CN112757298B - Intelligent inversion control method for manipulator - Google Patents

Intelligent inversion control method for manipulator Download PDF

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CN112757298B
CN112757298B CN202011608786.7A CN202011608786A CN112757298B CN 112757298 B CN112757298 B CN 112757298B CN 202011608786 A CN202011608786 A CN 202011608786A CN 112757298 B CN112757298 B CN 112757298B
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CN112757298A (en
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祁兴华
张川丰
侯世玺
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Suzhou Liankai Automation Co ltd
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    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator

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Abstract

The invention discloses an intelligent inversion control method for a manipulator, which comprises the following steps: s1, building a manipulator power model; s2, designing an inversion controller of the manipulator; s3, using fuzzy neural network to approach the unknowns in the inversion controllerState, eliminating τMUncertainty of (2). The control method not only can effectively solve the problem that the uncertainty is difficult to effectively process in the control of a common manipulator, but also adopts a fully-regulated fuzzy neural network to approach an inversion controller, thereby relaxing the limitation that the uncertain function and the interference upper bound need to be predicted and further improving the system robustness.

Description

Intelligent inversion control method for manipulator
Technical Field
The invention relates to a manipulator control technology, in particular to an intelligent inversion control method for a manipulator.
Background
The manipulator is a mechanical device which has the action function similar to that of a human arm, can grab and place objects in space or perform other operations, can replace heavy labor of people to realize mechanization and automation of production, can operate in a harmful environment to protect personal safety, and is widely applied to departments of mechanical manufacturing, metallurgy, electronics, light industry, atomic energy and the like.
Due to the fact that factors such as uncertainty of joint parameters of the manipulator exist, model uncertainty exists in a manipulator dynamic model, and the manipulator control accuracy based on model control is affected. At present, aiming at the problem that uncertainty factors such as model uncertainty and external interference influence the control precision of a manipulator joint, the uncertainty factors are mostly approximated or compensated through an uncertainty estimator, and the adaptive law of parameters in the estimator is determined through stability analysis. A neural network and a fuzzy system with universal approximation capability are widely applied to uncertainty approximation compensation, but the controller for manipulator control needs to estimate system uncertainty upper bound information in advance, so that certain limitations exist.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an intelligent inversion control method for a manipulator.
In order to achieve the purpose, the invention adopts the technical scheme that: a manipulator intelligent inversion control method comprises the following steps:
s1, building a mechanical arm power model
Consider a rigid manipulator with n joints, whose kinetic equation is:
Figure BDA0002871013720000011
wherein the ratio of q,
Figure BDA0002871013720000012
the position, speed and acceleration vector of each joint of the manipulator, M (q) epsilon Rn×nIn order to include an inertial matrix of the additional mass,
Figure BDA0002871013720000013
g (q) e R as a coupling matrix of centrifugal force and Coriolis forcen×1Is a vector of a gravity matrix and is,
Figure BDA0002871013720000014
for friction torque, τd∈Rn×1For unknown applied interference, tau epsilon Rn×1N is the degree of freedom of the joint;
s2 inversion controller of design manipulator
The inversion controller is
Figure BDA0002871013720000015
Wherein, tauM≥||τd|, sgn (e) is a sign function; tracking error e1＝q-qd，
Figure BDA0002871013720000021
Figure BDA0002871013720000022
c1Is a non-zero normal constant;
s3, utilizing fuzzy neural network to approach and invert the unknown state in the controller to eliminate tauMUncertainty of (2).
Preferably, in S2, the inversion controller is designed as follows:
defining a tracking error as
e1＝q-qd (2)
Wherein q isdIs the desired position of the joint;
derived from (2)
Figure BDA0002871013720000023
Selecting virtual control quantities
Figure BDA0002871013720000024
Wherein c is1Is a non-zero normal number;
taking the Lyapunov function as
Figure BDA0002871013720000025
Definition of
Figure BDA0002871013720000026
Derived from formula (5)
Figure BDA0002871013720000027
If e2When the value is equal to 0, then
Figure BDA0002871013720000028
The stability requirement is met, and the next design is continued;
the second step is that: e.g. of the type2Can be expressed as
Figure BDA0002871013720000029
Then, an inversion controller is designed to obtain an equation (8).
Preferably, the fuzzy neural network adopts a four-layer network structure, and each layer is respectively: the fuzzy inference system comprises an input layer, a fuzzy inference layer and an output layer.
