CN111702767A - Manipulator impedance control method based on inversion fuzzy self-adaptation - Google Patents

Manipulator impedance control method based on inversion fuzzy self-adaptation Download PDF

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CN111702767A
CN111702767A CN202010675488.3A CN202010675488A CN111702767A CN 111702767 A CN111702767 A CN 111702767A CN 202010675488 A CN202010675488 A CN 202010675488A CN 111702767 A CN111702767 A CN 111702767A
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manipulator
control
impedance
self
force
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罗萍
杨波
吕霞付
杨皓琨
伍尚欢
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Chongqing University of Post and Telecommunications
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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
    • 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

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Abstract

The invention relates to a manipulator impedance control method based on inversion fuzzy self-adaptation, and belongs to the field of automation. The target impedance parameter self-tuning is completed by adopting an inversion fuzzy self-adaptive algorithm introducing improved force compensation, so that the problems that a mechanical arm cannot quickly track contact force change and the system is uncertain are avoided, and the active compliance control of the mechanical arm is realized. A manipulator and a grabbing model of an unknown environment are established as the basis of impedance control; an adaptive control system based on position impedance control is designed; the original impedance control equation is improved to improve the quick response capability of the system force tracking; and designing a self-adaptive control law and a fuzzy control system according to the force error to finish the self-tuning of the target impedance parameter. The invention can improve the force/position tracking performance of the system and complete the self-tuning of the target impedance parameter, thereby realizing the force/position control without depending on an information model and having better robustness of the system.

Description

Manipulator impedance control method based on inversion fuzzy self-adaptation
Technical Field
The invention belongs to the field of automation, and relates to a manipulator impedance control method based on inversion fuzzy self-adaptation.
Background
With the wide use of industrial manipulators and the rapid increase of the industrial demands of high-precision working of manipulators, such as: the existing manipulator control methods face huge challenges in massage manipulators, picking manipulators, surface coating manipulators and the like. In order to ensure the safety of the task work and maintain the desired performance of free and limited movement, it is necessary to achieve uniform control of force and position using impedance control, taking into account the interaction forces between the manipulator and the environment. Because the external environment model is unknown or can not be accurately constructed, and the manipulator is a time-varying, strong-coupling and nonlinear system, the practical problems in various projects can not be solved by single impedance control. Impedance control is intended to establish a dynamic relationship between contact force and position, rather than controlling force or position alone. By specifying the relationship between contact force and position, it is possible to ensure that the manipulator performs position control in a restricted environment while maintaining a proper contact force. In addition, the impedance control has strong robustness to some uncertain factors and external interference and has less calculation amount when being implemented. Therefore, the research on the impedance control of the manipulator has wide application prospect.
At present, research aiming at an impedance control method of a manipulator is based on force impedance control and position impedance control, and self-adaption, fuzzy control, a neural network and the like are fused to overcome the problems of single impedance control. In the force-based impedance control method, the manipulator realizes the adjustment of the contact force and the displacement of the tail end by controlling the joint moment, and an accurate dynamic model of the manipulator must be known to realize the expected impedance model and contact force precision control, so the method is less used; the impedance control based on the position consists of two parts, namely a position control inner ring and an impedance control outer ring, wherein the position control inner ring processes three data of an expected position, a position compensation and an actual position, so that the actual position of the manipulator tracks the expected position; the impedance control outer ring processes the difference value of the expected force and the actual force to obtain a position correction quantity, and then the position of the manipulator is controlled by the position controller to realize the force control. Therefore, a relatively ideal control mode is to control and fuse some adaptive algorithms based on position impedance, and the problem is how to select or improve a proper adaptive algorithm according to the force error and the position error so as to realize the active compliance control of the manipulator without an information model.
Disclosure of Invention
In view of the above, the present invention provides a manipulator impedance control method based on inverse fuzzy adaptation. The method is based on an improved impedance control strategy, and integrates an adaptive algorithm to realize unified force/position control of the manipulator. In order to enable the system control to be free of a manipulator information model and have better robustness, the method provides a PID-impedance control strategy, solves the problem that the manipulator has poor response performance to the change of the contact force, and takes a force error system as the basis of an algorithm. And then designing a control law by combining an inversion theory according to the force error system and the position tracking error, and approximating the modeling information contained in the control law by using fuzzy control. And then, according to the system control index, the self-tuning of the target impedance parameter is completed, and the response performance of the manipulator to the contact force change and position tracking is improved.
