CN113093771A - Neural network-based underwater robot-manipulator system modeling method and system - Google Patents

Neural network-based underwater robot-manipulator system modeling method and system Download PDF

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CN113093771A
CN113093771A CN202110370197.8A CN202110370197A CN113093771A CN 113093771 A CN113093771 A CN 113093771A CN 202110370197 A CN202110370197 A CN 202110370197A CN 113093771 A CN113093771 A CN 113093771A
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underwater robot
manipulator
matrix
neural network
weight matrix
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CN113093771B (en
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程松松
方笑晗
潘天红
樊渊
朱明健
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Anhui University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/04—Control of altitude or depth
    • G05D1/06—Rate of change of altitude or depth
    • G05D1/0692—Rate of change of altitude or depth specially adapted for under-water vehicles
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control

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Abstract

The invention provides an underwater robot-manipulator modeling method and system based on an identification neural network, wherein an underwater robot-manipulator consists of an underwater robot naval vessel and a corresponding mechanical arm, and the modeling process comprises the following steps: firstly, establishing a coordinate system, and respectively defining a generalized coordinate system and generalized control force of the coordinate system; then establishing a kinetic equation of the underwater robot
Figure DDA0003008958920000011
The value of the function h (ζ, τ) is approximated by a single hidden layer feedforward neural network. For convenience of convergence analysis, only the weight matrix W from the hidden layer to the output layer is processedIUpdating, yielding value matrix WiIs a constant matrix. Finally, a method of verification is also presented. The invention relates to a modeling method of an underwater robot-manipulator system based on a neural network, which comprises the following steps: 1. designed underwater robot comprises a shipA body and a multi-link manipulator; 2. the designed recognition neural network can effectively recognize the dynamic model of the underwater robot; 3. the weight matrix updating law of the identification neural network can ensure the convergence of the position error of the underwater robot.

Description

Neural network-based underwater robot-manipulator system modeling method and system
Technical Field
The invention relates to the field of modeling of underwater robots and identification neural networks, in particular to a method for modeling an underwater robot-manipulator system based on an identification neural network.
Background
In recent years, with the development of oceans, the application of underwater robots is gradually attracting attention of various industries. An Underwater robot-Manipulator System (UVMS) is an automatic device capable of observing and performing autonomous operation Underwater, and has great potential application value in the aspects of submarine scientific investigation, resource exploration, pipeline laying, offshore culture and the like. The UVMS system consists of an underwater robot naval vessel and an underwater operation manipulator, and the operation tasks to be executed are completed together through the movement of the underwater robot naval vessel and the movement of the underwater manipulator joint.
The motion control of the underwater robot has the following technical difficulties:
UVMS has the dynamic characteristics of nonlinearity, strong coupling, time variation, high dimension and the like, so that the establishment of an accurate mathematical model is difficult.
The complexity of the underwater environment can make it difficult to build accurate kinetic models.
Prior art related to the present invention: an underwater robot-underwater manipulator system CN 108860527A.
The technical scheme of the prior art I is as follows:
the invention discloses an underwater robot-underwater manipulator system, and belongs to the field of underwater robots. The medicine consists of three parts: the underwater robot comprises an underwater robot body, an underwater manipulator and an auxiliary adjusting device. The underwater robot body is a cable-free autonomous underwater robot, and the power system of the underwater robot body adopts an under-actuated mode to realize the attitude and motion control of the underwater robot. The auxiliary adjusting device is installed under the underwater robot, the gravity center of the underwater robot can be adjusted by moving the sliding block, the influence of the underwater manipulator on the gravity center of the underwater robot in the motion process is compensated, and the attitude stability of the underwater robot is realized.
The first prior art has the following defects:
1) the built model is only a dynamic model of the underwater manipulator and is irrelevant to the underwater robot body.
2) And (3) establishing a dynamic model of the underwater manipulator, which is only a model under an ideal condition.
The second prior art related to the present invention: a underwater robot state and parameter joint estimation method CN102862666A based on self-adaptation UFK is disclosed.
The technical scheme of the prior art II is as follows:
an adaptive UFK-based underwater robot state and parameter joint estimation method is provided. Firstly, an extended reference model of the underwater robot is established, wherein the extended reference model comprises an underwater robot dynamics model and a propeller fault model. And (3) transmitting and updating an extended state formed by the underwater robot state and the propeller fault by adopting a main filter of the self-adaption UFK, and estimating the underwater robot state and the propeller fault information at the same time.
