1. An impedance control method of a robot-environment compliant contact process based on a Zener model is characterized by comprising the following steps:

step 1: establishing a robot dynamics model and an environmental model

The robot dynamic model is as follows:

wherein F ═ J^-T(q) τ is n-dimensional generalized joint operating force, X,Andm (q) is the position, velocity and acceleration of the end of the robot,G (q) is an inertia matrix, a Cogowski force vector, a centrifugal force vector and a gravity vector in a Cartesian space respectively;

the environment model is as follows:

wherein, F_eActing as an environmental force, K_eIs an environmentStiffness coefficient of the model, B_eIs the damping coefficient of the environment model, X is the end position of the mechanical arm, X_eIs the environmental location;

step 2: establishing impedance control model based on Zener model

Wherein E is_xIs the difference between the desired position and the actual position of the robot, E_f＝F_d-F_eFor the difference between the desired contact force and the actual contact force, M_d、B_d、K_dAndrespectively an inertia matrix, a damping matrix, a rigidity matrix and another rigidity matrix;

and step 3: establishing a location-based force tracking impedance control model

The position-based force tracking impedance control model comprises an impedance controller, a position controller, an environment model and a robot, wherein the position controller controls the robot, namely, the force F is controlled, the robot outputs a position X to the environment model, and the environment model outputs an environment acting force F_eWill expect an acting force F_dMinus environmental forces F_eTo obtain E_fInput to an impedance controller having an output E_xWill expect the position X_dSubtract E_xObtaining a reference track X_rTo control the position controller.

2. A method of impedance control of a robot-environment compliant contact process based on Zener model according to claim 1 wherein the position controller is a PID controller.

Background

With the rapid development of the robot technology, the application range of the robot is continuously expanded, the environment of the robot is more and more complex, and the interaction with the human is more and more, so that the requirements on the safety and the adaptability of the robot are higher and higher. Because only position control is carried out when the robot is in contact with the environment, the contact force is possibly overlarge, so that compliance control needs to be introduced to conform to the external force, the interaction force of the robot and the environment is kept in a reasonable range, and the safety of the robot is improved. Currently, the impedance control method in compliance control is used more.

The Voigt model and the Maxwell model of the impedance control model used at present are popularized from the field of rheology, have different properties, and need to be replaced if the properties need to be changed. The Zener model can combine the Voigt model and the Maxwell model into one, and has the properties of the Voigt model and the Maxwell model, and only parameters need to be adjusted.

Disclosure of Invention

Technical problem to be solved

In order to make up the defects of the existing Cartesian space force tracking impedance control method, the invention provides the Cartesian space force tracking impedance control method based on the Zener model, and the tail end of the robot can be stably switched among different properties.

Technical scheme

An impedance control method of a robot-environment compliant contact process based on a Zener model is characterized by comprising the following steps:

step 1: establishing a robot dynamics model and an environmental model

The robot dynamic model is as follows:

wherein F ═ J^-T(q) τ is n-dimensional generalized joint operating force, X,Andm (q) is the position, velocity and acceleration of the end of the robot,G (q) is an inertia matrix, a Cogowski force vector, a centrifugal force vector and a gravity vector in a Cartesian space respectively;

the environment model is as follows:

wherein, F_eActing as an environmental force, K_eIs the stiffness coefficient of the environment model, B_eIs the damping coefficient of the environment model, X is the end position of the mechanical arm, X_eIs the environmental location;

step 2: establishing impedance control model based on Zener model

Wherein E is_xIs the difference between the desired position and the actual position of the robot, E_f＝F_d-F_eFor the difference between the desired contact force and the actual contact force, M_d、B_d、K_dAndrespectively an inertia matrix, a damping matrix, a rigidity matrix and another rigidity matrix;

and step 3: establishing a location-based force tracking impedance control model

The position-based force tracking impedance control model comprises an impedance controller, a position controller, an environment model and a robot, wherein the position controller controls the robot, namely, the force F is controlled, the robot outputs a position X to the environment model, and the environment model outputs an environment acting force F_eWill desire to doForce F_dMinus environmental forces F_eTo obtain E_fInput to an impedance controller having an output E_xWill expect the position X_dSubtract E_xObtaining a reference track X_rTo control the position controller.