In order to achieve the purpose, the invention provides the following technical scheme:
a manipulator impedance control method based on inversion ambiguity self-adaptation comprises the following steps:
step 1: completing modeling of a manipulator and an environment system and inputting known system parameters and parameters required by algorithm execution;
step 2: executing an improved PID-impedance control strategy according to the input of the step 1 to obtain and output an error system of the tracking contact force of the manipulator;
and step 3: executing an inversion fuzzy self-adaptive algorithm according to the input of the step 1, and obtaining and outputting a self-setting result of the target impedance parameter according to the system index;
and 4, step 4: and (3) according to the force error system obtained in the step (2) and the self-tuning target impedance parameter obtained in the step (3), completing the active compliance control of the manipulator without depending on an information model.
Optionally, step 1 is implemented by the following steps: establishing an n-degree-of-freedom serial manipulator grabbing model and a joint space kinetic equation:
Figure BDA0002583880950000021
Figure BDA0002583880950000022
wherein q is ═ q1,q2,···,qn]TAs joint angle vector, Mq(q1) Is a positive definite inertial matrix vector, Cq(q1,q2)q2Is the centrifugal and Counterstmann force vector, Gq(q1) As a gravity torque vector, Fq(q1) For friction torque vectors, τ and τeRespectively representing a design torque vector and an external torque vector; establishing an environment model and adopting a second-order nonlinear function equation to approximate:
Figure BDA0002583880950000023
in the formula Be∈Rn×nAnd Ke∈Rn×nThe diagonal positive definite matrix is respectively expressed as an environmental damping parameter and a rigidity parameter; xe∈RnRepresented as an ambient position vector; inputting known system parameters includes: the degree of freedom of the manipulator, the size of each joint, and the like; parameters required for the execution of the input algorithm: an initial joint state vector, a design torque vector, a design displacement vector, a friction torque vector, and the like.
Optionally, the step 2 is specifically implemented by the following method: establishing a grabbing model of the manipulator and an equivalent impedance model of the manipulator and an unknown environment, and then introducing a force-compensated PID-target impedance control equation:
Figure BDA0002583880950000024
wherein M (X) ∈ Rn×nAn ideal inertia matrix of the manipulator is represented,
Figure BDA0002583880950000025
is an ideal damping matrix for the manipulator, K ∈ RnRepresenting the desired target stiffness of the manipulator, Kd、Kp、Kd∈Rn×nIs a diagonal positive definite matrix, X,
Figure BDA0002583880950000026
Respectively representing the displacement, displacement velocity and displacement acceleration vector, X, required by the manipulatord、
Figure BDA0002583880950000031
Representing the desired displacement, the desired displacement velocity and the desired displacement acceleration vector, FeIndicating the required contact force between the robot and the work environment.
Optionally, step 3 is specifically implemented by the following method: establishing a self-adaptive system control scheme based on position impedance by combining an error system of contact force and position tracking; completing the tracking of force/position and the self-tuning of target impedance parameters according to a designed self-adaptive law and a fuzzy control law; and then selecting the optimal target impedance parameter according to the control index of the manipulator system until the algorithm termination condition is met and outputting the optimal target impedance parameter.
Optionally, the step 4 is specifically realized by the following method: and (3) combining the force error system obtained in the step (2) and the self-tuning target impedance parameter obtained in the step (3) to finish the active compliance control of the manipulator without depending on an information model.
Optionally, in step 2, a PID-impedance control strategy is introduced: the manipulator can quickly track and control the force according to the change of the contact force, so that the responsiveness of the system is improved; in addition, the PID parameters can be designed according to the system requirements, and the adaptability of the control strategy is ensured.