The second prior art has the defects
1) The underwater robot only comprises a robot body and cannot complete grabbing actions.
2) The method can only estimate the state information and propeller information of the underwater robot, and cannot provide a dynamic model of the underwater robot.
The third prior art related to the present invention: a dynamic and kinematic estimation method for a deep sea operation type underwater robot CN 103942383A.
The third technical scheme in the prior art:
relates to the field of deep sea operation type ROV, in particular to a dynamics and kinematics estimation method of a deep sea operation type underwater robot. The method comprises the following steps: establishing a fixed coordinate system, a satellite coordinate system and a propeller coordinate system, and estimating a six-degree-of-freedom coordinate transformation matrix: estimating a working underwater robot quality matrix and an induced Coriolis force and centripetal force matrix; estimating hydrodynamic force applied to a working type ROV: estimating the static force borne by the operation type ROV: estimating a working ROV thrust; estimating an unknown interference term: final kinetic and kinematic models of the working ROV were determined.
Disadvantages of the third prior art
1) The modeling method is based on complex fluid mechanics, dynamics and ship maneuverability theory.
2) The underwater robot does not include a robot arm.
Disclosure of Invention
The invention aims to solve the technical problem of how to effectively establish a system model of an underwater robot and a manipulator.
The invention solves the technical problems through the following technical means:
the invention provides a neural network-based modeling method of an underwater robot-manipulator system, wherein the underwater robot-manipulator system consists of an underwater robot naval vessel and a corresponding manipulator, and a coordinate system for defining the underwater robot-manipulator system comprises a fixed coordinate system O-XYZ, a naval vessel coordinate system O-XYZ and a manipulator joint coordinate system Oi-xiyiziThe origin of the coordinate system of the naval vessel is coincident with the mass center of the naval vessel, and the generalized coordinate system and the generalized control force of the underwater robot-manipulator can be respectively defined as
ζ＝[x y z a b c q1 … qn]T (1)
τ＝[Fx Fy Fz Wx Wy Wz τ1 … τn] (2)
Wherein ζ ═ ηT qT]T∈R6+nIs a generalized position vector of the underwater robot-manipulator, where R6+nThe dimension representing the vector being 6+ n-dimensional, qTIs the transposition of a vector q, comprises the position and the posture of the underwater robot naval vessel and the variable of a manipulator joint, and the vector eta is [ x y z a b c ═ c]TWherein x, y and z respectively represent the position coordinates of the center of mass of the underwater robot naval body in a fixed coordinate system, a, b and c respectively represent the roll angle, the pitch angle and the heading angle of the underwater robot naval vessel, and a vector q is [ q ═ q [ q ] q [1… qn]T∈RnIs the angle variable of the robot joint arm, R represents the dimension of the vector, T is the transposition of the vector, and tau belongs to R6+nThe dynamic equation of the underwater robot-manipulator is expressed as
Figure BDA0003008958900000041
Wherein f (ζ (t)). epsilon.Rn+6And g (. zeta. (t)). epsilon.R(n+6)×(n+6)Is an unknown function, where the underwater robot-manipulator kinetic equation is described again as
Figure BDA0003008958900000042
Wherein the matrix A ∈ R(6+n)×(6+n)Is a Hurwitz matrix, h (ζ, τ) ═ f (ζ) + g (ζ) τ -a ζ,
under ideal conditions, the value of the function h (ζ, τ) is approximated by a single hidden layer feedforward neural network, equation (4) being described as
Figure BDA0003008958900000043
Wherein
Figure BDA0003008958900000044
Is an ideal weight matrix from hidden layer to output layer, NIIs the number of hidden layer neurons,
Figure BDA0003008958900000045
Figure BDA0003008958900000046
is an ideal weight matrix from the input layer to the hidden layer,
Figure BDA0003008958900000047
is an activation function, whereIs selected from sigmaI(z)＝tanh(z)，εI(ζ)∈R(6+n)Is the reconstruction error of the approximation of the neural network.
