and the like existing in an AUV control system are combined into disturbance lumped items, an observer system is constructed according to a measurable system state, the disturbance lumped items are approached online, and finally a corresponding controller is designed by using observed values of the disturbance lumped items, so that the tracking performance of the system on a preset track is improved.
The fifth concrete implementation mode: the fourth embodiment is different from the fourth embodiment in that the specific process of the fourth step is as follows:
error of observation
Figure BDA0002533010510000071
Comprises the following steps:
Figure BDA0002533010510000072
observation error of disturbance lumped term by adopting radial basis function neural network
Figure BDA0002533010510000073
And estimating, wherein the input x of the radial basis function neural network is as follows:
Figure BDA0002533010510000074
the radial basis function neural network outputs the observation error
Figure BDA0002533010510000075
The estimated values of (c) are:
Figure BDA0002533010510000076
in the formula,
Figure BDA0002533010510000077
as an estimate of the weight matrix,
Figure BDA0002533010510000078
are all made of
Figure BDA0002533010510000079
The sub-matrix of (1) is,
Figure BDA00025330105100000710
j＝1,2,3，
Figure BDA00025330105100000711
representing the estimated value of the ith neural network weight in the jth row, i is 1,2, …,6, phi (x) is an intermediate variable, phi (x) is [ phi (x) ] 1 (x),φ 2 (x),...,φ 6 (x)] T ，φ i (x) Represents the radial basis function of the gaussian version of the ith neural network.
The radial basis function neural network is a forward network based on a function approximation theory and has the characteristics of simple structure, concise training, high learning convergence speed and capability of approximating any nonlinear function. Learning of such a network is equivalent to finding the best-fit plane of the training data in a multidimensional space.
The sixth specific implementation mode: the difference between this embodiment and the fifth embodiment is that the specific process of the fifth step is as follows:
because of the physical limitation of the actuator, the maximum value of the execution input is a limited value, so the maximum output value is required to be used as the upper limit control input;
the control input vector τ is constrained by the saturation value:
sat(τ)＝[sat(τ 1 )，sat(τ 2 )，sat(τ 3 )] T (19)
wherein sat (τ) is an output value obtained by saturation limiting processing of a control input vector, and is defined by the control input vector τ and a saturation control function sat (τ) j ) Generation, tau j A jth value representing the control input vector τ, j being 1,2, 3;
sat(τ j ) Representing the nonlinear saturation characteristics of the actuator, the saturation control function is described as:
sat(τ j )＝τ j (t)+θ j (t) (20)
wherein
Figure BDA0002533010510000081
In the formula, theta j (t) is a saturation control term, τ mj For controlling the jth value τ of the input vector τ j A maximum allowable value of;
the adaptive backstepping control law is designed as follows:
Figure BDA0002533010510000082
in the formula, τ s Representing nominal values of control input vectors, alpha 2 To control law two, k virtually i Is positive definite diagonal matrix, i is 1,2, … 6, k i ∈R 3×3 A is a constant, a is more than 0 and less than 1,
Figure BDA0002533010510000083
is that
Figure BDA0002533010510000084
C is the control parameter to be designed and the adaptive gain, c is more than 0, lambda is a constant, and lambda is more than 0.
1. Theoretical basis
1.1 sports system mathematical model of benthonic AUV
The kinematic and kinetic equations of benthonic AUVs can be expressed using newton-euler equations based on the motion of rigid bodies in a fluid:
Figure BDA0002533010510000085
m is a mass inertia matrix, eta ═ x, y, psi] T The three-freedom-degree position and the three-freedom-degree attitude of the benthonic AUV in the horizontal plane under a fixed coordinate system are shown, and v is [ u, v [ ] 0 ,r] T Representing the velocity and angular velocity in the horizontal plane in the carrier coordinate system, J ∈ R 3×3 Representing a coordinate transformation matrix between the fixed coordinate system and the carrier coordinate system; c (v) ε R 3×3 Is a coriolis centripetal force matrix containing additional mass terms; d (v) ε R 3×3 Is a fluid damping matrix; g (η) is belonged to R 3 Restoring force and restoring moment vectors generated by the action of gravity and buoyancy on the boat body; tau epsilon to R 3 The control force and moment vectors generated when the actuator operates; tau is d ∈R 3 The disturbance vector caused by the external interference.