Optionally, in step 3, the adaptive law and the fuzzy control law: the design of the adaptive law adopts an inversion theory, a complex nonlinear system is decomposed into 2 subsystems, then a Lyapunov function and a middle virtual control quantity are designed for each subsystem, and the system is 'backed' to the whole system until the design of the whole adaptive control law is completed; and according to the modeling information of the manipulator system contained in the obtained adaptive law, in order to realize the control of no model information, a fuzzy system is adopted to approach system parameters, namely target impedance parameters.
The invention has the beneficial effects that: the invention is based on an improved impedance control strategy, and integrates an adaptive algorithm to realize unified force/position control of the manipulator. In order to enable the system control to be free of a manipulator information model and have better robustness, the method provides a PID-impedance control strategy, solves the problem that the manipulator has poor response performance to the change of the contact force, and takes a force error system as the basis of an algorithm. And then designing a control law by combining an inversion theory according to the force error system and the position tracking error, and approximating the modeling information contained in the control law by using fuzzy control. And then, according to the system control index, the self-tuning of the target impedance parameter is completed, and the response performance of the manipulator to the contact force change and position tracking is improved.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a general flow diagram of manipulator impedance control based on inverse fuzzy adaptation;
FIG. 2 is a series manipulator grabbing model analysis;
FIG. 3 is an equivalent impedance model of a robot and environment;
FIG. 4 is a control scheme for an adaptive system based on positional impedance;
fig. 5 is a simulated two-degree-of-freedom robot used in the experimental example of the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.
FIG. 1 is a general flow diagram of manipulator impedance control based on inverse fuzzy adaptation; the invention provides a manipulator impedance control method based on inversion fuzzy self-adaptation, which is based on an improved impedance control strategy and integrates a self-adaptive algorithm to realize unified force/position control of a manipulator, thereby completing the self-tuning of a target impedance parameter, improving the response performance of the manipulator to contact force change and position tracking and realizing that system control does not depend on a specific information model. The method firstly analyzes a grabbing model of the manipulator, and then completes dynamic modeling and environmental modeling, such as formula (1):
Figure BDA0002583880950000041
wherein q is ═ q1,q2,···,qn]TAs joint angle vector, Mq(q1) Is a positive definite inertial matrix vector, Cq(q1,q2)q2Is the centrifugal and Counterstmann force vector, Gq(q1) As a gravity torque vector, Fq(q1) For friction torque vectors, τ and τeRespectively representing a design torque vector and an external torque vector; establishing an environment model and adopting a second-order nonlinear function equation to approximate, as formula (2):
Figure BDA0002583880950000051
in the formula Be∈Rn×nAnd Ke∈Rn×nAnd the diagonal positive definite matrix is respectively expressed as an environmental damping parameter and a rigidity parameter. Xe∈RnRepresented as an ambient position vector. To facilitate understanding of the meaning of the individual parameters, a serial robot gripping model analysis is given in fig. 2.
Further, an impedance model of the manipulator equivalent to the environment is established, and an improved PID-impedance control strategy is introduced, such as formula (3):
Figure BDA0002583880950000052
wherein M (X) ∈ Rn×nAn ideal inertia matrix of the manipulator is represented,
Figure BDA0002583880950000053
is an ideal damping matrix for the manipulator, K ∈ RnRepresenting the desired target stiffness of the manipulator, Kd、Kp、Ki∈Rn×nIs a diagonal positive definite matrix, X,
Figure BDA0002583880950000054
Respectively representing the displacement, displacement velocity and displacement acceleration vector, X, required by the manipulatord、
Figure BDA0002583880950000055
Representing the desired displacement, the desired displacement velocity and the desired displacement acceleration vector, FeIndicating the required contact force between the robot and the work environment. To facilitate understanding of the meaning of the various parameters, an equivalent impedance model of the robot and the environment is given in fig. 3.
Further, the control law is designed according to the formula (3), such as the formula (4):
Figure BDA0002583880950000056
in the formula, z1For a defined displacement error vector, α denotes z2By selecting α so that z is2Adaptive parameters approaching 0, λ > 0,
Figure BDA0002583880950000057
to approximate a non-linear fuzzy system.