Preferably: the position controller is a PID controller.

Advantageous effects

The invention provides an impedance control method of a robot-environment compliant contact process based on a Zener model, wherein the effect of an impedance controller can be equivalent to that the tail end of the robot is equivalent to the Zener model (namely, a damper is connected with a spring in series and then connected with the spring in parallel), and only the tail end is equivalent at the moment and is not related to the degree of freedom of the robot. Compared with the traditional model which makes the robot end show a spring or the spring and the damper connected in parallel, the model can make the mechanical arm show more appropriate characteristics by adjusting parameters without frequently switching the model.

Drawings

The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.

FIG. 1 is a comparison of three impedance models;

FIG. 2 is a force tracking impedance control block diagram based on position control.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

The invention provides a Cartesian space force tracking impedance control method with a wider performance range by adopting a Zener model. Comprises the following steps:

1. establishing a robot dynamics model and an environment model;

2. establishing an impedance control model based on a Zener model;

3. a location-based force tracking impedance control model is established.

Step one, establishing a robot dynamics model and an environment model

In order to force control a robot, it is necessary to study the relationship between motion and force using robot dynamics. There are many kinetic methods, such as the Lagrangian method. Converting the derived kinetic equations into cartesian space may facilitate later controller design.

After the robot is contacted with the environment, the robot is acted by the environment, and the robot is not an independent control object but is fused with the environment into a new system. The environment is typically modeled as a spring system or a spring-damper system.

Step two, establishing an impedance control model based on a Zener model

The Voigt impedance control model is expressed as

Wherein, X_e＝X-X₀X is the actual position, X₀As an initial position, X_e、Andrespectively displacement, velocity and acceleration of the end-effector, M_d、B_dAnd K_dRespectively an inertia matrix, a damping matrix and a stiffness matrix, F_eIs the actual contact force.

The expression of the Maxwell impedance control model is

Wherein, X_eStill the displacement of the end effector, while also being understood as the sum of the spring and damper displacements. M_d、B_dAnd K_dRespectively an inertia matrix, a damping matrix and a stiffness matrix, F_eThe contact force of the robot end and the environment. Displacement P of the damper_e＝P-P₀P and P₀The actual and neutral positions of the damper, respectively. If the two equations are combined to eliminate the variable p_eThen, Maxwell impedance control model expression can be expressed as follows

Of the above two resistance control models, the Voigt model mainly exhibits elastic deformation, the Maxwell model mainly exhibits plastic deformation, and the Zener model may combine these two models.

The expression of Zener impedance control model is

Wherein, X_eIs still the displacement of the end effector, M_d、B_d、K_dAndrespectively an inertia matrix, a damping matrix, a stiffness matrix and another stiffness matrix, F_eThe contact force of the robot end and the environment. Displacement P of the damper_e＝P-P₀P and P₀The actual and neutral positions of the damper, respectively. Such as the elimination variable p_eThen the Zener impedance control model expression can be in the form of

By passingRegulating M_d、B_d、K_dAndthe Zener impedance control model may be embodied as a Voigt model, a Maxwell model, or an intermediate form therebetween.

Step three, establishing a force tracking impedance control model based on position

The force tracking impedance controller based on position control adds a force control outer ring on the basis of a position control inner ring, converts error signals of actual contact force and expected contact force into position adjustment quantity through the impedance controller, adjusts an ideal motion track of the tail end of the robot through superposition of the position adjustment quantity and a reference track, and finally enables the tail end of the robot to move according to the calculated ideal motion track through the position controller, so that force tracking is achieved.