Model uncertainty and ocean current disturbance can cause more serious tracking error, and the tracking error is considered as a disturbance lumped term and a feasible mathematical expression form is considered. Therefore, equation (23) can be transformed as:
Figure BDA0002533010510000091
in formula (II) is τ' d Representing disturbances of a systemLumped terms, whose expressions are as follows:
Figure BDA0002533010510000092
in the formula, subscript 0 denotes each term coefficient of the nominal model, and Δ denotes an indeterminate value.
The invention aims to design a suitable controller tau to enable the pose quantity eta of the benthonic AUV motion control system to track the expected value eta in a limited time under the condition of external interference d And make the tracking error e 1 ＝η-η d Converge in a limited time and the control input is limited to less than a saturation value.
In conjunction with the actual engineering background, 3 assumptions were made:
assume 1 pose state η and its first derivative
Figure BDA0002533010510000093
Can be measured.
Suppose 2 the disturbance observer observation error is bounded.
Suppose 3 pose expected values η d Known and bounded to both its first and second derivatives.
Suppose 4 perturbing lumped terms are bounded, i.e. | τ' d | | ≦ χ, wherein χ is an unknown normal number.
1.2 definition of finite time control
Consider the following system:
Figure BDA0002533010510000094
in the formula, f is U 0 ×R→R n At U 0 X is continuous over R, U 0 A neighborhood at 0 with the origin x. For the system (26) under consideration, the nonlinear control system finite time stability theory is defined as follows: suppose there is a neighborhood defined at the origin
Figure BDA0002533010510000095
The smoothing function V (x) above, and there are real numbers p > 0, 0 < alpha<1 and d>0, such that V (x) is
Figure BDA0002533010510000096
Upper positive definite sum
Figure BDA0002533010510000097
In that
Figure BDA0002533010510000098
The upper half is negatively determined or
Figure BDA0002533010510000099
In that
Figure BDA00025330105100000910
The upper half is negative, the origin of the system is stable for a finite time, and the stop time depends on the initial value.
x(0)＝x 0 (27)
1.3 reverse step control method
Defining tracking error
Figure BDA00025330105100000911
The error system is obtained according to equation (26):
Figure BDA0002533010510000101
defining a virtual error:
z＝e 2 -α 1 (30)
wherein alpha is 1 Is a virtual control law.
Taking an integral term:
Figure BDA0002533010510000102
the error system becomes:
Figure BDA0002533010510000103
if the design control law τ makes z bounded, then e 1 And e 2 Is bounded.
1.4 sliding mode disturbance observer design
The disturbance lumped term tau 'is present in the system (24)' d In order to realize the estimation of the disturbance value in a short time, a sliding mode disturbance observer is adopted for approximation, and a sliding mode surface function is selected as follows:
s＝ρ-v (33)
where ρ is an intermediate variable, which can be described in terms of:
Figure BDA0002533010510000104
in the formula, k 7 ∈R 3×3 For positive definite diagonal matrix, 0<r<1，L∈R 3×3 Is a positive fixed diagonal matrix.
The perturbed lumped term observation is:
Figure BDA0002533010510000105
aiming at a disturbance observer with a system (32) design form (35), the sliding mode surface type (33) is used for a limited time t 0 Internally converging to zero, perturbing the lumped term at finite time t 0 The internal perturbed observer is a valid estimate.