Further, an adaptive system control scheme based on position impedance is established in combination with an error system of contact force and position tracking. And completing the tracking of force/position and the self-tuning of target impedance parameters according to the designed self-adaptive law and fuzzy control law. And then, selecting the optimal target impedance parameter according to the manipulator system control index until the algorithm termination condition, namely the system control index, is met and outputting the optimal target impedance parameter. To facilitate understanding of the overall control system, an adaptive system control scheme based on positional impedance is presented in fig. 4.
And finally, combining the force error system obtained in the step 2 and the self-tuning target impedance parameter obtained in the step 3 to complete the self-tuning of the target impedance parameter, improving the response performance of the manipulator to contact force change and position tracking, and realizing that the system control does not depend on a specific information model.
The stability analysis was performed on the adaptive control laws designed above: for the whole system, the Lyapunov function is designed to be
Figure BDA0002583880950000058
Wherein gamma is greater than 0, then
Figure BDA0002583880950000059
Then
Figure BDA0002583880950000061
Will be provided with
Figure BDA0002583880950000062
Substituting into the formula to obtain
Figure BDA0002583880950000063
From (theta-theta)*)T(θ-θ*) Not less than 0, to obtain 2 theta*Tθ-2θTθ≤-θTθ+θ*Tθ*When substituted into the above formula have
Figure BDA0002583880950000064
From (theta + theta)*)T(θ+θ*) Not less than 0, to obtain-theta*Tθ-θTθ*≤θ*Tθ*+θTTheta, then have
Figure BDA0002583880950000065
Namely, it is
Figure BDA0002583880950000066
Then there is
Figure BDA0002583880950000067
Take lambda1Is greater than 1, due to
Figure BDA00025838809500000615
Namely, it is
Figure BDA0002583880950000069
Is provided with
Figure BDA00025838809500000610
Definition of
Figure BDA00025838809500000611
Is provided with
Figure BDA00025838809500000612
In the formula
Figure BDA00025838809500000613
Solving the equation to obtain
Figure BDA00025838809500000614
Where V (0) is the initial value of V, the conclusion is: v is bounded on and all signals of the closed loop system are bounded.
In order to verify the effectiveness of the control method, the simulation two-degree-of-freedom manipulator adopted in the experimental example is provided with a simulation platform under a Windows764 operating system Matlab/Simulink. Assuming that values of system simulation parameters are shown in table 1, fig. 5 illustrates a simulated two-degree-of-freedom manipulator adopted in the experimental example of the present invention.
TABLE 1 System simulation parameters
Figure BDA0002583880950000071
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (7)

1. A manipulator impedance control method based on inversion fuzzy self-adaptation is characterized by comprising the following steps: the method comprises the following steps:
step 1: completing modeling of a manipulator and an environment system and inputting known system parameters and parameters required by algorithm execution;
step 2: executing an improved PID-impedance control strategy according to the input of the step 1 to obtain and output an error system of the tracking contact force of the manipulator;
and step 3: executing an inversion fuzzy self-adaptive algorithm according to the input of the step 1, and obtaining and outputting a self-setting result of the target impedance parameter according to the system index;
and 4, step 4: and (3) according to the force error system obtained in the step (2) and the self-tuning target impedance parameter obtained in the step (3), completing the active compliance control of the manipulator without depending on an information model.
2. The manipulator impedance control method based on inversion ambiguity adaptation of claim 1, wherein: the step 1 is realized by the following steps: establishing an n-degree-of-freedom serial manipulator grabbing model and a joint space kinetic equation:
Figure FDA0002583880940000011
Figure FDA0002583880940000012
wherein q is ═ q1,q2,···,qn]TAs joint angle vector, Mq(q1) Is a positive definite inertial matrix vector, Cq(q1,q2)q2Is the centrifugal and Counterstmann force vector, Gq(q1) As a gravity torque vector, Fq(q1) For friction torque vectors, τ and τeRespectively representing a design torque vector and an external torque vector; establishing an environment model and adopting a second-order nonlinear function equation to approximate:
Figure FDA0002583880940000013
in the formula Be∈Rn×nAnd Ke∈Rn×nThe diagonal positive definite matrix is respectively expressed as an environmental damping parameter and a rigidity parameter; xe∈RnRepresented as an ambient position vector; inputting known system parameters includes: the degree of freedom of the manipulator, the size of each joint, and the like; parameters required for the execution of the input algorithm: an initial joint state vector, a design torque vector, a design displacement vector, a friction torque vector, and the like.
