CN111702767A - A Manipulator Impedance Control Method Based on Inversion Fuzzy Adaptive - Google Patents

Abstract

The invention relates to a manipulator impedance control method based on inversion fuzzy self-adaptation, and belongs to the field of automation. The self-tuning of target impedance parameters is completed by adopting the inversion fuzzy adaptive algorithm with improved force compensation, which avoids the problem that the manipulator cannot quickly track the change of contact force and system uncertainty, and realizes the active compliance control of the manipulator. The grasping model of the manipulator and unknown environment is established as the basis for impedance control; an adaptive control system based on position impedance control is designed; the original impedance control equation is improved to improve the fast response capability of the system force tracking; according to the force error, an automatic control system is designed. The adaptive control law and fuzzy control system complete the self-tuning of target impedance parameters. The invention can improve the tracking performance of the system force/position and complete the self-tuning of the target impedance parameter, realize the force/position control without relying on the information model, and the system has better robustness.

Description

A Manipulator Impedance Control Method Based on Inversion Fuzzy Adaptive

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 technique

With the wide use of industrial manipulators and the sharp increase in the demand for high-precision work of manipulators, such as massage manipulators, picking manipulators, surface coating manipulators, etc., the existing manipulator control methods face huge challenges. In order to ensure the safety of the task operation and maintain the desired performance of free and restricted motion, considering the interaction force between the manipulator and the environment, it is necessary to use impedance control to achieve unified control of force and position. Because the external environment model is unknown or cannot be accurately constructed, and the manipulator itself is a time-varying, strongly coupled, nonlinear system, a single impedance control cannot solve practical problems in various projects. Impedance control aims to establish a dynamic relationship between contact force and position, rather than controlling force or position individually. By specifying the relationship between contact force and position, it enables position control of the manipulator in a constrained environment while maintaining proper contact force. In addition, impedance control has strong robustness to some uncertain factors and external disturbances, and has less computational complexity in implementation. Therefore, research on impedance control of manipulators has broad application prospects.

At present, the research on the impedance control method for the manipulator is probably from the perspective of force-based impedance control and position-based impedance control, integrating adaptive, fuzzy control, neural network, etc. to overcome the problems existing in single impedance control. In the force-based impedance control method, the manipulator realizes the adjustment of the end contact force and displacement by controlling the joint torque. The precise dynamic model of the manipulator must be known to achieve the desired impedance model and contact force precision control, so less Using this method; the position-based impedance control consists of two parts, namely the position control inner loop and the impedance control outer loop. The position control inner loop processes the three data of desired position, position compensation and actual position, so that the actual position of the manipulator can be improved. The desired position is tracked by the position; the outer impedance control loop is to process the difference between the desired force and the actual force, obtain the position correction value, and then control the position of the manipulator through the position controller to realize the force control. Therefore, the relatively ideal control method is to integrate some adaptive algorithms based on the position impedance control. The problem is how to select or improve the appropriate adaptive algorithm according to the force error and position error, so as to realize the active compliance control of the manipulator without the need for an information model.

SUMMARY OF THE INVENTION

In view of this, the purpose of the present invention is to provide a method for controlling the impedance of a manipulator based on inversion fuzzy self-adaptation. The method is based on the improved impedance control strategy and integrates the adaptive algorithm to realize the unified force/position control of the manipulator. In order to make the system control without manipulator information model and have good robustness, this method proposes a PID-impedance control strategy, which solves the problem of poor response performance of the manipulator to the change of contact force, and uses the force error system as the basis of the algorithm . Then, according to the force error system and position tracking error, combined with the inversion theory, the control law is designed, and the modeling information contained in the control law is approximated by fuzzy control. Then, according to the system control index, the self-tuning of the target impedance parameters is completed, and the response performance of the manipulator to the contact force change and position tracking is improved.