Defining: if 0 < a is present 1 < 1 and 0 < a 2 < 2, then for r i (i ═ 1, …, n), the following inequality is satisfied:
Figure BDA0002533010510000106
Figure BDA0002533010510000107
in addition, sign represents a sign function in the present invention, for a vector
ξ＝[ζ 1 …ζ n ] T (38)
The following equation exists
ζ α ＝[|ζ 1 | α sign(ζ 1 )…|ζ n | α sign(ζ n )] T (39)
sign(ζ)＝[sign(ζ 1 )…sign(ζ n )] T (40)
And (3) proving that: the following Lypunov function was used:
Figure BDA0002533010510000111
derivation of the above equation can result in:
Figure BDA0002533010510000112
from the formula (41) and the formula (42)
Figure BDA0002533010510000113
Then it can be known from the finite time theory that the sliding mode disturbance observer can estimate the disturbance in a finite time.
1.5 control input saturation constraints
Due to the physical limitations of the actuator, the control signal τ is constrained by the saturation value. In this connection, it is possible to use,
sat(τ)＝[sat(τ 1 )…sat(τ n )] T (44)
sat (τ) is the vector of the actual control input, formed by the actuator andsaturation control function sat (τ) i ) (i ═ 1,2, …, n) results, representing the nonlinear saturation characteristics of the actuator. The saturation control function may be described as:
sat(τ i )＝τ i (t)+θ i (t) (45)
wherein
Figure BDA0002533010510000114
In the formula, τ mi The maximum allowable value of the control input.
1.6 finite time trajectory tracking controller design
When a sliding-mode observer is used, a disturbance lumped term estimation error is generated
Figure BDA0002533010510000115
And because the disturbance lumped term value range is difficult to determine, the observer parameters are difficult to select, so the RBF neural network is adopted to approximate the disturbance lumped term estimation error, namely
Figure BDA0002533010510000116
Wherein
Figure BDA0002533010510000121
Phi (x) is the radial basis function, theta * ∈R m The optimal weight of the neural network is m, and the hidden node number of the neural network is m. And theta * Satisfy the requirement of
Figure BDA0002533010510000122
Figure BDA0002533010510000123
And is
Figure BDA0002533010510000124
m is the number of hidden nodes, epsilon * Is the optimal approximation error.
Optimal weight value theta * Is defined as:
Figure BDA0002533010510000125
the radial basis function phi (x) in the invention is a Gaussian basis function:
Figure BDA0002533010510000126
in the formula (d) i ＝[d i1 ,d i2 ,…,d im ]Is the center of the ith neuron of the hidden layer; b i ＝[b i1 ,b i2 ,…,b im ]Is the width of the gaussian basis function of the ith neuron.
Taking the neural network input as
Figure BDA0002533010510000127
Then the error of observation
Figure BDA0002533010510000128
The estimate of (d) can be written as:
Figure BDA0002533010510000129
in the formula,
Figure BDA00025330105100001210
as an estimate of the weight matrix,
Figure BDA00025330105100001211
are all made of
Figure BDA00025330105100001212
The sub-matrix of (1) is,
Figure BDA00025330105100001213
j＝1,2,3，
Figure BDA00025330105100001214
representing the estimated weight of the ith neural network in the jth row, i is 1,2, …,6, phi (x) is an intermediate variable, phi (x) is [ phi (x) ] 1 (x),φ 2 (x),…,φ 6 (x)] T ，φ i (x) Represents the radial basis function of the gaussian version of the ith neural network.
By integrating the analysis processes, the following self-adaptive backstepping control law is designed:
Figure BDA00025330105100001215
in the formula: alpha is alpha 1 Is a virtual control law, alpha 2 Is a virtual control law two, z is a virtual error, epsilon is a virtual error integral term, k i ∈R 3×3 And (i is 1,2,3,4,5 and 6) is a positive fixed diagonal matrix, 0 & lta & lt 1, lambda & gt 0, and c & gt 0 are control parameters to be designed and adaptive gain. It can be seen that when the bentable AUV error system mathematical model (24) is converted into an error system (32) through error transformation (28) and (30), if the control input vector tau and the virtual control law alpha are used 1 、α 2 And the adaptive law is designed in the form of equation (51), the transformation error z is consistent and ultimately bounded, and the tracking error e 1 And the limited time convergence performance is met.
