CN111604908A - Force and position hybrid control method for mechanical arm of overhead line maintenance robot - Google Patents

Force and position hybrid control method for mechanical arm of overhead line maintenance robot Download PDF

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Publication number
CN111604908A
CN111604908A CN202010499199.2A CN202010499199A CN111604908A CN 111604908 A CN111604908 A CN 111604908A CN 202010499199 A CN202010499199 A CN 202010499199A CN 111604908 A CN111604908 A CN 111604908A
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mechanical arm
force
sliding mode
mode controller
control method
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CN111604908B (en
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刘荣海
郑欣
郭新良
蔡晓斌
沈锋
杨迎春
焦宗寒
许宏伟
周静波
虞鸿江
陈国坤
代克顺
何运华
孔旭晖
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Electric Power Research Institute of Yunnan Power Grid Co Ltd
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Electric Power Research Institute of Yunnan Power Grid Co Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • 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
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
    • 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
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02G—INSTALLATION OF ELECTRIC CABLES OR LINES, OR OF COMBINED OPTICAL AND ELECTRIC CABLES OR LINES
    • H02G1/00—Methods or apparatus specially adapted for installing, maintaining, repairing or dismantling electric cables or lines
    • H02G1/02—Methods or apparatus specially adapted for installing, maintaining, repairing or dismantling electric cables or lines for overhead lines or cables
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

The application discloses a force and position hybrid control method for an overhead line maintenance robot mechanical arm, which is completely independent of dynamic modeling of a system and can determine the uncertainty limit a priori. During actual use, the sliding mode controller decomposes a dynamic model of the mechanical arm executing operation on the curved surface into force, position and redundant joint subspaces; in the design of a sliding mode controller, an ideal part and a robust part of a sliding mode control method are approached by a TSK fuzzy system and an adaptive PI controller respectively; and adjusting parameters of the controller on line according to an adaptive rule in the Lyapunov second stability determination. Compared with the traditional force and position hybrid control method, the force and position hybrid control method is independent of a robot model, and only needs a small amount of mechanical and geometric characteristic information about the robot and the environment.

Description

Force and position hybrid control method for mechanical arm of overhead line maintenance robot
Technical Field
The application relates to the technical field of electrical equipment, in particular to a force and position hybrid control method for an overhead line maintenance robot mechanical arm.
Background
The operation condition of the high-voltage overhead transmission line directly influences the distribution condition of the power system, and plays a key role in the safe and stable operation of the power system, so that the operation condition of the high-voltage overhead transmission line needs to be regularly checked. At present, the inspection mode of the high-voltage overhead transmission line is converted from manual inspection to special robot inspection, and the overhead line inspection robot is used for inspecting the high-voltage transmission line so as to improve the operation safety of the transmission line.
The overhead line maintenance robot needs to simultaneously adjust the contact force of the mechanical arm end effector on an operation object and the position of the end effector in the task execution, and the control problem is the force and position mixed control problem of the mechanical arm. At present, the force position hybrid control of the mechanical arm of the overhead line maintenance robot generally adopts a mechanical arm force control method with robustness on uncertainty and parameter change.
However, this force-level hybrid control method relies on complete or partial knowledge of the system dynamics, i.e., a vector machine that decomposes a mathematical model into a regression matrix and some unknown parameters using the structure of the dynamics. When the established mathematical model is complex, the identification of unknown parameters in the vector machine becomes difficult, the controllability of the mechanical arm of the overhead line maintenance robot of the system is reduced, and the smooth completion of the routing inspection task of the mechanical arm of the overhead line maintenance robot on the overhead transmission line is further influenced.
Disclosure of Invention
The application provides a force and position hybrid control method for an overhead line maintenance robot mechanical arm, which aims to solve the problem that the existing force and position hybrid control method depends on complete or partial system dynamics knowledge, so that the controllability of the overhead line maintenance robot mechanical arm is reduced, and the smooth completion of the inspection task of the overhead line maintenance robot mechanical arm on an overhead transmission line is influenced.
