CN110653825A - Six-degree-of-freedom mechanical arm control method based on full-order sliding mode - Google Patents

Six-degree-of-freedom mechanical arm control method based on full-order sliding mode Download PDF

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Publication number
CN110653825A
CN110653825A CN201910986452.4A CN201910986452A CN110653825A CN 110653825 A CN110653825 A CN 110653825A CN 201910986452 A CN201910986452 A CN 201910986452A CN 110653825 A CN110653825 A CN 110653825A
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sliding mode
mechanical arm
control
degree
joint
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徐龙
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Nanjing Longyue Automation Technology Co., Ltd
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徐龙
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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
    • B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
    • 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
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

Abstract

A full-order sliding mode-based six-degree-of-freedom mechanical arm control method solves the problem that the existing six-degree-of-freedom mechanical arm sliding mode control technology cannot overcome the defect of discontinuous shaking of control signals. The invention provides a brand-new full-order sliding mode control method, wherein a control signal is a continuous non-smooth control signal, a traditional sliding mode control signal contains a sign function item, and a switching signal cannot be directly used for mechanical arm control. The control method provided by the invention does not need to add extra equipment or a filter observer, is used for eliminating discontinuity of the control signal and carrying out signal smoothing processing, thereby increasing the precision of tracking control.

Description

Six-degree-of-freedom mechanical arm control method based on full-order sliding mode
Technical Field
The invention relates to the field of tracking of an expected spatial trajectory of an end effector of a six-degree-of-freedom mechanical arm, in particular to a control method of the six-degree-of-freedom mechanical arm based on a full-order sliding mode.
Background
With the background of the promotion of smart manufacturing in the 4.0 th era of industry, a variety of industrial robots have been developed and widely used in the industrial field. The design of a conventional industrial robot employs a reducer, such as a harmonic reducer, a gear, etc., between a motor and a connecting rod. Therefore, the speed of the robot is relatively low. The existing widely used simple controllers (e.g. PID controllers) can ensure that the influence of the load on the motor rotor is reduced due to the speed reducer. However, it is very difficult to achieve high performance control requirements, such as high speed and high precision, and the robot motor cannot be directly driven. Furthermore, the high robustness of the inability to achieve tracking control requires under unknown uncertainty conditions such as robot system model uncertainty, unknown payload uncertainty, and unmodeled friction uncertainty.
At present, in the field of sliding mode control methods for tracking the tail end of a six-degree-of-freedom mechanical arm, the application of the traditional sliding mode control method is mainly used, and the switching control characteristic of the sliding mode control method is related to a sign function sgn () from the aspect of mathematical mechanism. The sliding mode control and the PID composite controller are applied to ensure the global asymptotic stability of the output tracking error of the robot, and the actual effect requirement of limited time cannot be ensured. Meanwhile, since the output contains a sign function term, when the output is sent into a control system as an input signal, which means that a high-frequency switching signal is required during the design of the sliding mode controller, a jitter phenomenon occurs, and the smoothness of control cannot be ensured. The continuous sliding mode control method of the robust differential estimator is adopted, but the robust differential estimator needs to be additionally added, the design is complicated, an inverse sharp peak exists in the initial stage due to the tracking characteristic of the differential estimator, the response speed is low, the speed regulation performance is further reduced, and the requirement on the control precision cannot be met.