And (3) proving that: get
Figure BDA0002533010510000131
Then
Figure BDA0002533010510000132
Will be alpha 1 Substituting formula (32) to obtain:
Figure BDA0002533010510000133
wherein α ═-λ min (k 1 )，β＝-λ min (k 4 )；
According to the finite time control theory, as long as z converges within a finite time, then e 1 Convergence takes place in a finite time.
Get
Figure BDA0002533010510000134
In the formula:
Figure BDA0002533010510000135
for the corresponding estimation error, λ ═ diag [ λ ═ λ 1 ,λ 2 ,λ 3 ,λ 4 ,λ 5 ,λ 6 ]。
Then
Figure BDA0002533010510000136
R and a 2 、
Figure BDA0002533010510000137
Substituting to obtain:
Figure BDA0002533010510000138
the latter three terms of formula (57) were analyzed: due to the fact that
Figure BDA0002533010510000139
Is a scalar quantity, therefore
Figure BDA00025330105100001310
And because of
Figure BDA00025330105100001311
Therefore, it is
Figure BDA0002533010510000141
Defining variables:
Figure BDA0002533010510000142
because of the fact that
Figure BDA0002533010510000143
And is
Figure BDA0002533010510000144
Then when
Figure BDA0002533010510000145
Time of flight
Figure BDA0002533010510000146
Therefore, it is not only easy to use
Figure BDA0002533010510000147
When in use
Figure BDA0002533010510000148
When the temperature of the water is higher than the set temperature,
Figure BDA0002533010510000149
therefore, it is not only easy to use
Figure BDA00025330105100001410
Combining formula (62) and formula (64) to obtain
Figure BDA00025330105100001411
Substituting h into inequalities (61) and (60) to obtain
Figure BDA00025330105100001412
Due to z T k 3 z＞0，z T k 6 z is greater than 0, therefore
Figure BDA00025330105100001413
Wherein k is 3min ＝λ min (k 3 )z T z、k 6min ＝λ min (k 6 )z T z, so that the following formulae (36) and (37) can be obtained
Figure BDA0002533010510000151
Wherein,
Figure BDA0002533010510000152
therefore, according to the finite time control theory, the benthonic track tracking error can be converged within finite time by selecting proper parameters, and the verification is finished.
The invention obtains the performance of quickly tracking the expected pose by introducing the sliding mode disturbance observer system and the finite time control method, and relaxes the requirement on control parameter selection to a certain extent.
According to the method, ocean current disturbance and model uncertainty are combined into a disturbance lumped term, a finite time disturbance observer is used for approximating a disturbance lumped term value and introducing a neural network estimation observation error, and a finite time backstepping control method is selected to weaken buffeting, so that a mode of processing several factors influencing the track tracking accuracy of the benthonic AUV horizontal plane is included in the design of the controller and is closer to the actual engineering requirement.
2. Simulation part
2.1 simulation preparation
In order to verify the effectiveness of the motion control method designed by the invention, the motion control method is applied to a benthonic AUV horizontal plane motion model for simulation verification, and the influence caused by disturbance lumped terms of model uncertainty and ocean current disturbance combination is considered. The corresponding parameters of the benthonic AUV model are shown in tables 1-3, respectively.
TABLE 1 submersible AUV hydrodynamic coefficient
Figure BDA0002533010510000153
TABLE 2 submersible AUV inertia coefficient
Figure BDA0002533010510000161
TABLE 3 OBFN position and posture simulation initial value table
Figure BDA0002533010510000162
Disturbance lumped term
In order to facilitate simulation analysis, the invention quantifies model uncertainty and combines the model uncertainty with external interference into disturbance lumped terms H ═ 2sin0.2t +0.01,2sin0.2t +0.01 and sin0.2t +0.01] T And incorporated into the simulation module.