Further, the modeling method of the underwater robot-manipulator system based on the neural network further comprises the following steps:
for weight matrix W from hidden layer to output layer onlyIUpdating, yielding value matrix WiAs a constant matrix, the identified neural network is constructed as follows
Figure BDA0003008958900000048
Wherein
Figure BDA0003008958900000049
Is to identify the location coordinates of the neural network structure,
Figure BDA00030089589000000410
is the estimated hidden-to-output layer weight matrix,
Figure BDA00030089589000000411
is an estimated z value, defining the position coordinate error of the vessel as
Figure BDA00030089589000000412
V is a state feedback item defined as
Figure BDA00030089589000000413
Wherein the parameter alpha epsilon R is selected such that the matrix A-alpha I(6+n)Is a reversible matrix of the phase-change material,
by the above definition, the estimated position coordinate error is identified as
Figure BDA00030089589000000414
Wherein
Figure BDA00030089589000000415
Further, the modeling method of the underwater robot-manipulator system based on the neural network further comprises the step of analyzing convergence of position coordinate errors and estimated weight matrix errors, and comprises the following steps:
suppose that: ideal weight matrix WIIs bounded and satisfies
Figure BDA0003008958900000051
The values of the activation functions are bounded and satisfied
Figure BDA0003008958900000052
The reconstruction error of the system is satisfied for any Zeta ∈ omega
Figure BDA0003008958900000053
Figure BDA0003008958900000054
And
Figure BDA0003008958900000055
are all known normal numbers;
leading: for a Hurwitz matrix A, there is a symmetric positive definite matrix P such that the following holds
ATP+PA＝-βI6+n (8)
Wherein β is a constant not equal to zero;
then, if the assumption is satisfied, the update law of the network weight matrix is identified as follows
Figure BDA0003008958900000056
Wherein l1And l2Is learning the rate factor, then identifying an estimated position coordinate error
Figure BDA0003008958900000057
And estimate weight matrix error
Figure BDA0003008958900000058
Are consistent and ultimately bounded;
and (3) proving that: defining the Lyapunov function as
Figure BDA0003008958900000059
Respectively deriving the two formulas
Figure BDA00030089589000000510
For a trace, tr (xy) tr (YX) YX holds, where X ∈ Rn×1，Y∈R1×nThen L is2The derivation of (t) with respect to time can be simplified to
Figure BDA0003008958900000061
Order to
Figure BDA0003008958900000062
The combined vertical type (11), (12), (13) can be obtained by substituting the formula (10)
Figure BDA0003008958900000063
Therefore, as long as the position coordinate error is satisfied
Figure BDA0003008958900000064
Then there are
Figure BDA0003008958900000065
The system is therefore consistently and ultimately bounded, ultimately converging on a region
Figure BDA0003008958900000066
Provided that the parameter a is chosen sufficientlyIs large, then
Figure BDA0003008958900000067
Can be approximately considered as converging to the origin.
The invention also provides a modeling system of the underwater robot-manipulator system based on the neural network, wherein the underwater robot-manipulator consists of an underwater robot naval vessel and a corresponding manipulator, the modeling system comprises a modeling module, and the modeling module executes the following operations:
the coordinate system of the underwater robot-manipulator system is defined by a fixed coordinate system O-XYZ, a naval vessel self coordinate system O-XYZ and a manipulator joint coordinate system Oi-xiyiziThe origin of the coordinate system of the naval vessel is coincident with the mass center of the naval vessel, and the generalized coordinate system and the generalized control force of the underwater robot-manipulator can be respectively defined as
ζ＝[x y z a b c q1 … qn]T (1)
τ＝[Fx Fy Fz Wx Wy Wz τ1 … τn] (2)
Wherein ζ ═ ηT qT]T∈R6+nIs a generalized position vector of the underwater robot-manipulator, where R6+nThe dimension representing the vector being 6+ n-dimensional, qTIs the transposition of a vector q, comprises the position and the posture of the underwater robot naval vessel and the variable of a manipulator joint, and the vector eta is [ x y z a b c ═ c]TWherein x, y and z respectively represent the position coordinates of the center of mass of the underwater robot naval body in a fixed coordinate system, a, b and c respectively represent the roll angle, the pitch angle and the heading angle of the underwater robot naval vessel, and a vector q is [ q ═ q [ q ] q [1… qn]T∈RnIs the angle variable of the robot joint arm, R represents the dimension of the vector, T is the transposition of the vector, and tau belongs to R6+nThe generalized control force item of the system comprises generalized thrust borne by the underwater robot naval vessel and joint driving force of an underwater manipulator, so that the underwater robot-machineThe kinetic equation of the hand is expressed as
Figure BDA0003008958900000071
Wherein f (ζ (t)). epsilon.Rn+6And g (. zeta. (t)). epsilon.R(n+6)×(n+6)Is an unknown function, where the underwater robot-manipulator kinetic equation is described again as
Figure BDA0003008958900000072
Wherein the matrix A ∈ R(6+n)×(6+n)Is a Hurwitz matrix, h (ζ, τ) ═ f (ζ) + g (ζ) τ -a ζ,
under ideal conditions, the value of the function h (ζ, τ) is approximated by a single hidden layer feedforward neural network, equation (4) being described as
Figure BDA0003008958900000073
Wherein
Figure BDA0003008958900000074
Is an ideal weight matrix from hidden layer to output layer, NIIs the number of hidden layer neurons,
Figure BDA0003008958900000075
Figure BDA0003008958900000076
is an ideal weight matrix from the input layer to the hidden layer,
Figure BDA0003008958900000077
is an activation function, where σ is chosenI(z)＝tanh(z)，εI(ζ)∈R(6+n)Is the reconstruction error of the approximation of the neural network.