The application provides a force and position hybrid control method of an overhead line maintenance robot mechanical arm, which is characterized by comprising the following steps:
establishing a mechanical arm dynamic model, and performing dynamic decomposition to obtain a decomposition dynamic equation of mechanical arm motion;
designing a sliding mode controller by using a decomposition kinetic equation;
respectively approaching an ideal part and a robust part of a sliding mode controller by adopting a TSK fuzzy system and an adaptive PI controller;
and adjusting parameters of the sliding mode controller on line according to a self-adaptive rule in the Lyapunov second stability determination.
Optionally, a mechanical arm dynamics model is established, and dynamics decomposition is performed to obtain a decomposition dynamics equation of mechanical arm motion, including,
establishing a mechanical arm dynamic model, wherein the mechanical arm kinematic equation is as follows:
Figure BDA0002524055190000011
wherein q is a joint displacement vector, M (q) represents an inertia matrix of the robot,
Figure BDA0002524055190000012
representing the coincidence of the coriolis matrix and the term associated with centripetal force, g (q) is a vector containing terms corresponding to the gravitational effect, τ is the vector of the input torque acting on the joint,
Figure BDA0002524055190000013
is the interaction force between the end effector and the environment, and J is the coupled joint velocity vector
Figure BDA0002524055190000014
And task space velocity vector
Figure BDA0002524055190000015
Jacobian matrix of (a):
Figure BDA0002524055190000016
in the formula,
Figure BDA0002524055190000021
is the position and direction vector of the end effector;
the environment is assumed to be a deformable plane without friction,
Figure BDA0002524055190000022
proportional to the environmental deformation:
Figure BDA0002524055190000023
in the formula,
Figure BDA0002524055190000024
is an environmental stiffness matrix, xeRepresenting a point on a stationary environment;
rigidity matrix
Figure BDA0002524055190000025
The decomposition is as follows:
Figure BDA0002524055190000026
the manipulation dynamics are decomposed into three orthogonal subspaces, namely force, position, redundant joint subspaces, and the following elements are introduced:
I＝J+J+J-,I＝K+K+K-，
wherein,
Figure BDA0002524055190000027
velocity vector of joint
Figure BDA0002524055190000028
And task space velocity vector
Figure BDA0002524055190000029
The decomposition is as follows:
Figure BDA00025240551900000210
Figure BDA00025240551900000211
by using
Figure BDA00025240551900000212
The second derivative of the pose vector of the end effector of (a) is:
Figure BDA00025240551900000213
by using
Figure BDA00025240551900000214
And the second derivative of the manipulator joint displacement vector to obtain:
Figure BDA00025240551900000215
get
Figure BDA00025240551900000216
To obtain a derivative function as:
Figure BDA00025240551900000217
and obtaining a decomposition kinetic equation of the mechanical arm motion by using the decomposition vectors of the joint space and the task space:
Figure BDA00025240551900000218
optionally, a sliding-mode controller is designed using the equations of decomposed dynamics, including,
define the slip plane and tracking error as:
Figure BDA00025240551900000219
where λ is a constant and subscript d represents the expected value of the variable;
defining the reference speed as:
Figure BDA00025240551900000220
by using
Figure BDA00025240551900000221
Will slideThe moving surface is converted into:
Figure BDA00025240551900000222
by using
Figure BDA00025240551900000223
The mechanical arm dynamics equation is converted into:
Figure BDA00025240551900000224
wherein:
Figure BDA0002524055190000031
designing a sliding mode controller as follows:
τ＝-(τeq+τrb),τeq＝-(τe+z)，
wherein, taueqAnd τrbRepresenting the ideal and robust parts of the control input, respectively.