Disturbance observer parameters
The disturbance observer designed for verifying the method of the invention can effectively approach the external disturbance, and the simulation parameters are shown in table 4.
Table 4 disturbance observer parameter values
Figure BDA0002533010510000163
Controller parameters
The system is required to converge faster and control actuator inputs are required, from which the following simulation parameters are selected, as shown in table 5.
TABLE 5 motion control parameter values
Figure BDA0002533010510000164
Parameters are taken for the neural network term as follows:
λ i 15, c is 2; taking the number of nodes of the hidden layer of the RBF neural network as j-6, and expressing the center of the Gaussian function as d-d 1 ,…,d 6 ]The value is shown as formula (70), and the base width b j ＝40。
Figure BDA0002533010510000171
2.2 simulation analysis
Consider that the control law test is more representative if the desired trajectory is more complex. Therefore, the invention selects a more complex horizontal plane navigation track as the expected track, and the specific expression thereof is as follows:
η d (t)＝[x(t),y(t),ψ(t)] T (71)
Figure BDA0002533010510000172
wherein eta d Is the desired trajectory.
In simulation analysis, the influence of model uncertainty, disturbance lumped terms formed by external interference and saturated input on the benthonic AUV is considered. Fig. 1 to 3 show a horizontal plane 3-degree-of-freedom trajectory tracking curve of the bentable AUV. Fig. 4 to 6 show the estimation of the disturbance lumped term by the disturbance observer. Fig. 7 to 9 show the control input of the bentable AUV.
As can be seen from fig. 1 to 9, the method provided by the present invention can better observe external interference and can realize tracking of a desired trajectory in a short time, and further, control input is limited, a good dynamic process is obtained, and the performance of tracking the trajectory is quickly realized.
The above-described calculation examples of the present invention are merely to explain the calculation model and the calculation flow of the present invention in detail, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications of the present invention can be made based on the above description, and it is not intended to be exhaustive or to limit the invention to the precise form disclosed, and all such modifications and variations are possible and contemplated as falling within the scope of the invention.

Claims (3)

1. A method for quickly tracking and controlling a horizontal track of a benthonic AUV is characterized by comprising the following steps:
step one, considering model uncertainty and ocean current disturbance as a disturbance lumped term tau' d Establishing a kinematics and dynamics equation of the benthonic AUV considering the disturbance lumped term;
in the first step, a kinematics and dynamics equation of the bentable AUV considering the disturbance lumped term is established, which specifically includes:
Figure FDA0003693642420000011
wherein v is [ u, v ] 0 ,r] T V represents the velocity and angular velocity vector of the benthonic AUV in the horizontal plane under the carrier coordinate system, u represents the surging velocity, v represents the surging velocity 0 Representing the yaw velocity, and r representing the yaw angular velocity; superscript T represents transpose; eta ═ x, y, psi] T Representing three-degree-of-freedom pose vectors of the benthonic AUV in a horizontal plane under a fixed coordinate system, x and y respectively representing longitudinal and transverse position coordinates of the benthonic AUV under the fixed coordinate system, and psi representing a heading angle; j (η) represents a coordinate transformation matrix between the fixed coordinate system and the carrier coordinate system, J (η) being equal to R 3×3 R represents a real number; tau' d A perturbed lumped term representing the system; τ represents a control input vector;
Figure FDA0003693642420000012
is the first derivative of η and is,
Figure FDA0003693642420000013
representing the velocity and angular velocity vectors of the benthonic AUV under a fixed coordinate system;
Figure FDA0003693642420000014
is the first derivative of v and is,
