CN112757298A - Intelligent inversion control method for manipulator - Google Patents
Intelligent inversion control method for manipulator Download PDFInfo
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- CN112757298A CN112757298A CN202011608786.7A CN202011608786A CN112757298A CN 112757298 A CN112757298 A CN 112757298A CN 202011608786 A CN202011608786 A CN 202011608786A CN 112757298 A CN112757298 A CN 112757298A
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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
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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
- 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, utilizing fuzzy neural network to approach and invert the unknown state in the controller to eliminate tauMUncertainty 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
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 is used for manipulator control and 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:
wherein the ratio of q,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,g (q) e R as a coupling matrix of centrifugal force and Coriolis forcen×1In the form of a gravity matrix vector,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
Wherein, tauM≥||τd|, sgn (e) is a sign function; tracking error e1=q-qd, c1Is a non-zero normal number;
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)
Selecting virtual control quantities
Wherein c is1Is a non-zero normal number;
taking the Lyapunov function as
If e2When the value is equal to 0, thenThe stability requirement is met, and the next design is continued;
the second step is that: e.g. of the type2Can be expressed as
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,representing tracking offset vector e1The elements (A) and (B) in (B),andis the ith input variableCentre vectors and base widths of membership functions of jth fuzzy sets, i.e.
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. WhereinRepresenting 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
In the formula Ik(k=1,...,Ny) The k-th output of the rule layer is represented,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.
Further, the input-output relationship of the fuzzy neural network is defined as follows:
according to the universal approximation theory, there is an optimal control forceSatisfy the requirement of
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:
wherein the content of the first and second substances,andare respectively W*,b*And c*Is determined by the estimated value of (c),
defining an approximation error:
using Taylor series expansion, one can obtain
Wherein the content of the first and second substances,b*and c*Is the optimum value for b and c,andis b*And c*Estimated value of, OnvIs a high-order term of the magnetic field,
then (18) is substituted into (17) to obtain
according to the formulae (8), (17), (19), we can also obtain
The adaptive law of the weight, the base width and the central vector of the fuzzy neural network can be designed as follows:
wherein the content of the first and second substances,is e2Element (iii) σω,σb,σcIs a normal number, and is,is thatIs determined by the estimated value of (c),is omegaiThe optimum value of (d);
and (3) proving that: defining the lyapunov function as
Derivative and substitute (20) into
Bringing (21) to (23) into (25) to obtain
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 uncertain functions and 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:
wherein the ratio of q,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,g (q) e R as a coupling matrix of centrifugal force and Coriolis forcen×1In the form of a gravity matrix vector,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 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)
Selecting virtual control quantities
Wherein c is1Is a non-zero positive constant.
Taking the Lyapunov function as
If e2When the value is equal to 0, thenThe 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
The manipulator inversion controller can be designed as
Wherein, tauM≥||τd||;
Defining a Lyapunov function
Is derived by
Substituting the formula (8) into the formula (10) to obtain
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 approximate the inversionA controller (8) to overcome the disadvantage that the inversion controller requires detailed information of the system. 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,representing tracking offset vector e1The elements (A) and (B) in (B),andthe centre vector and the base width of the membership function of the ith input variable, the jth fuzzy set, respectively, i.e.
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. WhereinRepresenting 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
In the formula Ik(k=1,...,Ny) The k-th output of the rule layer is represented,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.
Further, the input-output relationship of the fuzzy neural network is defined as follows:
according to the universal approximation theory, there is an optimal control forceSatisfy the requirement of
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:
wherein the content of the first and second substances,andare respectively W*,b*And c*Is determined by the estimated value of (c),
defining an approximation error:
using Taylor series expansion, one can obtain
Wherein the content of the first and second substances,b*and c*Is the optimum value for b and c,andis b*And c*Estimated value of, OnvIs a high-order term of the magnetic field,
then (18) is substituted into (17) to obtain
according to the formulae (8), (17), (19), we can also obtain
The adaptive law of the weight, the base width and the central vector of the fuzzy neural network can be designed as follows:
wherein the content of the first and second substances,is e2Element (iii) σω,σb,σcIs a normal number, and is,is thatIs determined by the estimated value of (c),is omegaiThe optimum value of (d);
and (3) proving that: defining the lyapunov function as
Derivative and substitute (20) into
Bringing (21) to (23) into (25) to obtain
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 (4)
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:
wherein the ratio of q,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,g (q) e R as a coupling matrix of centrifugal force and Coriolis forcen×1In the form of a gravity matrix vector,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
Wherein, tauM≥||τd|, sgn (e) is a sign function; tracking error e1=q-qd, c1Is a non-zero normal number;
s3, utilizing fuzzy neural network to approach and invert the unknown state in the controller to eliminate tauMUncertainty of (2).
2. The manipulator intelligent inversion control method of claim 1, wherein in S2, the inversion controller is designed by the following steps:
defining a tracking error as
e1=q-qd (2)
Wherein q isdIs the desired position of the joint;
derived from (2)
Selecting virtual control quantities
Wherein c is1Is a non-zero normal number;
taking the Lyapunov function as
If e2When the value is equal to 0, thenThe stability requirement is met, and the next design is continued;
the second step is that: e.g. of the type2Can be expressed as
Then, an inversion controller is designed to obtain an equation (8).
3. The manipulator intelligent inversion control method according to claim 1, wherein the fuzzy neural network adopts a four-layer network structure, and each layer is: the fuzzy inference system comprises an input layer, a fuzzy inference layer and an output layer.
4. The manipulator intelligent inversion control method according to claim 3, wherein 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,representing tracking offset vector e1The elements (A) and (B) in (B),andthe centre vector and the base width of the membership function of the ith input variable, the jth fuzzy set, respectively, i.e.
Easy to calculate, using NpiRepresenting individual numbers of membership functions, and we define the adaptive parameter vectors b and c to represent the set of all the basis width and center vectors of gaussian membership functions respectively,namely, it is WhereinRepresenting 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
In the formula Ik(k=1,...,Ny) The k-th output of the rule layer is represented,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.
Further, the input-output relationship of the fuzzy neural network is defined as follows:
according to the universal approximation theory, there is an optimal control forceSatisfy the requirement of
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:
wherein the content of the first and second substances,andare respectively W*,b*And c*Is determined by the estimated value of (c),
defining an approximation error:
using Taylor series expansion, one can obtain
Wherein the content of the first and second substances,b*and c*Is the optimum value for b and c,andis b*And c*Estimated value of, OnvIs a high-order term of the magnetic field,
then (18) is substituted into (17) to obtain
according to the formulae (8), (17), (19), we can also obtain
The adaptive law of the weight, the base width and the central vector of the fuzzy neural network can be designed as follows:
wherein the content of the first and second substances,is e2Element (iii) σω,σb,σcIs a normal number, and is,is thatIs determined by the estimated value of (c),is omegaiThe optimum value of (d);
and (3) proving that: defining the lyapunov function as
Derivative and substitute (20) into
Bringing (21) to (23) into (25) to obtain
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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