Optionally, the TSK fuzzy system and the adaptive PI controller are used to approximate the ideal and robust parts of the sliding-mode controller, respectively, including,
blurring system and s with TSKjIs input, tauj fuzzFor output, defining the j' th joint of the mechanical arm to meet the following conditions:
when in use
Figure BDA0002524055190000032
When the temperature of the water is higher than the set temperature,
Figure BDA0002524055190000033
by using a univariate fuzzy generator, process reasoning and central mean deblurring, the output of the jth joint of the mechanical arm maintains the following relationship:
Figure BDA0002524055190000034
consider the following minimum input as s1,...,smAnd n is output as
Figure BDA0002524055190000035
The fuzzy sliding mode controller:
Figure BDA0002524055190000036
to pair
Figure BDA0002524055190000037
Uncertainty, error bound, and θ injMaking an estimate of ejReplacement of
Figure BDA0002524055190000038
Estimate error of
Figure BDA0002524055190000039
Equivalent part tau to be input by fuzzy sliding mode controllereqEstimated as
Figure BDA00025240551900000310
The control equation is
Figure BDA00025240551900000311
The kinematic equation of the mechanical arm is used as the dynamic equation of the manipulator arm contacting with the environment, and the control moment is assumed to be
Figure BDA00025240551900000312
Wherein,
Figure BDA00025240551900000313
expressing the law of adaptation as
Figure BDA00025240551900000314
Wherein γ is a common principle.
Optionally, parameters of the sliding mode controller are adjusted online according to an adaptive rule in the Lyapunov second stability determination, including,
ideal controllers, τ, under precise and well-known conditions of the object model, according to Lyapunov's second stability theoremidThe following approximate relationship exists with a stable system: tau isid＝-τeq-KDs＝-(τeq+KDs)，
Using tauid＝-τeq-KDs＝-(τeq+KDAnd s) adjusting parameters of the sliding mode controller on line.
The application provides a force and position hybrid control method for an overhead line maintenance robot mechanical arm, which is completely independent of dynamic modeling of a system and can determine the uncertainty limit a priori. During actual use, the sliding mode controller decomposes a dynamic model of the mechanical arm executing operation on the curved surface into force, position and redundant joint subspaces; in the design of a sliding mode controller, an ideal part and a robust part of a sliding mode control method are approached by a TSK fuzzy system and an adaptive PI controller respectively; and then, adjusting the parameters of the controller on line according to an adaptive rule in the Lyapunov second stability determination. Compared with the traditional force and position hybrid control method, the force and position hybrid control method for the mechanical arm of the overhead line maintenance robot does not depend on a robot model, and only needs a small amount of mechanical and geometric characteristic information about the robot and the environment. In addition, the method eliminates the need to determine uncertainty bounds, which are evaluated using the proposed strategy.
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In order to more clearly explain the technical solution of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a force-position hybrid control method for an overhead line inspection robot mechanical arm according to the present application;
FIG. 2 is a schematic diagram of a sliding mode controller design;
FIG. 3 is an idealized part of the sliding mode controller and the robust part replacement principle;
fig. 4 is a parameter schematic diagram of an online adjustment sliding mode controller.
Detailed Description
The application provides a force and position hybrid control method for an overhead line maintenance robot mechanical arm, which is used for adjusting the contact force of an end effector of the mechanical arm on an operation object and the position of the end effector.
Fig. 1 is a flowchart of a force and position hybrid control method for an overhead line inspection robot mechanical arm according to the present application, and as shown in fig. 1, the force and position hybrid control method for an overhead line inspection robot mechanical arm includes:
and S100, establishing a mechanical arm dynamic model, and performing dynamic decomposition to obtain a decomposition dynamic equation of mechanical arm motion.
In the application, a mechanical arm dynamic model is established, and dynamic decomposition is carried out to obtain a decomposition dynamic equation of mechanical arm motion, including,
and (3) establishing a mechanical arm dynamic model, wherein the mechanical arm kinematic equation is as follows:
Figure BDA0002524055190000041
wherein q is a joint displacement vector, M (q) represents an inertia matrix of the robot,
Figure BDA0002524055190000042
representing the coincidence of the coriolis matrix and the term associated with centripetal force, g (q) is a vector containing terms corresponding to the gravitational effect, τ is the vector of the input torque acting on the joint,
Figure BDA0002524055190000043
is the interaction force between the end effector and the environment, and J is the coupled joint velocity vector
Figure BDA0002524055190000044
And task space velocity vector
Figure BDA0002524055190000045
Jacobian matrix of (a):
Figure BDA0002524055190000046
in the formula,
Figure BDA0002524055190000047
is the position and orientation vector of the end effector.