Preferably, in the fuzzy neural network, the network input is a tracking deviation e1Output as control force tauFNN，
A first layer: input layer
Each node of the layer is directly connected with each component of the input quantity, and the input quantity is transmitted to the second layer;
a second layer: blurring layer
A gaussian-type function is used as the membership function,
Figure BDA0002871013720000031
representing tracking offset vector e1The elements (A) and (B) in (B),
Figure BDA0002871013720000032
and
Figure BDA0002871013720000033
the centre vector and the base width of the membership function of the ith input variable, the jth fuzzy set, respectively, i.e.
Figure BDA0002871013720000034
Easy to calculate, using NpiRepresenting individual numbers of membership functions, and we define the sets of adaptive parameter vectors b and c representing all the basis width and center vectors of Gaussian membership functions, respectively, i.e.
Figure BDA0002871013720000035
Figure BDA0002871013720000036
Wherein
Figure BDA0002871013720000037
Representing the total number of membership functions;
and a third layer: rule layer
The layer uses a fuzzy inference mechanism, and the output of each node is the product of all input signals of the node, i.e. the output of each node is the product of all input signals of the node
Figure BDA0002871013720000038
In the formula Ik(k＝1,...,Ny) The k-th output of the rule layer is represented,
Figure BDA0002871013720000039
representing the connection weight matrix between the fuzzification layer and the regular layer, here taken as the unit vector, NyIs the total number of rules;
a fourth layer: output layer
The nodes of the layer represent output variables, each node yo(o＝1,...,No) The output of (2) being the sum of all input signals of the node, i.e.
Figure BDA00028710137200000310
Further, the input-output relationship of the fuzzy neural network is defined as follows:
Figure BDA00028710137200000311
wherein the content of the first and second substances,
Figure BDA0002871013720000041
Figure BDA0002871013720000042
according to the universal approximation theory, there is an optimal control force
Figure BDA0002871013720000043
Satisfy the requirement of
Figure BDA0002871013720000044
Where ε is the minimum reconstruction error vector, W*,b*And c*Optimal parameters of W, b and c respectively;
the output control force of the fuzzy neural network is assumed to be of the following form:
Figure BDA0002871013720000045
wherein the content of the first and second substances,
Figure BDA0002871013720000046
and
Figure BDA0002871013720000047
are respectively W*,b*And c*Is determined by the estimated value of (c),
defining an approximation error:
Figure BDA0002871013720000048
using Taylor series expansion, one can obtain
Figure BDA0002871013720000049
Wherein the content of the first and second substances,
Figure BDA00028710137200000410
b*and c*Is the optimum value for b and c,
Figure BDA00028710137200000411
and
Figure BDA00028710137200000412
is a b*And c*Estimated value of, OnvIs a high-order term of the magnetic field,
Figure BDA00028710137200000413
Figure BDA00028710137200000414
then (18) is substituted into (17) to obtain
Figure BDA00028710137200000415
Wherein the content of the first and second substances,
Figure BDA00028710137200000416
according to the formulae (8), (17), (19), we can also obtain
Figure BDA0002871013720000051
The adaptive law of the weight, the base width and the central vector of the fuzzy neural network can be designed as follows:
Figure BDA0002871013720000052
Figure BDA0002871013720000053
Figure BDA0002871013720000054
wherein the content of the first and second substances,
Figure BDA0002871013720000055
is e2Element (iii) σω,σb,σcIs a normal number, and is,
Figure BDA0002871013720000056
is that
Figure BDA0002871013720000057
Is determined by the estimated value of (c),
Figure BDA0002871013720000058
is omegaiThe optimum value of (d);
and (3) proving that: defining the lyapunov function as
Figure BDA0002871013720000059
Derivative and substitute (20) into
Figure BDA00028710137200000510
Bringing (21) to (23) into (25) to obtain
Figure BDA00028710137200000511
If τ is satisfiedM≥||τdIf the manipulator intelligent inversion control method is stable, the manipulator intelligent inversion control method is stable.
Due to the application of the technical scheme, compared with the prior art, the invention has the following advantages: according to the manipulator intelligent inversion control method, the full-adjustment fuzzy neural network structure is adopted, the self-adaptive fuzzy neural network control system based on the inversion design is designed, and the limitation that an uncertain function and an interference upper bound need to be predicted is relaxed, so that the defect that an inversion control strategy needs system accurate information is overcome, and the system robustness is further improved.