Further, the modeling system of the underwater robot-manipulator system based on the neural network further comprises a weight matrix updating module, and the weight matrix updating module executes the following operations:
for weight matrix W from hidden layer to output layer onlyIUpdating, yielding value matrix WiAs a constant matrix, the identified neural network is constructed as follows
Figure BDA0003008958900000081
Wherein
Figure BDA0003008958900000082
Is to identify the location coordinates of the neural network structure,
Figure BDA0003008958900000083
is the estimated hidden-to-output layer weight matrix,
Figure BDA0003008958900000084
is an estimated z value, defining the position coordinate error of the vessel as
Figure BDA0003008958900000085
V is a state feedback item defined as
Figure BDA0003008958900000086
Wherein the parameter alpha epsilon R is selected such that the matrix A-alpha I(6+n)Is a reversible matrix of the phase-change material,
by the above definition, the estimated position coordinate error is identified as
Figure BDA0003008958900000087
Wherein
Figure BDA0003008958900000088
Further, the modeling system of the underwater robot-manipulator system based on the neural network further comprises a module for analyzing convergence of the position coordinate error and the estimated weight matrix error, and the module for analyzing convergence of the position coordinate error and the estimated weight matrix error performs the following operations:
suppose that: ideal weight matrix WIIs bounded and satisfies
Figure BDA0003008958900000089
The values of the activation functions are bounded and satisfied
Figure BDA00030089589000000810
The reconstruction error of the system is satisfied for any Zeta ∈ omega
Figure BDA00030089589000000811
Figure BDA00030089589000000812
And
Figure BDA00030089589000000813
are all known normal numbers;
leading: for a Hurwitz matrix A, there is a symmetric positive definite matrix P such that the following holds
ATP+PA＝-βI6+n (8)
Wherein β is a constant not equal to zero;
then, if the assumption is satisfied, the update law of the network weight matrix is identified as follows
Figure BDA00030089589000000814
Wherein l1And l2Is learning the rate factor, then identifying an estimated position coordinate error
Figure BDA0003008958900000091
And estimate weight matrix error
Figure BDA0003008958900000092
Are consistent and ultimately bounded;
and (3) proving that: defining the Lyapunov function as
Figure BDA0003008958900000093
Respectively deriving the two formulas
Figure BDA0003008958900000094
For a trace, tr (xy) tr (YX) YX holds, where X ∈ Rn×1，Y∈R1×nThen L is2The derivation of (t) with respect to time can be simplified to
Figure BDA0003008958900000095
Order to
Figure BDA0003008958900000096
The combined vertical type (11), (12), (13) can be obtained by substituting the formula (10)
Figure BDA0003008958900000101
Therefore, as long as the position coordinate error is satisfied
Figure BDA0003008958900000102
Then there are
Figure BDA0003008958900000103
The system is therefore consistently and ultimately bounded, ultimately converging on a region
Figure BDA0003008958900000104
Provided that the parameter a is chosen large enough
Figure BDA0003008958900000105
Can be approximately considered as converging to the origin.