Figure FDA0003693642420000015
representing the acceleration and angular acceleration vectors of the bentable AUV under a carrier coordinate system; m is a group of 0 A nominal value representing a mass inertia matrix; superscript-1 represents the inverse of the matrix, C 0 (v) A nominal value representing a coriolis centripetal force matrix; d 0 (v) A nominal value representing a fluid damping matrix; g 0 Nominal values representing the restoring force and restoring moment vectors;
the fixed coordinate system O-XYZ is as follows: taking any point on the sea surface or in the sea as an origin O, wherein the X axis is positioned on the horizontal plane, and the specified north direction is taken as the positive direction; the Y axis is positioned on the horizontal plane, and the specified east-righting direction is taken as the positive direction; the Z axis is vertical to the XOY coordinate plane and takes the geocentric direction as positive;
the carrier coordinate system O 0 -X 0 Y 0 Z 0 Comprises the following steps: the position of the center of gravity of the bentable AUV is taken as an origin O 0 ，X 0 The shaft is arranged in the longitudinal section of the benthonic AUV, is parallel to the waterline plane of the benthonic AUV and takes the heading direction of the boat as the positive direction; y is 0 The shaft is vertical to the longitudinal section of the bentable AUV, is parallel to the horizontal plane and takes the starboard direction as the positive direction; z 0 The shaft is arranged in the longitudinal section of the benthonic AUV, is vertical to the water line plane of the benthonic AUV and takes the submarine bottom direction as the positive direction;
Figure FDA0003693642420000016
in the formula, Δ M represents an uncertainty value of the mass inertia matrix; Δ c (v) represents the uncertainty value of the coriolis centripetal force matrix; Δ d (v) represents the uncertainty value of the fluid damping matrix; Δ g represents the uncertainty values of the restoring force and restoring moment vectors; tau is d Representing uncertain values of disturbance vectors caused by external interference;
step two, based on the kinematics and the kinetic equation established in the step one, establishing an error system of the track tracking by using a backstepping control method;
the specific process of the second step is as follows:
defining a tracking error:
Figure FDA0003693642420000021
in the formula, e 1 Indicating a tracking error; e.g. of the type 2 Representing a velocity tracking error; eta d ＝[x d ,y d ,ψ d ] T Representing the expected value x of the three-degree-of-freedom pose of the benthonic AUV in the horizontal plane under the fixed coordinate system d Is the expected value of x, y d Is the desired value of y,. psi d A desired value of ψ;
Figure FDA0003693642420000022
is eta d The first derivative of (a);
Figure FDA0003693642420000023
is e 1 The first derivative of (a); v. of d Representing the horizontal speed and angular speed expectation vector of the benthonic AUV under a carrier coordinate system;
then the error system for establishing trajectory tracking according to equation (2) is:
Figure FDA0003693642420000024
in the formula,
Figure FDA0003693642420000025
is e 2 The first derivative of (a);
Figure FDA0003693642420000026
is the first derivative of J (η);
Figure FDA0003693642420000027
is v is d The first derivative of (a);
defining a virtual error z:
z＝e 2 -α 1 (6)
in the formula, alpha 1 Is a virtual control law one;
taking the virtual error integral term as epsilon:
Figure FDA0003693642420000028
the error system of the trajectory tracking is changed to:
Figure FDA0003693642420000029
in the formula,
Figure FDA00036936424200000210
is the first derivative of ε;
Figure FDA00036936424200000211
is the first derivative of z;
Figure FDA00036936424200000212
is alpha 1 The first derivative of (a);
step three, designing a sliding mode disturbance observer according to the track tracking error system established in the step two,lumped term tau 'for disturbance by using designed sliding mode disturbance observer' d Performing approximation to obtain a disturbance lumped term tau' d The observed value of (a);
the third step comprises the following specific processes:
selecting a sliding mode surface function s as follows:
s＝ρ-v (9)
where ρ is an intermediate variable,
Figure FDA0003693642420000031
is the first derivative of ρ, and
Figure FDA0003693642420000032
in the form of:
Figure FDA0003693642420000033
in the formula, k 7 For positive definite diagonal matrix, k 7 ∈R 3×3 (ii) a L is positive definite diagonal matrix, L is diag 1 ,L 2 ,L 3 ]∈R 3×3 ，L 1 ,L 2 ,L 3 Are all the elements in the L, and the elements in the L,
Figure FDA0003693642420000034
Figure FDA0003693642420000035
the maximum value of the disturbance in three degrees of freedom; r is more than 0 and less than 1; sign stands for sign function; s ═ s 1 ,s 2 ,s 3 ] T ，s 1 ,s 2 ,s 3 Are all elements in s, with | s r ＝[|s 1 | r ,|s 2 | r ,|s 3 | r ] T - | represents the absolute value;
then the lumped term τ 'is disturbed' d Observed value of
Figure FDA0003693642420000036
In the formula,
Figure FDA0003693642420000037
is a disturbance lumped term τ' d The observed value of (a);
Figure FDA0003693642420000038
is the first derivative of s;
step four, adopting the radial basis function neural network to observe the error of the disturbance lumped term
Figure FDA0003693642420000039
Estimating to obtain observation error
Figure FDA00036936424200000310
An estimated value of (d);
step five, according to the disturbance lumped term tau' d Observed value and observation error of
Figure FDA00036936424200000311
The controller is designed according to the estimated value of the model, so that the pose of the benthonic AUV tracks the expected value in the limited time, and the tracking error converges in the limited time.
2. The method for rapidly tracking and controlling the horizontal trajectory of the benthonic AUV according to claim 1, wherein the specific process of the fourth step is as follows:
error of observation
Figure FDA00036936424200000312
Comprises the following steps:
Figure FDA00036936424200000313
using radial basis function nervesNetwork to disturbance lumped term observation error
Figure FDA00036936424200000314
And estimating, wherein the input n of the radial basis function neural network is as follows: n ═ e 1 T ,e 2 T ,η d T ,v d T ]Then the radial basis function neural network outputs the observation error
Figure FDA00036936424200000315
The estimated values of (c) are:
Figure FDA00036936424200000316
in the formula,
Figure FDA0003693642420000041
as an estimate of the weight matrix,
Figure FDA0003693642420000042
Figure FDA0003693642420000043
are all made of
Figure FDA0003693642420000044
The sub-matrix of (1) is,
Figure FDA0003693642420000045
Figure FDA0003693642420000046
representing the estimated weight of the ith neural network in the jth row, i is 1,2, …,6, phi (n) is an intermediate variable, phi (n) is [ phi (n) ] 1 (n),φ 2 (n),…,φ 6 (n)] T ，φ i (n) represents the radial basis function of the gaussian version of the ith neural network.
3. The method for rapidly tracking and controlling the horizontal trajectory of the benthonic AUV according to claim 2, wherein the specific process of the fifth step is as follows:
the control input vector τ is constrained by the saturation value:
sat(τ)＝[sat(τ 1 )，sat(τ 2 )，sat(τ 3 )] T (19)
wherein sat (τ) is an output value obtained by saturation limiting processing of a control input vector, τ j A jth value representing the control input vector τ, j being 1,2, 3;
sat(τ j ) Representing the nonlinear saturation characteristics of the actuator, the saturation control function is described as:
sat(τ j )＝τ j (t)+θ j (t) (20)
wherein
Figure FDA0003693642420000047
In the formula, theta j (t) is a saturation control term, τ mj For controlling the jth value τ of the input vector τ j A maximum allowable value of;
the adaptive backstepping control law is designed as follows:
Figure FDA0003693642420000048
in the formula, τ s Representing nominal values of control input vectors, alpha 2 To control law two, k virtually i Is positive definite diagonal matrix, i is 1,2, … 6, k i ∈R 3×3 A is a constant, a is more than 0 and less than 1,
Figure FDA0003693642420000049
is that
Figure FDA00036936424200000410
C is the control parameter to be designed and the adaptive gain, c is more than 0, lambda is a constant, and lambda is more than 0.
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