Drawings
FIG. 1 is a block diagram of a manipulator intelligent inversion controller according to the present invention;
Detailed Description
The technical solution of the present invention is further explained with reference to the drawings and the specific embodiments.
A manipulator intelligent inversion control method comprises the following steps:
s1, building a manipulator power model
Consider a rigid manipulator with n joints, whose kinetic equation is:
Figure BDA0002871013720000061
wherein the ratio of q,
Figure BDA0002871013720000062
the position, speed and acceleration vector of each joint of the manipulator, M (q) epsilon Rn×nIn order to include an inertia matrix of the additional mass,
Figure BDA0002871013720000063
g (q) e R as a coupling matrix of centrifugal force and Coriolis forcen×1In the form of a gravity matrix vector,
Figure BDA0002871013720000064
for friction torque, τd∈Rn×1For unknown applied interference, T is equal to Rn×1N is the degree of freedom of the joint;
s2 inversion controller of design manipulator
The control object of the robot position tracking control system is to design an appropriate control input τ so that each joint position q of the robot tracks the desired position qd. The designed structure diagram of the intelligent inversion control is shown in fig. 1, and the design steps are as follows:
the first step is as follows:
defining a tracking error as
e1＝q-qd (2)
Derived from (2)
Figure BDA0002871013720000065
Selecting virtual control quantities
Figure BDA0002871013720000066
Wherein c is1Is a non-zero positive constant.
Taking the Lyapunov function as
Figure BDA0002871013720000067
Definition of
Figure BDA0002871013720000071
Derived from formula (5)
Figure BDA0002871013720000072
If e2When the value is equal to 0, then
Figure BDA0002871013720000073
The stability requirement is met, so the design is required to be continued;
the second step is that: e.g. of the type2Can be expressed as
Figure BDA0002871013720000074
The manipulator inversion controller can be designed as
Figure BDA0002871013720000075
Wherein, tauM≥||τd||；
Defining a Lyapunov function
Figure BDA0002871013720000076
Is derived by
Figure BDA0002871013720000077
Substituting the formula (8) into the formula (10) to obtain
Figure BDA0002871013720000078
From the above equation, the designed manipulator inversion controller is stable. However, the above-mentioned controllers require detailed system information and an upper uncertainty bound τ in practical systemsMIt is difficult to determine, and these problems indicate that the above controller is difficult to implement in practical applications. Therefore, to overcome these problems, a smart inversion controller is proposed.
S3, utilizing fuzzy neural network to approach and invert the unknown state in the controller to eliminate tauMUncertainty of (2).
The designed manipulator intelligent inversion controller adopts a fuzzy neural network to approach the inversion controller (8), so that the defect that the inversion controller needs detailed system information is overcome. The fuzzy neural network comprises input layer, fuzzy inference layer and output layer, the network input is tracking deviation e1Output as control force tauFNN. The signal propagation and the function of the layers in the fuzzy neural network are represented as follows:
a first layer: input layer
Each node of the layer is directly connected to each component of the input quantity, passing the input quantity to the next layer.
A second layer: blurring layer
A gaussian-type function is used as the membership function,
Figure BDA0002871013720000081
representing tracking offset vector e1The elements (A) and (B) in (B),
Figure BDA0002871013720000082
and
Figure BDA0002871013720000083
the centre vector and the base width of the membership function of the ith input variable, the jth fuzzy set, respectively, i.e.
Figure BDA0002871013720000084
Easy to calculate, using NpiRepresenting individual numbers of membership functions, and we define the sets of adaptive parameter vectors b and c representing all the basis width and center vectors of Gaussian membership functions, respectively, i.e.
Figure BDA0002871013720000085
Figure BDA0002871013720000086
Wherein
Figure BDA0002871013720000087
Representing the total number of membership functions;
and a third layer: rule layer
The layer uses a fuzzy inference mechanism, and the output of each node is the product of all input signals of the node, i.e. the output of each node is the product of all input signals of the node
Figure BDA0002871013720000088
In the formula Ik(k＝1,...,Ny) The k-th output of the rule layer is represented,
Figure BDA0002871013720000089
representing the connection weight matrix between the fuzzification layer and the regular layer, here taken as the unit vector, NyIs the total number of rules;
a fourth layer: output layer
The nodes of the layer represent output variables, each node yo(o＝1,...,No) The output of (2) being the sum of all input signals of the node, i.e.