The invention has the advantages that:
the invention relates to a modeling method of an underwater robot-manipulator system based on a neural network, which comprises the following steps:
1. the designed underwater robot comprises a ship body and a multi-link manipulator;
2. the designed recognition neural network can effectively recognize the dynamic model of the underwater robot;
3. the weight matrix updating law of the identification neural network can ensure the convergence of the position error of the underwater robot.
Drawings
Fig. 1 is a graph of an underwater robot of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The underwater robot-manipulator in the invention is composed of an underwater robot naval vessel and a corresponding manipulator, as shown in figure 1, aiming at the surrounding environment of the underwater robot and the complexity of the underwater robot, the coordinate system of the underwater robot-manipulator system comprises a fixed coordinate system O-XYZ, a naval vessel coordinate system O-XYZ and a manipulator joint coordinate system Oi-xiyiziThe original point of the coordinate system of the naval vessel is coincided with the mass center of the naval vessel.
The generalized coordinate system and the generalized control force of the underwater robot-manipulator can be respectively defined as
ζ＝[x y z a b c q1 … qn]T (1)
τ＝[Fx Fy Fz Wx Wy Wz τ1 … τn] (2)
Wherein ζ ═ ηT qT]T∈R6+nIs a generalized position vector of the underwater robot-manipulator, where R6+nThe dimension representing the vector being 6+ n-dimensional, qTIs the transpose of the vector q. Including the position and attitude of the underwater robot vessel itself and the robot joint variables. Vector η ═ x y z a b c]TAnd x, y and z respectively represent the position coordinates of the center of mass of the ship body of the underwater robot in a fixed coordinate system. and a, b and c respectively represent the roll angle, the pitch angle and the heading angle of the underwater robot naval vessel. Wherein the vector q is [ q ]1… qn]T∈RnIs the robot joint arm angle variable, R represents the dimension of the vector, and T is the transpose of the vector. Tau epsilon to R6+nThe method is a system generalized control force item and comprises generalized thrust borne by an underwater robot naval vessel and joint driving force of an underwater manipulator. The kinetic equation of the robot-manipulator of the underwater robot can be expressed as
Figure BDA0003008958900000111
Wherein f (ζ (t)). epsilon.Rn+6And g (. zeta. (t)). epsilon.R(n+6)×(n+6)Is an unknown function, here we describe again the underwater robot-manipulator kinetic equation as
Figure BDA0003008958900000112
Wherein the matrix A ∈ R(6+n)×(6+n)Is a Hurwitz matrix, h (ζ, τ) ═ f (ζ) + g (ζ) τ -a ζ.
Under ideal conditions, we approximate the value of the function h (ζ, τ) through a single hidden layer feedforward neural network, and equation (4) can be described as
Figure BDA0003008958900000121
Wherein
Figure BDA0003008958900000122
Is an ideal weight matrix from hidden layer to output layer, NIIs the number of hidden layer neurons,
Figure BDA0003008958900000123
Figure BDA0003008958900000124
is an ideal weight matrix from the input layer to the hidden layer,
Figure BDA0003008958900000125
is an activation function where we can choose σI(z)＝tanh(z)。εI(ζ)∈R(6+n)Is the reconstruction error of the approximation of the neural network.
The kinetic equation describes the relationship between the coordinate position of the controlled object (underwater robot-manipulator) and the input force of the driving unit. The dynamic equations are provided to facilitate the control of the coordinate position of the actual underwater robot-manipulator, for example, from the point a to the point B along a straight line, what control force should be applied to the underwater robot-manipulator.
For convenience of convergence analysis, we only need to consider the weight matrix W from hidden layer to output layerIUpdating, yielding value matrix WiIs a constant matrix.
The identified neural network is constructed as follows
Figure BDA0003008958900000126
Wherein
Figure BDA0003008958900000127
Is to identify the location coordinates of the neural network structure,
Figure BDA0003008958900000128
is the estimated hidden-to-output layer weight matrix,
Figure BDA0003008958900000129
is the estimated z value. Defining the position coordinate error of the naval vessel as
Figure BDA00030089589000001210
V is a state feedback item defined as
Figure BDA00030089589000001211
Wherein the parameter alpha epsilon R is selected such that the matrix A-alpha I(6+n)Is an invertible matrix.
By the above definition, the estimated position coordinate error is identified as
Figure BDA00030089589000001212
Wherein
Figure BDA00030089589000001213
We propose a hypothesis that is widely applied to neural network stability analysis.