The environment is assumed to be a deformable plane without friction,
Figure BDA0002524055190000048
proportional to the environmental deformation:
Figure BDA0002524055190000049
in the formula,
Figure BDA00025240551900000410
is an environmental stiffness matrix, xeRepresenting points on a stationary environment.
In the present application, the stiffness matrix is
Figure BDA00025240551900000411
The decomposition is as follows:
Figure BDA0002524055190000051
the manipulation dynamics are decomposed into three orthogonal subspaces, namely force, position, redundant joint subspaces, and the following elements are introduced:
I＝J+J+J-,I＝K+K+K-(5)
wherein,
Figure BDA0002524055190000052
velocity vector of joint
Figure BDA0002524055190000053
And task space velocity vector
Figure BDA0002524055190000054
The decomposition is as follows:
Figure BDA0002524055190000055
Figure BDA0002524055190000056
by using
Figure BDA0002524055190000057
The second derivative of the pose vector of the end effector of (a) is:
Figure BDA0002524055190000058
by using
Figure BDA0002524055190000059
And the second derivative of the manipulator joint displacement vector to obtain:
Figure BDA00025240551900000510
get
Figure BDA00025240551900000511
To obtain a derivative function as:
Figure BDA00025240551900000512
and obtaining a decomposition kinetic equation of the mechanical arm motion by using the decomposition vectors of the joint space and the task space:
Figure BDA00025240551900000513
where the components of F, x and q are decomposed into three orthogonal subspaces to facilitate the design of the sliding-mode controller.
And S200, designing a sliding mode controller by using a decomposition kinetic equation.
Fig. 2 is a schematic diagram of a design of a sliding mode controller, as shown in fig. 2, which is designed by using a decomposition kinetic equation in the present application, including,
define the slip plane and tracking error as:
Figure BDA00025240551900000514
where λ is a constant and the subscript d represents the expected value of the variable.
Defining the reference speed as:
Figure BDA00025240551900000515
by using
Figure BDA00025240551900000516
Converting the sliding surface into:
Figure BDA00025240551900000517
by using
Figure BDA00025240551900000518
The mechanical arm dynamics equation is converted into:
Figure BDA00025240551900000519
wherein:
Figure BDA0002524055190000061
Figure BDA0002524055190000062
designing a sliding mode controller as follows:
τ＝-(τeq+τrb),τeq＝-(τe+z) (17)
wherein, taueqAnd τrbRepresenting the ideal and robust parts of the control input, respectively.
And step S300, respectively approaching an ideal part and a robust part of the sliding mode controller by adopting a TSK (Takagi-Sugeno-Kang) fuzzy system and an adaptive PI controller.
Fig. 3 shows an ideal part and a robust part replacement principle of the sliding mode controller, and as shown in fig. 3, the TSK fuzzy system and the adaptive PI controller are adopted in the present application to respectively approach the ideal part and the robust part of the sliding mode controller, including,
blurring system and s with TSKjIs input, tauj fuzzFor output, defining the j' th joint of the mechanical arm to meet the following conditions:
when in use
Figure BDA0002524055190000063
When the temperature of the water is higher than the set temperature,
Figure BDA0002524055190000064
by using a univariate fuzzy generator, process reasoning and central mean deblurring, the output of the jth joint of the mechanical arm maintains the following relationship:
Figure BDA0002524055190000065
consider the following minimum input as s1,...,smAnd n is output as
Figure BDA0002524055190000066
Fuzzy slide ofA mold controller:
Figure BDA0002524055190000067
to pair
Figure BDA0002524055190000068
Uncertainty, error bound, and θ injMaking an estimate of ejReplacement of
Figure BDA0002524055190000069
The estimation error is:
Figure BDA00025240551900000610
equivalent part tau to be input by fuzzy sliding mode controllereqEstimated as:
Figure BDA00025240551900000611
the control equation is:
Figure BDA00025240551900000612
taking a mechanical arm kinematic equation as a dynamic equation of the manipulator arm in contact with the environment, and assuming that the control moment is as follows:
Figure BDA00025240551900000613
wherein,
Figure BDA00025240551900000614
the adaptation law is expressed as:
Figure BDA00025240551900000615
Figure BDA00025240551900000616
Figure BDA00025240551900000617
and S400, adjusting parameters of the sliding mode controller on line according to the self-adaptive rule in the Lyapunov second stability determination.