Figure BDA00028710137200000810
Further, the input-output relationship of the fuzzy neural network is defined as follows:
Figure BDA0002871013720000091
wherein the content of the first and second substances,
Figure BDA0002871013720000092
Figure BDA0002871013720000093
according to the universal approximation theory, there is an optimal control force
Figure BDA0002871013720000094
Satisfy the requirement of
Figure BDA0002871013720000095
Where ε is the minimum reconstruction error vector, W*,b*And c*Optimal parameters of W, b and c respectively;
the output control force of the fuzzy neural network is assumed to be of the following form:
Figure BDA0002871013720000096
wherein the content of the first and second substances,
Figure BDA0002871013720000097
and
Figure BDA0002871013720000098
are respectively W*,b*And c*Is determined by the estimated value of (c),
defining an approximation error:
Figure BDA0002871013720000099
using Taylor series expansion, one can obtain
Figure BDA00028710137200000910
Wherein the content of the first and second substances,
Figure BDA00028710137200000911
b*and c*Is the optimum value for b and c,
Figure BDA00028710137200000912
and
Figure BDA00028710137200000913
is a b*And c*Estimated value of (a), OnvIs a high-order term of the signal,
Figure BDA00028710137200000914
Figure BDA00028710137200000915
then (18) is substituted into (17) to obtain
Figure BDA00028710137200000916
Wherein the content of the first and second substances,
Figure BDA0002871013720000101
according to the formulae (8), (17), (19), we can also obtain
Figure BDA0002871013720000102
The adaptive law of the weight, the base width and the central vector of the fuzzy neural network can be designed as follows:
Figure BDA0002871013720000103
Figure BDA0002871013720000104
Figure BDA0002871013720000105
wherein the content of the first and second substances,
Figure BDA0002871013720000106
is e2Element (iii) σω,σb,σcIs a normal number, and is,
Figure BDA0002871013720000107
is that
Figure BDA0002871013720000108
Is determined by the estimated value of (c),
Figure BDA0002871013720000109
is omegaiThe optimum value of (d);
and (3) proving that: defining the lyapunov function as
Figure BDA00028710137200001010
Derivative and substitute (20) into
Figure BDA00028710137200001011
Bringing (21) - (23) into (25) to obtain
Figure BDA00028710137200001012
If τ is satisfiedM≥||τdIf the manipulator intelligent inversion control method is stable, the manipulator intelligent inversion control method is stable.
The above embodiments are merely illustrative of the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims (1)

1. An intelligent inversion control method for a manipulator is characterized by comprising the following steps:
s1, building a mechanical arm power model
Consider a rigid manipulator with n joints, whose kinetic equation is:
Figure FDA0003650611830000011
wherein the ratio of q,
Figure FDA0003650611830000012
the position, speed and acceleration vector of each joint of the manipulator, M (q) epsilon Rn×nIn order to include an inertia matrix of the additional mass,
Figure FDA0003650611830000013
g (q) e R as a coupling matrix of centrifugal force and Coriolis forcen×1In the form of a gravity matrix vector,
Figure FDA0003650611830000014
for friction torque, τd∈Rn×1For unknown applied interference, tau epsilon Rn×1N is the degree of freedom of the joint;
s2, designing an inversion controller of a manipulator
Defining a tracking offset as
e1＝q-qd (2)
Wherein q isdIs the desired position of the joint;
derived from formula (2)
Figure FDA0003650611830000015
Selecting virtual control quantities
Figure FDA0003650611830000016
Wherein c is1Is a non-zero normal constant;
taking the Lyapunov function as
Figure FDA0003650611830000017
Definition of
Figure FDA0003650611830000018
Derived from formula (5)
Figure FDA0003650611830000019
If e2When the value is equal to 0, then
Figure FDA00036506118300000110
The stability requirement is met, and the next design is continued;
e2can be expressed as
Figure FDA00036506118300000111
Then an inversion controller is designed to obtain an expression (8),
Figure FDA0003650611830000021
wherein, tauM≥||τd||，sgn(e2) Is a sign function; tracking offset e1＝q-qd，
Figure FDA0003650611830000022
Figure FDA0003650611830000023
c1、c2Is a non-zero normal number;
s3, utilizing fuzzy neural network to approach and invert the unknown state in the controller to eliminate tauMSpecifically:
in the fuzzy neural network, the network input is tracking deviation e1Output as control force tauFNN，
A first layer: input layer
Each node of the layer is directly connected with each component of the input quantity, and the input quantity is transmitted to the second layer;
a second layer: obscuration layer
Using Gaussian functions as membership functions
Figure FDA0003650611830000024
Figure FDA0003650611830000025
Representative tracking deviation e1Wherein i is 1, n,
Figure FDA0003650611830000026
and
Figure FDA0003650611830000027
are the ith input variable respectivelyThe central vector and the base width of the membership function of the jth fuzzy set, where i 1piI.e. by
Figure FDA0003650611830000028
Easy to calculate, using NpiRepresenting individual numbers of membership functions and defining adaptive parameter vectors b and c representing the set of all base width and center vectors of Gaussian membership functions, respectively, i.e.