Disclosure of Invention
The invention aims to provide a full-order sliding mode-based six-degree-of-freedom mechanical arm control method, and solves the problem that the existing six-degree-of-freedom mechanical arm sliding mode control technology cannot overcome the defect of discontinuous shaking of control signals.
In order to achieve the purpose, the invention provides a six-degree-of-freedom mechanical arm control method based on a full-order sliding mode.
According to the method, the interference of the outside to the system is considered in the tracking control problem of the tail end of the six-degree-of-freedom mechanical arm, the proposed full-order sliding mode control can well inhibit the external interference, and the high-precision tracking control effect is obtained.
The invention is realized by the following steps:
step one, establishing a dynamic model of a six-degree-of-freedom mechanical arm in joint coordinates by using a Euler-Lagrange method
Figure DEST_PATH_IMAGE001
In the formula (I), the compound is shown in the specification,
Figure 86260DEST_PATH_IMAGE002
respectively representing joint angles, angular velocities and angular acceleration vectors;
Figure 100002_DEST_PATH_IMAGE003
represents a positive definite symmetric inertial matrix;
Figure 395101DEST_PATH_IMAGE004
representing the centrifugal and coriolis force vectors;
Figure 100002_DEST_PATH_IMAGE005
representing a gravitational acceleration matrix;
Figure 361920DEST_PATH_IMAGE006
representing input torque vectors of each joint;
Figure 100002_DEST_PATH_IMAGE007
representing an external unknown disturbing force action.
Step two, order
Figure 805671DEST_PATH_IMAGE008
The above-mentioned robot arm system can then be reshaped to be expressed as follows
In the formula (I), the compound is shown in the specification,
Figure 100002_DEST_PATH_IMAGE011
,,and
Figure 397823DEST_PATH_IMAGE014
。
assuming external interference to the system
Figure 809213DEST_PATH_IMAGE007
Has an upper bound on its first order differential and satisfies the following conditionPiece
Figure 100002_DEST_PATH_IMAGE015
And
Figure 214524DEST_PATH_IMAGE016
then, can obtain
Figure 100002_DEST_PATH_IMAGE017
Satisfies the following conditions
Figure 369562DEST_PATH_IMAGE018
。
Step three, obtaining a joint angle expected value by solving the inverse kinematics joint angle of the six-degree-of-freedom mechanical arm
Figure 100002_DEST_PATH_IMAGE019
And joint angular velocity desired value
Figure 310973DEST_PATH_IMAGE020
Then we can define the error in joint angle and joint angular velocity as follows
And
therefore, an error dynamic equation can be obtained from the system equation and the error equation:
Figure 100002_DEST_PATH_IMAGE023
，
step four, designing a sliding mode surface controlled by a full-order sliding mode as follows:
Figure 100002_DEST_PATH_IMAGE025
design parameters
Figure 756178DEST_PATH_IMAGE026
And
Figure 100002_DEST_PATH_IMAGE027
。
when the error system reaches the slip form surfaceThe dynamic behavior of the system can be characterized as:
Figure 100002_DEST_PATH_IMAGE029
；
realizing convergence of the system state;
rate of control
Figure 684393DEST_PATH_IMAGE030
Is designed as
Wherein
Figure DEST_PATH_IMAGE033
For equivalent control terms, andthe sign function term is hidden in the first order reciprocal term of the sign function term for the integral of the switching control term, and the shake is well inhibited.
Advantageous effects
A full-order sliding mode control-based six-degree-of-freedom mechanical arm tail end tracking control method provides a brand-new full-order sliding mode control method, wherein a control signal is a continuous non-smooth control signal, a traditional sliding mode control signal contains a sign function item, and a switching signal cannot be directly used for mechanical arm control.
The control method provided by the invention does not need to add extra equipment or a filter observer, is used for eliminating discontinuity of the control signal and carrying out signal smoothing processing, thereby increasing the precision of tracking control. The control method provides high robustness performance, has good effect of inhibiting external interference, and improves control precision.