Suppose that: ideal weight matrix WIIs bounded and satisfies
Figure BDA00030089589000001214
The values of the activation functions are bounded and satisfied
Figure BDA0003008958900000131
The reconstruction error of the system is satisfied for any Zeta ∈ omega
Figure BDA0003008958900000132
Figure BDA0003008958900000133
And
Figure BDA0003008958900000134
are all known normal numbers.
Leading: for a Hurwitz matrix A, there is a symmetric positive definite matrix P such that the following holds
ATP+PA＝-βI6+n (8)
Where β is a constant not equal to zero.
Then, if the assumption is satisfied, the update law of the network weight matrix is identified as follows
Figure BDA0003008958900000135
Wherein l1And l2Is learning the rate factor, then identifying an estimated position coordinate error
Figure BDA0003008958900000136
And estimate weight matrix error
Figure BDA0003008958900000137
Is consistent and ultimately bounded.
And (3) proving that: defining the Lyapunov function as
Figure BDA0003008958900000138
Respectively deriving the two formulas
Figure BDA0003008958900000139
For a trace, tr (xy) tr (YX) YX holds, where X ∈ Rn×1，Y∈R1×n. Then L is2The derivation of (t) with respect to time can be simplified to
Figure BDA00030089589000001310
Order to
Figure BDA0003008958900000141
The combined vertical type (11), (12), (13) can be obtained by substituting the formula (10)
Figure BDA0003008958900000142
Therefore, as long as the position coordinate error is satisfied
Figure BDA0003008958900000143
Then there are
Figure BDA0003008958900000144
The system is therefore consistently and ultimately bounded, ultimately converging on a region
Figure BDA0003008958900000145
Provided that the parameter a is chosen large enough
Figure BDA0003008958900000146
Can be approximately considered as converging to the origin.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (6)

1. The modeling method of the underwater robot-manipulator system based on the neural network is characterized by comprising the following steps: the underwater robot-manipulator consists of an underwater robot naval vessel and a corresponding manipulator, and a coordinate system for defining the underwater robot-manipulator system comprises a fixed coordinate system O-XYZ, a naval vessel coordinate system O-XYZ and a machineHand joint coordinate system oi-xiyiziThe origin of the coordinate system of the naval vessel is coincident with the mass center of the naval vessel, and the generalized coordinate system and the generalized control force of the underwater robot-manipulator can be respectively defined as
ζ＝[x y z a b c q1…qn]T (1)
τ＝[Fx Fy Fz Wx Wy Wz τ1…τn] (2)
Wherein ζ ═ ηT qT]T∈R6+nIs a generalized position vector of the underwater robot-manipulator, where R6+nThe dimension representing the vector being 6+ n-dimensional, qTIs the transposition of a vector q, comprises the position and the posture of the underwater robot naval vessel and the variable of a manipulator joint, and the vector eta is [ x y z a b c ═ c]TWherein x, y and z respectively represent the position coordinates of the center of mass of the underwater robot naval body in a fixed coordinate system, a, b and c respectively represent the roll angle, the pitch angle and the heading angle of the underwater robot naval vessel, and a vector q is [ q ═ q [ q ] q [1…qn]T∈RnIs the angle variable of the robot joint arm, R represents the dimension of the vector, T is the transposition of the vector, and tau belongs to R6+nThe dynamic equation of the underwater robot-manipulator is expressed as
Figure FDA0003008958890000012
Wherein f (ζ (t)). epsilon.Rn+6And g (. zeta. (t)). epsilon.R(n+6)×(n+6)Is an unknown function, where the underwater robot-manipulator kinetic equation is described again as
Figure FDA0003008958890000013
Wherein the matrix A ∈ R(6+n)×(6+n)Is a Hurwitz matrix, h (ζ, τ) ═ f (ζ) + g (ζ) τ -a ζ,
under ideal conditions, the value of the function h (ζ, τ) is approximated by a single hidden layer feedforward neural network, equation (4) being described as
Figure FDA0003008958890000011
Wherein
Figure FDA0003008958890000021
Is an ideal weight matrix from hidden layer to output layer, NIIs the number of hidden layer neurons,
Figure FDA0003008958890000022
is an ideal weight matrix from the input layer to the hidden layer,
Figure FDA0003008958890000023
is an activation function, where σ is chosenI(z)＝tanh(z)，εI(ζ)∈R(6+n)Is the reconstruction error of the approximation of the neural network.