The steps are as follows:

step one, establishing a robot dynamics model and an environment model

The above equation is the kinetic equation of the joint space. Wherein tau is n-dimensional generalized joint moment, q,andrespectively n-dimensional joint variables, velocity and acceleration. D (q) is the inertial matrix of the arm, is a function of q, and is a positive definite symmetric matrix of n.Is the Copenforces and centrifugal force vector of n × 1, and P (q) is the gravity vector of n × 1.

The kinematic equations may also be transformed into cartesian space.

The above equation is the dynamic equation of cartesian space. Wherein F ═ J^-T(q) τ is n-dimensional generalized joint operating force, X,Andm (q) is the position, velocity and acceleration of the end of the robot,G (q) are an inertia matrix, a Cogowski force and centrifugal force vector, and a gravity vector, respectively, in a Cartesian space.

After the robot is contacted with the environment, the robot is acted by the environment, and the robot is not an independent control object but is fused with the environment into a new system. The environment is typically modeled as a spring-damper system. The environmental acting force is expressed as

Wherein, F_eActing as an environmental force, K_eIs the stiffness coefficient of the environment model, B_eIs the damping coefficient of the environment model, X is the end position of the mechanical arm, X_eIs the ambient location.

Step two, establishing an impedance control model based on a Zener model

The Voigt impedance control model is expressed as

Wherein, X_e＝X-X₀X is the actual position, X₀As an initial position, X_e、Andrespectively displacement, velocity and acceleration of the end-effector, M_d、B_dAnd K_dRespectively an inertia matrix, a damping matrix and a stiffness matrix, F_eIs the actual contact force.

The expression of the Maxwell impedance control model is

Wherein, X_eStill the displacement of the end effector, while also being understood as the sum of the spring and damper displacements. M_d、B_dAnd K_dRespectively an inertia matrix, a damping matrix and a stiffness matrix, F_eThe contact force of the robot end and the environment. Displacement P of the damper_e＝P-P₀P and P₀The actual and neutral positions of the damper, respectively. If the two equations are combined to eliminate the variable p_eThen, Maxwell impedance control model expression can be expressed as follows

Of the above two resistance control models, the Voigt model mainly exhibits elastic deformation, the Maxwell model mainly exhibits plastic deformation, and the Zener model may combine these two models.

The expression of Zener impedance control model is

Wherein, X_eIs still the displacement of the end effector, M_d、B_d、K_dAndrespectively an inertia matrix, a damping matrix, a stiffness matrix and another stiffness matrix, F_eThe contact force of the robot end and the environment. Displacement P of the damper_e＝P-P₀P and P₀The actual and neutral positions of the damper, respectively. Such as the elimination variable p_eThen the Zener impedance control model expression can be in the form of

By regulating M_d、B_d、K_dAndthe Zener impedance control model may be embodied as a Voigt model, a Maxwell model, or an intermediate form therebetween.

Step three, establishing a force tracking impedance control model based on position

FIG. 2 is a block diagram of a position based force tracking impedance control. The force tracking impedance controller based on position control adds a force control outer ring on the basis of a position control inner ring, converts error signals of actual contact force and expected contact force into position adjustment quantity through the impedance controller, adjusts an ideal motion track of the tail end of the robot through superposition of the position adjustment quantity and a reference track, and finally enables the tail end of the robot to move according to the calculated ideal motion track through the position controller, so that force tracking is achieved.

The position controller can be any existing position controller, accurate position control of the robot can be achieved, namely, a position control inner ring is formed, the position inner ring outputs the position of the robot, the actual environment contact force is formed in the position of the robot through an environment model, the actual environment acting force is subtracted from the expected contact force to form a force error signal, the force error signal can form a position error signal through the impedance controller, a reference track can be obtained by subtracting the position error signal from the expected position, the reference track is output to the position controller, force tracking impedance control of the robot can be achieved, and a closed control loop is completed.

While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.