To achieve the above object, the present invention provides the following technical solutions:

A manipulator impedance control method based on inversion fuzzy self-adaptation, the method includes the following steps:

Step 1: Complete the modeling of the manipulator and the environmental system and input the known system parameters and parameters required for algorithm execution;

Step 2: Execute the improved PID-impedance control strategy according to the input of step 1, obtain the error system of the manipulator tracking contact force and output it;

Step 3: Execute the inversion fuzzy adaptive algorithm according to the input of step 1, and obtain the self-tuning result of the target impedance parameter according to the system index and output it;

Step 4: According to the force error system obtained in step 2 and the self-tuning target impedance parameter obtained in step 3, the active compliance control of the manipulator without relying on the information model is completed.

Optionally, the step 1 is implemented in the following manner: establishing an n-degree-of-freedom serial manipulator grasping model and joint space dynamics equation:

where q=[q ₁ ,q ₂ ,...,q _n ] ^T is the joint angle vector, M _q (q ₁ ) is the positive definite inertia matrix vector, C _q (q ₁ ,q ₂ )q ₂ is the centrifugal force and Coriolis force vector, G _q (q ₁ ) is the gravitational torque vector, F _q (q ₁ ) is the friction torque vector, τ and τ _e represent the design torque vector and the external torque vector respectively; order nonlinear function equation to approximate:

In the formula, B _e ∈ R ^n×n and _Ke ∈ R ^n×n are diagonal positive definite matrices, which are respectively expressed as environmental damping parameters and stiffness parameters; X _e ∈ R ⁿ is expressed as environmental position vector; input known system parameters Including: the degree of freedom of the manipulator, the size of each joint, etc.; input parameters required for the execution of the algorithm: initial joint state vector, design torque vector, design displacement vector, friction torque vector, etc.

Optionally, the step 2 is specifically implemented in the following manner: establishing a grasping model of the manipulator and an equivalent impedance model with the unknown environment, and then introducing a force-compensated PID-target impedance control equation:

是机械手的理想阻尼矩阵，K∈Rⁿ表示机械手的理想目标刚度，K_d、K_p、K_d∈R^n×n为对角正定矩阵，X、

分别表示机械手所需的位移、位移速度和位移加速度矢量，X_d、

表示所需位移、所需位移速度和所需位移加速度矢量，F_e表示机械手和工作环境之间所需的接触作用力。In the formula, M(X)∈R ^n×n represents the ideal inertia matrix of the manipulator,

is the ideal damping matrix of the manipulator, K∈R ⁿ represents the ideal target stiffness of the manipulator, K _d , K _p , K _d ∈ R ^n×n are diagonal positive definite matrices, X,

respectively represent the displacement, displacement velocity and displacement acceleration vector required by the manipulator, X _d ,

Represents the required displacement, the required displacement velocity and the required displacement acceleration vector, and _Fe represents the required contact force between the manipulator and the working environment.

Optionally, the step 3 is specifically implemented in the following ways: combining the contact force and the error system of position tracking, establishing an adaptive system control scheme based on position impedance; according to the designed adaptive law and fuzzy control law, complete the force/ Position tracking and self-tuning of target impedance parameters; then according to the control index of the manipulator system, the optimal target impedance parameters are selected until the algorithm termination conditions are met and the optimal target impedance parameters are output.

Optionally, the step 4 is specifically implemented by the following method: combining the force error system obtained in step 2 and the self-tuning target impedance parameter obtained in step 3 to complete the active compliance control of the manipulator without relying 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, which improves the responsiveness of the system; in addition, the PID parameters can be designed according to the system requirements to ensure the adaptability of the control strategy.

Optionally, in the step 3, the adaptive law and the fuzzy control law: the design of the adaptive law adopts the inversion theory, decomposes the complex nonlinear system into 2 subsystems, and then designs the Lyapunov function and the intermediate system for each subsystem. The virtual control quantity has been "backward" to the entire system until the entire adaptive control law design is completed; according to the obtained adaptive law term containing the modeling information of the manipulator system, in order to realize the control without model information, a fuzzy system is used to approximate the system parameter, the target impedance parameter.