2. The modeling method of a neural network-based underwater robot-manipulator system as claimed in claim 1, wherein: also comprises the following steps:
for weight matrix W from hidden layer to output layer onlyIUpdating, yielding value matrix WiAs a constant matrix, the identified neural network is constructed as follows
Figure FDA0003008958890000024
Wherein
Figure FDA0003008958890000025
Is to identify the location coordinates of the neural network structure,
Figure FDA0003008958890000026
is the estimated hidden-to-output layer weight matrix,
Figure FDA0003008958890000027
is an estimated z value, defining the position coordinate error of the vessel as
Figure FDA0003008958890000028
V is a state feedback item defined as
Figure FDA0003008958890000029
Wherein the parameter alpha epsilon R is selected such that the matrix A-alpha I(6+n)Is a reversible matrix of the phase-change material,
by the above definition, the estimated position coordinate error is identified as
Figure FDA00030089588900000210
Wherein
Figure FDA00030089588900000211
3. The modeling method of a neural network-based underwater robot-manipulator system according to claim 2, characterized in that: the method also comprises a step of analyzing the convergence of the position coordinate error and the estimation weight matrix error, and comprises the following steps:
suppose that: ideal weight matrix WIIs bounded and satisfies
Figure FDA00030089588900000212
The values of the activation functions are bounded and satisfied
Figure FDA00030089588900000213
The reconstruction error of the system is satisfied for any Zeta ∈ omega
Figure FDA00030089588900000214
Figure FDA00030089588900000215
And
Figure FDA00030089588900000216
are all known normal numbers;
leading: for a Hurwitz matrix A, there is a symmetric positive definite matrix P such that the following holds
ATP+PA＝-βI6+n (8)
Wherein β is a constant not equal to zero;
then, if the assumption is satisfied, the update law of the network weight matrix is identified as follows
Figure FDA0003008958890000031
Wherein l1And l2Is learning the rate factor, then identifying an estimated position coordinate error
Figure FDA0003008958890000032
And estimate weight matrix error
Figure FDA0003008958890000033
Are consistent and ultimately bounded;
and (3) proving that: defining the Lyapunov function as
Figure FDA0003008958890000034
Respectively deriving the two formulas
Figure FDA0003008958890000035
For a trace, tr (xy) tr (YX) YX holds, where X ∈ Rn×1，Y∈R1×nThen L is2The derivation of (t) with respect to time can be simplified to
Figure FDA0003008958890000036
Order to
Figure FDA0003008958890000037
The combined vertical type (11), (12), (13) can be obtained by substituting the formula (10)
Figure FDA0003008958890000041
Therefore, as long as the position coordinate error is satisfied
Figure FDA0003008958890000042
Then there are
Figure FDA0003008958890000043
The system is therefore consistently and ultimately bounded, ultimately converging on a region
Figure FDA0003008958890000044
Provided that the parameter a is chosen large enough
Figure FDA0003008958890000045
Can be approximately considered as converging to the origin.
4. The modeling system of the underwater robot-manipulator system based on the neural network is characterized in that: the underwater robot-manipulator consists of an underwater robot naval vessel and a corresponding manipulator, the modeling system comprises a modeling module, and the modeling module executes the following operations:
the coordinate system of the underwater robot-manipulator system is defined by a fixed coordinate system O-XYZ, a naval vessel self coordinate system O-XYZ and a manipulator joint coordinate system Oi-xiyiziThe origin of the coordinate system of the naval vessel is coincident with the mass center of the naval vessel, and the generalized coordinate system and the generalized control force of the underwater robot-manipulator can be respectively defined as
ζ＝[x y z a b c q1…qn]T (1)
τ＝[Fx Fy Fz Wx Wy Wz τ1…τn] (2)
Wherein ζ ═ ηT qT]T∈R6+nIs a generalized position vector of the underwater robot-manipulator, where R6+nThe dimension representing the vector being 6+ n-dimensional, qTIs the transposition of a vector q, comprises the position and the posture of the underwater robot naval vessel and the variable of a manipulator joint, and the vector eta is [ x y z a b c ═ c]TWherein x, y and z respectively represent the position coordinates of the center of mass of the underwater robot naval body in a fixed coordinate system, a, b and c respectively represent the roll angle, the pitch angle and the heading angle of the underwater robot naval vessel, and a vector q is [ q ═ q [ q ] q [1…qn]T∈RnIs the angle variable of the robot joint arm, R represents the dimension of the vector, T is the transposition of the vector, and tau belongs to R6+nThe dynamic equation of the underwater robot-manipulator is expressed as
Figure FDA0003008958890000051
Wherein f (ζ (t)). epsilon.Rn+6And g (. zeta. (t)). epsilon.R(n+6)×(n+6)Is an unknown function, where the underwater robot-manipulator kinetic equation is described again as
Figure FDA0003008958890000052
Wherein the matrix A ∈ R(6+n)×(6+n)Is a Hurwitz matrix, h (ζ, τ) ═ f (ζ) + g (ζ) τ -a ζ,
under ideal conditions, the value of the function h (ζ, τ) is approximated by a single hidden layer feedforward neural network, equation (4) being described as
Figure FDA0003008958890000053
Wherein
Figure FDA0003008958890000054
Is an ideal weight matrix from hidden layer to output layer, NIIs the number of hidden layer neurons,
Figure FDA0003008958890000055
is an ideal weight matrix from the input layer to the hidden layer,
Figure FDA0003008958890000056
is an activation function, where σ is chosenI(z)＝tanh(z)，εI(ζ)∈R(6+n)Is the reconstruction error of the approximation of the neural network.