Figure FDA0003650611830000029
Figure FDA00036506118300000210
Wherein
Figure FDA00036506118300000211
Representing the total number of membership functions;
and a third layer: rule layer
The layer adopts a fuzzy inference mechanism, and the output of each node is the product of all input signals of the node, i.e. the output of each node is the product of all input signals of the node
Figure FDA00036506118300000212
In the formula IkDenotes the kth output of the regular layer, where k is 1y，
Figure FDA00036506118300000213
Representing the connection weight matrix between the fuzzification layer and the regular layer, here taken as the unit vector, NyIs the total number of rules;
a fourth layer: output layer
The nodes of the layer represent output variables, each node yoIs the sum of all input signals of the node, where O1oI.e. by
Figure FDA0003650611830000031
Further, the input-output relationship of the fuzzy neural network is defined as follows:
Figure FDA0003650611830000032
wherein the content of the first and second substances,
Figure FDA0003650611830000033
Figure FDA0003650611830000034
according to the universal approximation theory, there is an optimal control force
Figure FDA0003650611830000035
Satisfy the requirement of
Figure FDA0003650611830000036
Where ε is the minimum reconstruction error vector, W*,b*,c*And l are the optimal parameters for W, b, c and l, respectively; the output control force of the fuzzy neural network is assumed to be of the following form:
Figure FDA0003650611830000037
wherein the content of the first and second substances,
Figure FDA0003650611830000038
and
Figure FDA0003650611830000039
are respectively W*,b*，c*And l*Is determined by the estimated value of (c),
Figure FDA00036506118300000310
is composed of
Figure FDA00036506118300000311
Is determined by the estimated value of (c),
defining an approximation error:
Figure FDA00036506118300000312
using Taylor series expansion, one can obtain
Figure FDA00036506118300000313
Wherein the content of the first and second substances,
Figure FDA00036506118300000314
b*and c*Is the optimum value for b and c,
Figure FDA00036506118300000315
and
Figure FDA00036506118300000316
is a b*And c*Estimated value of, OnvIs a high-order term of the magnetic field,
Figure FDA00036506118300000317
Figure FDA00036506118300000318
then formula (18) may be substituted for formula (17)
Figure FDA0003650611830000041
Wherein the content of the first and second substances,
Figure FDA0003650611830000042
wherein the content of the first and second substances,
Figure FDA0003650611830000043
according to the formulae (8), (17) and (19), can be obtained
Figure FDA0003650611830000044
The adaptive law of the weight, the base width and the central vector of the fuzzy neural network can be designed as follows:
Figure FDA0003650611830000045
Figure FDA0003650611830000046
Figure FDA0003650611830000047
wherein the content of the first and second substances,
Figure FDA0003650611830000048
is e2Element (iii) σω,σb,σcIs a normal number, and is,
Figure FDA0003650611830000049
is that
Figure FDA00036506118300000410
Is determined by the estimated value of (c),
Figure FDA00036506118300000411
is omegaiOptimum value of r1，r2，r3Is a normal number;
and (3) proving that: defining the lyapunov function as
Figure FDA00036506118300000412
Wherein the content of the first and second substances,
Figure FDA00036506118300000413
representative matrix
Figure FDA00036506118300000414
The trace of (a) is determined,
Figure FDA00036506118300000415
the formula (24) is derived and substituted for the formula (20)
Figure FDA00036506118300000416
The formula (21) -the formula (23) is brought into the formula (25) to obtain
Figure FDA0003650611830000051
If τ is satisfiedM≥||τdIf the manipulator intelligent inversion control method is stable, the manipulator intelligent inversion control method is stable.
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