Drawings
Fig. 1 is a control flow chart of the full-order sliding mode control on the six-degree-of-freedom mechanical arm.
Detailed Description
A full-order sliding mode control-based tracking control method for the tail end of a six-degree-of-freedom mechanical arm is based on a full-order sliding mode theory tail end control method and achieves tracking control over an expected space track of a six-degree-of-freedom mechanical arm tail end actuator.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments.
Step one, therefore, establishing a dynamic model in joint coordinates by using a Euler-Lagrange method:
Figure 612532DEST_PATH_IMAGE001
（1）
in the formula (I), the compound is shown in the specification,
Figure 997377DEST_PATH_IMAGE002
respectively representing joint angles, angular velocities and angular acceleration vectors;
Figure 655891DEST_PATH_IMAGE003
represents a positive definite symmetric inertial matrix;
Figure 821293DEST_PATH_IMAGE004
representing the centrifugal and coriolis force vectors;representing a gravitational acceleration matrix;
Figure 157914DEST_PATH_IMAGE006
represents eachAn input torque vector of the joint;
Figure 987330DEST_PATH_IMAGE007
representing an external unknown disturbing force action.
Referring to fig. 1, firstly, the invention performs tail end trajectory control on a mechanical arm based on a full-order sliding mode control technology under an environment considering external interference. Wherein the desired joint angle is solved for by inverse kinematics through the desired trajectory and alignment
Figure 577711DEST_PATH_IMAGE019
And desired joint angular velocityIt is the desired target that is being tracked that is being controlled.
Step two, design of full-order sliding mode controller
The terminal track tracking controller requires accurate tracking of a given joint angle and speed thereof, the system has strong robustness on external disturbance and internal parameter perturbation influence, and an expected output value is a given expected value
Figure 805485DEST_PATH_IMAGE019
And
Figure 868119DEST_PATH_IMAGE020
。
defining joint angle error
Figure DEST_PATH_IMAGE035
Is composed of
Figure 149058DEST_PATH_IMAGE021
And joint angular velocity error
Figure 588130DEST_PATH_IMAGE036
Is composed of
Figure 802074DEST_PATH_IMAGE022
And according to the mechanical arm mathematical model (1) in the step one, an angular acceleration deviation dynamic equation is as follows:
Figure DEST_PATH_IMAGE037
（2）
the design of the full-order sliding mode controller comprises a sliding mode surface and a control rate, and aims at formula (2), wherein the sliding mode surface is designed as follows:
Figure 238871DEST_PATH_IMAGE038
（3）
in which the parameters are counted
Figure 803845DEST_PATH_IMAGE026
And,
Figure DEST_PATH_IMAGE039
,i=2,j=6。
once the error system of equation (2) reaches the sliding mode surface s =0, the system dynamics can be characterized as:
Figure 115057DEST_PATH_IMAGE029
（4）
therefore, the convergence of the system state is realized.
It is noted from equation (3) that the full-order sliding control surface needs to obtain the system state
Figure 457177DEST_PATH_IMAGE040
And this is clearly not available in real time for a system (2) of relative order 2. Therefore, it is considered here that the actual system differentiation implementation is obtained by direct forward and backward differentiation in many ways, i.e. there is
Figure DEST_PATH_IMAGE041
（5）
Wherein
Figure 5052DEST_PATH_IMAGE042
Is a time delay of one sampling step, having
Figure DEST_PATH_IMAGE043
，
Figure 989189DEST_PATH_IMAGE044
（6）
According to the arrival conditions of sliding forms
Figure DEST_PATH_IMAGE045
Control rate of
Figure 443304DEST_PATH_IMAGE030
Is designed as
Figure 956325DEST_PATH_IMAGE046
（7）
Wherein
Figure DEST_PATH_IMAGE047
As equivalent control termsFor switching control items, k>0 is the switching gain.
The above description is only for the purpose of creating a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be able to substitute or change the technical solution and the inventive concept of the present invention within the technical scope of the present invention.