The beneficial effects of the present invention are as follows: the present invention realizes the unified force/position control of the manipulator based on the improved impedance control strategy and the fusion of the adaptive algorithm. In order to make the system control without manipulator information model and have good robustness, this method proposes a PID-impedance control strategy, which solves the problem of poor response performance of the manipulator to the change of contact force, and uses the force error system as the basis of the algorithm . Then, according to the force error system and position tracking error, combined with the inversion theory, the control law is designed, and the modeling information contained in the control law is approximated by fuzzy control. Then, according to the system control index, the self-tuning of the target impedance parameters is completed, and the response performance of the manipulator to the contact force change and position tracking is improved.

Other advantages, objects, and features of the present invention will be set forth in the description that follows, and will be apparent to those skilled in the art based on a study of the following, to the extent that is taught in the practice of the present invention. The objectives and other advantages of the present invention may be realized and attained by the following description.

Description of drawings

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be preferably described in detail below with reference to the accompanying drawings, wherein:

Fig. 1 is the overall flow chart of the manipulator impedance control based on inversion fuzzy self-adaptation;

Figure 2 is the analysis of the grasping model of the serial manipulator;

Figure 3 is the equivalent impedance model of the manipulator and the environment;

Fig. 4 is the adaptive system control scheme based on position impedance;

FIG. 5 is a simulated two-degree-of-freedom manipulator used in the experimental example of the present invention.

Detailed ways

The embodiments of the present invention are described below through specific specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments are only used to illustrate the basic idea of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

Among them, the accompanying drawings are only used for exemplary description, and represent only schematic diagrams, not physical drawings, and should not be construed as limitations of the present invention; in order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings will be omitted, The enlargement or reduction does not represent the size of the actual product; it is understandable to those skilled in the art that some well-known structures and their descriptions in the accompanying drawings may be omitted.

The same or similar numbers 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 are terms “upper”, “lower”, “left” and “right” , "front", "rear" and other indicated orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the indicated device or element must be It has a specific orientation, is constructed and operated in a specific orientation, so the terms describing the positional relationship in the accompanying drawings are only used for exemplary illustration, and should not be construed as a limitation of the present invention. situation to understand the specific meaning of the above terms.

Fig. 1 is the overall flow chart of the manipulator impedance control based on inversion fuzzy adaptation; the present invention provides a manipulator impedance control method based on inversion fuzzy adaptation. It can complete the self-tuning of target impedance parameters, improve the response performance of the manipulator to contact force changes and position tracking, and realize system control without relying on specific information models. The present invention first analyzes the grasping model of the manipulator, and then completes dynamic modeling and environmental modeling, such as formula (1):

where q=[q ₁ ,q ₂ ,...,q _n ] ^T is the joint angle vector, M _q (q ₁ ) is the positive definite inertia matrix vector, C _q (q ₁ ,q ₂ )q ₂ is the centrifugal force and Coriolis force vector, G _q (q ₁ ) is the gravitational torque vector, F _q (q ₁ ) is the friction torque vector, τ and τ _e represent the design torque vector and the external torque vector respectively; order nonlinear function equation to approximate, such as formula (2):

In the formula, Be ∈ R _n ^×n and Ke ∈ R ^n×n _are diagonal positive definite matrices, which are denoted as environmental damping parameters and stiffness parameters, respectively. X _e ∈ R ⁿ is represented as an environment location vector. In order to facilitate the understanding of the meaning of each parameter, the grasping model analysis of the serial manipulator is given in Figure 2.

Further, the equivalent impedance model of the manipulator and the environment is established, and an improved PID-impedance control strategy is introduced, such as formula (3):

是机械手的理想阻尼矩阵，K∈Rⁿ表示机械手的理想目标刚度，K_d、K_p、K_i∈R^n×n为对角正定矩阵，X、

分别表示机械手所需的位移、位移速度和位移加速度矢量，X_d、

表示所需位移、所需位移速度和所需位移加速度矢量，F_e表示机械手和工作环境之间所需的接触作用力。为便于理解各个参数的含义，在图3中给出机械手与环境的等效阻抗模型。In the formula, M(X)∈R ^n×n represents the ideal inertia matrix of the manipulator,

is the ideal damping matrix of the manipulator, K∈R ⁿ represents the ideal target stiffness of the manipulator, K _d , K _p , K _i ∈ R ^n×n are diagonal positive definite matrices, X,

respectively represent the displacement, displacement velocity and displacement acceleration vector required by the manipulator, X _d ,

Represents the required displacement, the required displacement velocity and the required displacement acceleration vector, and _Fe represents the required contact force between the manipulator and the working environment. In order to facilitate the understanding of the meaning of each parameter, the equivalent impedance model of the manipulator and the environment is given in Figure 3.