Fig. 4 is a schematic diagram of parameters of a sliding mode controller for online adjustment, as shown in fig. 4, according to the adaptive rule in the Lyapunov second stability determination, parameters of the sliding mode controller for online adjustment in the present application, including,
ideal controllers, τ, under precise and well-known conditions of the object model, according to Lyapunov's second stability theoremidThe following approximate relationship exists with a stable system:
τid＝-τeq-KDs＝-(τeq+KDs) (27)
using tauid＝-τeq-KDs＝-(τeq+KDAnd s) adjusting parameters of the sliding mode controller on line.
The application provides a force and position hybrid control method for an overhead line maintenance robot mechanical arm, which is completely independent of dynamic modeling of a system and can determine the uncertainty limit a priori. During actual use, the sliding mode controller decomposes a dynamic model of the mechanical arm executing operation on the curved surface into force, position and redundant joint subspaces; in the design of a sliding mode controller, an ideal part and a robust part of a sliding mode control method are approached by a TSK fuzzy system and an adaptive PI controller respectively; and then, adjusting the parameters of the controller on line according to an adaptive rule in the Lyapunov second stability determination. Compared with the traditional force and position hybrid control method, the force and position hybrid control method for the mechanical arm of the overhead line maintenance robot does not depend on a robot model, and only needs a small amount of mechanical and geometric characteristic information about the robot and the environment. In addition, the method eliminates the need to determine uncertainty bounds, which are evaluated using the proposed strategy.
The above-described embodiments of the present application do not limit the scope of the present application.

Claims (5)

1. A force and position hybrid control method for an overhead line maintenance robot mechanical arm is characterized by comprising the following steps:
establishing a mechanical arm dynamic model, and performing dynamic decomposition to obtain a decomposition dynamic equation of mechanical arm motion;
designing a sliding mode controller by using a decomposition kinetic equation;
respectively approaching an ideal part and a robust part of a sliding mode controller by adopting a TSK fuzzy system and an adaptive PI controller;
and adjusting parameters of the sliding mode controller on line according to a self-adaptive rule in the Lyapunov second stability determination.
2. The force-position hybrid control method of the overhead line inspection robot manipulator of claim 1, wherein a manipulator dynamics model is established and a dynamics decomposition is performed to obtain a decomposition dynamics equation of the manipulator motion, comprising,
establishing a mechanical arm dynamic model, wherein the mechanical arm kinematic equation is as follows:
Figure FDA0002524055180000011
wherein q is a joint displacement vector, M (q) represents an inertia matrix of the robot,
Figure FDA0002524055180000012
representing the coincidence of the coriolis matrix and the term associated with centripetal force, g (q) is a vector containing terms corresponding to the gravitational effect, τ is the vector of the input torque acting on the joint,
Figure FDA0002524055180000013
is the interaction force between the end effector and the environment, and J is a relationshipNodal velocity vector
Figure FDA0002524055180000014
And task space velocity vector
Figure FDA0002524055180000015
Jacobian matrix of (a):
Figure FDA0002524055180000016
in the formula,
Figure FDA0002524055180000017
is the position and direction vector of the end effector;
the environment is assumed to be a deformable plane without friction,
Figure FDA0002524055180000018
proportional to the environmental deformation:
Figure FDA0002524055180000019
in the formula,
Figure FDA00025240551800000110
is an environmental stiffness matrix, xeRepresenting a point on a stationary environment;
rigidity matrix
Figure FDA00025240551800000111
The decomposition is as follows:
Figure FDA00025240551800000112