5. The modeling system of a neural network-based underwater robot-manipulator system as claimed in claim 4, wherein: the weight matrix updating module executes the following operations:
for weight matrix W from hidden layer to output layer onlyIUpdating, yielding value matrix WiAs a constant matrix, the identified neural network is constructed as follows
Figure FDA0003008958890000057
Wherein
Figure FDA0003008958890000058
Is to identify the location coordinates of the neural network structure,
Figure FDA0003008958890000059
is the estimated hidden-to-output layer weight matrix,
Figure FDA00030089588900000510
is an estimated z value, defining the position coordinate error of the vessel as
Figure FDA00030089588900000511
V is a state feedback item defined as
Figure FDA00030089588900000512
Wherein the parameter alpha epsilon R is selected such that the matrix A-alpha I(6+n)Is a reversible matrix of the phase-change material,
by the above definition, the estimated position coordinate error is identified as
Figure FDA0003008958890000061
Wherein
Figure FDA0003008958890000062
6. The modeling system of a neural network-based underwater robot-manipulator system as claimed in claim 5, wherein: the device also comprises a module for analyzing the convergence of the position coordinate errors and the estimated weight matrix errors, wherein the module for analyzing the convergence of the position coordinate errors and the estimated weight matrix errors executes the following operations:
suppose that: ideal weight matrix WIIs bounded and satisfies
Figure FDA0003008958890000063
The values of the activation functions are bounded and satisfied
Figure FDA0003008958890000064
The reconstruction error of the system is satisfied for any Zeta ∈ omega
Figure FDA0003008958890000065
Figure FDA0003008958890000066
And
Figure FDA0003008958890000067
are all known normal numbers;
leading: for a Hurwitz matrix A, there is a symmetric positive definite matrix P such that the following holds
ATP+PA＝-βI6+n (8)
Wherein β is a constant not equal to zero;
then, if the assumption is satisfied, the update law of the network weight matrix is identified as follows
Figure FDA0003008958890000068
Wherein l1And l2Is learning the rate factor, then identifying an estimated position coordinate error
Figure FDA0003008958890000069
And estimate weight matrix error
Figure FDA00030089588900000610
Are consistent and ultimately bounded;
and (3) proving that: defining the Lyapunov function as
Figure FDA00030089588900000611
Respectively deriving the two formulas
Figure FDA0003008958890000071
For a trace, tr (xy) tr (YX) YX holds, where X ∈ Rn×1，Y∈R1×nThen L is2The derivation of (t) with respect to time can be simplified to
Figure FDA0003008958890000072
Order to
Figure FDA0003008958890000073
The combined vertical type (11), (12), (13) can be obtained by substituting the formula (10)
Figure FDA0003008958890000074
Therefore, as long as the position coordinate error is satisfied
Figure FDA0003008958890000075
Then there are
Figure FDA0003008958890000076
The system is therefore consistently and ultimately bounded, ultimately converging on a region
Figure FDA0003008958890000081
Provided that the parameter a is chosen large enough
Figure FDA0003008958890000082
Can be approximately considered as converging to the origin.
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