Further, the control law is designed according to formula (3), such as formula (4):

为逼近非线性的模糊系统。In the formula, z ₁ is the defined displacement error vector, and α represents the estimated value of z _2. By selecting α, z ₂ tends to be close to 0, and λ > 0 is an adaptive parameter,

for approximating nonlinear fuzzy systems.

Furthermore, combined with the error system of contact force and position tracking, an adaptive system control scheme based on position impedance is established. According to the designed adaptive law and fuzzy control law, the tracking of force/position and the self-tuning of target impedance parameters are completed. Then, according to the control index of the manipulator system, the optimal target impedance parameter is selected until the algorithm termination condition, that is, the system control index, is satisfied, and the optimal target impedance parameter is output. In order to facilitate the understanding of the overall control system, an adaptive system control scheme based on position impedance is presented in Fig. 4 .

Finally, combining the force error system obtained in step 2 and the self-tuning target impedance parameters obtained in step 3, the self-tuning of the target impedance parameters is completed, the response performance of the manipulator to the contact force change and position tracking is improved, and the system control is not dependent on the specific information model.

Stability analysis of the adaptive control law designed above: For the whole system, the Lyapunov function is designed as

where γ>0, then

but

代入上式，得Will

Substitute into the above formula, we get

From (θ-θ ^* ) ^T (θ-θ ^* )≥0, we get 2θ ^*T θ-2θ ^T θ≤-θ ^T θ+θ ^*T θ ^* , substituting into the above formula has

From (θ+θ ^* ) ^T (θ+θ ^* )≥0, we get -θ ^*T θ-θ ^T θ ^* ≤θ ^*T θ ^* +θ ^T θ, then we have

which is

then there are

即

有Take λ ₁ > 1, because

which is

Have

有definition

Have

in the formula

Solving the above equation, we get

Where V(0) is the initial value of V, the conclusion is: V is bounded, and all signals of the closed-loop system are bounded.

In order to verify the effectiveness of the invented control method, the simulated two-degree-of-freedom manipulator is used in the experimental example, and the simulation platform is under the Windows764 operating system Matlab/Simulink. It is assumed that the values of the system simulation parameters are shown in Table 1, and FIG. 5 is the simulated two-degree-of-freedom manipulator used in the experimental example of the present invention.

Table 1 System simulation parameters

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be Modifications or equivalent replacements, without departing from the spirit and scope of the technical solution, should all be included in the scope of 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:

wherein q is ═ q₁,q₂,···,q_n]^TAs joint angle vector, M_q(q₁) Is a positive definite inertial matrix vector, C_q(q₁,q₂)q₂Is the centrifugal and Counterstmann force vector, G_q(q₁) As a gravity torque vector, F_q(q₁) For friction torque vectors, τ and τ_eRespectively representing a design torque vector and an external torque vector; establishing an environment model and adopting a second-order nonlinear function equation to approximate:

in the formula B_e∈R^n×nAnd K_e∈R^n×nThe diagonal positive definite matrix is respectively expressed as an environmental damping parameter and a rigidity parameter; x_e∈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:

wherein M (X) ∈ R^n×nAn ideal inertia matrix of the manipulator is represented,

is an ideal damping matrix for the manipulator, K ∈ RⁿRepresenting the desired target stiffness of the manipulator, K_d、K_p、K_d∈R^n×nIs a diagonal positive definite matrix, X,

Respectively representing the displacement, displacement velocity and displacement acceleration vector, X, required by the manipulator_d、

Representing the desired displacement, the desired displacement velocity and the desired displacement acceleration vector, F_eIndicating 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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