Claims (1)

1. A six-degree-of-freedom mechanical arm control method based on a full-order sliding mode is characterized by comprising the following steps of:
step one, establishing a dynamic model of the six-degree-of-freedom mechanical arm in joint coordinates by using a Euler-Lagrange method:
Figure 390499DEST_PATH_IMAGE001
in the formula:
Figure DEST_PATH_IMAGE002
respectively representing joint angles, angular velocities and angular acceleration vectors;
Figure DEST_PATH_IMAGE003
represents a positive definite symmetric inertial matrix;
Figure DEST_PATH_IMAGE004
representing the centrifugal and coriolis force vectors;
Figure DEST_PATH_IMAGE005
representing a gravitational acceleration matrix;
Figure DEST_PATH_IMAGE006
representing input torque vectors of each joint;representing an external unknown disturbance force;
step two, order
Figure DEST_PATH_IMAGE008
Then, the mechanical arm dynamics model can be reshaped to obtain the following expression:
Figure DEST_PATH_IMAGE009
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE010
,
Figure DEST_PATH_IMAGE011
,
Figure DEST_PATH_IMAGE012
and
Figure DEST_PATH_IMAGE013
；
assuming external interference to the system
Figure DEST_PATH_IMAGE014
And its first order differential has an upper bound and satisfies the following condition:
Figure DEST_PATH_IMAGE015
and
Figure DEST_PATH_IMAGE016
then, can obtain
Figure DEST_PATH_IMAGE017
Satisfies the following conditions
Figure DEST_PATH_IMAGE018
；
Step three, obtaining a joint angle expected value by solving the inverse kinematics joint angle of the degree of freedom mechanical armAnd joint angular velocity desired value
Figure DEST_PATH_IMAGE020
Defining the errors of the joint angle and the joint angular velocity as follows:
Figure DEST_PATH_IMAGE021
and
Figure DEST_PATH_IMAGE022
therefore, an error dynamic equation can be obtained from the system equation and the error equation:
Figure DEST_PATH_IMAGE023
；
step four, designing a sliding mode surface controlled by a full-order sliding mode as follows:
Figure DEST_PATH_IMAGE024
design parameters
Figure DEST_PATH_IMAGE025
And
Figure DEST_PATH_IMAGE026
；
when the error system reaches the slip form surfaceThe dynamic behavior of the system can be characterized as:
Figure DEST_PATH_IMAGE028
；
realizing convergence of the system state;
rate of control
Figure DEST_PATH_IMAGE029
The design is as follows:
Figure DEST_PATH_IMAGE030
wherein
Figure DEST_PATH_IMAGE031
For equivalent control terms, and
Figure DEST_PATH_IMAGE032
the sign function term is hidden in the first order reciprocal term of the sign function term for the integral of the switching control term, and the shake is well inhibited.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115157274A (en) * 2022-04-30 2022-10-11 魅杰光电科技(上海)有限公司 Sliding mode control mechanical arm system and sliding mode control method thereof

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US5049796A (en) * 1989-05-17 1991-09-17 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Robust high-performance control for robotic manipulators
CN105182745A (en) * 2015-08-11 2015-12-23 浙江工业大学 Mechanical-arm servo-system neural-network full-order sliding mode control method with dead-zone compensation
CN107942684A (en) * 2017-12-26 2018-04-20 电子科技大学 Mechanical arm trace tracking method based on the adaptive non-singular terminal sliding formwork of fractional order
CN108983606A (en) * 2018-07-09 2018-12-11 南京理工大学 A kind of Sliding mode self-adaptation control method of mechanical arm system
CN108972560A (en) * 2018-08-23 2018-12-11 北京邮电大学 A kind of activation lacking mechanical arm Hierarchical sliding mode control method based on fuzzy optimization
CN109927032A (en) * 2019-03-28 2019-06-25 东南大学 A kind of mechanical arm Trajectory Tracking Control method based on High-Order Sliding Mode observer

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5049796A (en) * 1989-05-17 1991-09-17 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Robust high-performance control for robotic manipulators
CN105182745A (en) * 2015-08-11 2015-12-23 浙江工业大学 Mechanical-arm servo-system neural-network full-order sliding mode control method with dead-zone compensation
CN107942684A (en) * 2017-12-26 2018-04-20 电子科技大学 Mechanical arm trace tracking method based on the adaptive non-singular terminal sliding formwork of fractional order
CN108983606A (en) * 2018-07-09 2018-12-11 南京理工大学 A kind of Sliding mode self-adaptation control method of mechanical arm system
CN108972560A (en) * 2018-08-23 2018-12-11 北京邮电大学 A kind of activation lacking mechanical arm Hierarchical sliding mode control method based on fuzzy optimization
CN109927032A (en) * 2019-03-28 2019-06-25 东南大学 A kind of mechanical arm Trajectory Tracking Control method based on High-Order Sliding Mode observer

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115157274A (en) * 2022-04-30 2022-10-11 魅杰光电科技(上海)有限公司 Sliding mode control mechanical arm system and sliding mode control method thereof
CN115157274B (en) * 2022-04-30 2024-03-12 魅杰光电科技(上海)有限公司 Mechanical arm system controlled by sliding mode and sliding mode control method thereof

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