the manipulation dynamics are decomposed into three orthogonal subspaces, namely force, position, redundant joint subspaces, and the following elements are introduced:
I＝J+J+J-,I＝K+K+K-，
wherein,
Figure FDA00025240551800000113
velocity vector of joint
Figure FDA00025240551800000114
And task space velocity vector
Figure FDA00025240551800000115
The decomposition is as follows:
Figure FDA00025240551800000116
Figure FDA00025240551800000117
by using
Figure FDA00025240551800000118
The second derivative of the pose vector of the end effector of (a) is:
Figure FDA00025240551800000119
by using
Figure FDA00025240551800000120
And the second derivative of the manipulator joint displacement vector to obtain:
Figure FDA00025240551800000121
get
Figure FDA00025240551800000122
To obtain a derivative function as:
Figure FDA00025240551800000123
and obtaining a decomposition kinetic equation of the mechanical arm motion by using the decomposition vectors of the joint space and the task space:
Figure FDA0002524055180000021
3. the force-position hybrid control method of the overhead line inspection robot mechanical arm according to claim 2, characterized in that a sliding mode controller is designed using a decomposition kinetic equation, comprising,
define the slip plane and tracking error as:
Figure FDA0002524055180000022
where λ is a constant and subscript d represents the expected value of the variable;
defining the reference speed as:
Figure FDA0002524055180000023
by using
Figure FDA0002524055180000024
Converting the sliding surface into:
Figure FDA0002524055180000025
by using
Figure FDA0002524055180000026
The mechanical arm dynamics equation is converted into:
Figure FDA0002524055180000027
wherein:
Figure FDA0002524055180000028
designing a sliding mode controller as follows:
τ＝-(τeq+τrb),τeq＝-(τe+z)，
wherein, taueqAnd τrbRepresenting the ideal and robust parts of the control input, respectively.
4. The force-position hybrid control method of the overhead line inspection robot mechanical arm of claim 1, characterized in that a TSK fuzzy system and an adaptive PI controller are used to approximate an ideal part and a robust part of a sliding mode controller, respectively, comprising,
blurring system and s with TSKjIs input, tauj fuzzFor output, defining the j' th joint of the mechanical arm to meet the following conditions:
when in use
Figure FDA0002524055180000029
When the temperature of the water is higher than the set temperature,
Figure FDA00025240551800000210
by using a univariate fuzzy generator, process reasoning and central mean deblurring, the output of the jth joint of the mechanical arm maintains the following relationship:
Figure FDA00025240551800000211
consider the following minimum input as s1,...,smAnd n is output as
Figure FDA00025240551800000212
The fuzzy sliding mode controller:
Figure FDA00025240551800000213
to pair
Figure FDA00025240551800000214
Uncertainty, error bound, and θ injMaking an estimate of ejReplacement of
Figure FDA00025240551800000215
Estimate error of
Figure FDA00025240551800000216
Equivalent part tau to be input by fuzzy sliding mode controllereqEstimated as
Figure FDA0002524055180000031
The control equation is
Figure FDA0002524055180000032
The kinematic equation of the mechanical arm is used as the dynamic equation of the manipulator arm contacting with the environment, and the control moment is assumed to be
Figure FDA0002524055180000033
Wherein,
Figure FDA0002524055180000034
expressing the law of adaptation as
Figure FDA0002524055180000035
Wherein γ is a common principle.
5. The force position hybrid control method of the overhead line inspection robot mechanical arm according to claim 1, characterized in that parameters of the sliding mode controller are adjusted online according to an adaptive rule in the Lyapunov second stability determination, including,
ideal controllers, τ, under precise and well-known conditions of the object model, according to Lyapunov's second stability theoremidThe following approximate relationship exists with a stable system: tau isid＝-τeq-KDs＝-(τeq+KDs)，
Using tauid＝-τeq-KDs＝-(τeq+KDAnd s) adjusting parameters of the sliding mode controller on line.
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