3. The manipulator impedance control method based on inversion ambiguity adaptation as claimed in claim 2, wherein: the step 2 is specifically realized by the following steps: establishing a grabbing model of the manipulator and an equivalent impedance model of the manipulator and an unknown environment, and then introducing a force-compensated PID-target impedance control equation:
Figure FDA0002583880940000014
wherein M (X) ∈ Rn×nAn ideal inertia matrix of the manipulator is represented,
Figure FDA0002583880940000015
is an ideal damping matrix for the manipulator, K ∈ RnRepresenting the desired target stiffness of the manipulator, Kd、Kp、Kd∈Rn×nIs a diagonal positive definite matrix, X,
Figure FDA0002583880940000016
Respectively representing the displacement, displacement velocity and displacement acceleration vector, X, required by the manipulatord、
Figure FDA0002583880940000017
Representing the desired displacement, the desired displacement velocity and the desired displacement acceleration vector, FeIndicating the required contact force between the robot and the work environment.
4. The method of claim 3, wherein the manipulator impedance control method based on inverse fuzzy adaptation is characterized in that: the step 3 is specifically realized by the following steps: establishing a self-adaptive system control scheme based on position impedance by combining an error system of contact force and position tracking; completing the tracking of force/position and the self-tuning of target impedance parameters according to a designed self-adaptive law and a fuzzy control law; and then selecting the optimal target impedance parameter according to the control index of the manipulator system until the algorithm termination condition is met and outputting the optimal target impedance parameter.
5. The method of claim 4, wherein the manipulator impedance control method based on inverse fuzzy adaptation is characterized in that: the step 4 is specifically realized by the following method: and (3) combining the force error system obtained in the step (2) and the self-tuning target impedance parameter obtained in the step (3) to finish the active compliance control of the manipulator without depending on an information model.
6. The method of claim 5, wherein the manipulator impedance control method based on inverse fuzzy adaptation is characterized in that: in the step 2, a PID-impedance control strategy is introduced: the manipulator can quickly track and control the force according to the change of the contact force, so that the responsiveness of the system is improved; in addition, the PID parameters can be designed according to the system requirements, and the adaptability of the control strategy is ensured.
7. The manipulator impedance control method based on inversion ambiguity adaptation of claim 6, wherein: in step 3, the adaptive law and the fuzzy control law: the design of the adaptive law adopts an inversion theory, a complex nonlinear system is decomposed into 2 subsystems, then a Lyapunov function and a middle virtual control quantity are designed for each subsystem, and the system is 'backed' to the whole system until the design of the whole adaptive control law is completed; and according to the modeling information of the manipulator system contained in the obtained adaptive law, in order to realize the control of no model information, a fuzzy system is adopted to approach system parameters, namely target impedance parameters.
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CN112757298A (en) * 2020-12-29 2021-05-07 苏州连恺自动化有限公司 Intelligent inversion control method for manipulator
CN113009819A (en) * 2021-02-09 2021-06-22 南京航空航天大学 Force control-based elliptical vibration cutting machining method
CN114043480A (en) * 2021-11-25 2022-02-15 上海智能制造功能平台有限公司 Adaptive impedance control algorithm based on fuzzy control
CN114434449A (en) * 2022-04-02 2022-05-06 北京科技大学 Novel particle swarm adaptive impedance control method and device
CN114434449B (en) * 2022-04-02 2022-08-09 北京科技大学 Novel particle swarm adaptive impedance control method and device
CN114578697A (en) * 2022-05-09 2022-06-03 西南石油大学 Multi-constraint self-adaptive control method of motor-driven manipulator
CN117426255A (en) * 2023-12-07 2024-01-23 南京农业大学 Automatic agaricus bisporus picking system and method based on vision and force sense feedback
CN117426255B (en) * 2023-12-07 2024-04-12 南京农业大学 Automatic agaricus bisporus picking system and method based on vision and force sense feedback

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