CN110116409B - Four-channel teleoperation bilateral control method based on disturbance observer - Google Patents

Four-channel teleoperation bilateral control method based on disturbance observer Download PDF

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CN110116409B
CN110116409B CN201910437931.0A CN201910437931A CN110116409B CN 110116409 B CN110116409 B CN 110116409B CN 201910437931 A CN201910437931 A CN 201910437931A CN 110116409 B CN110116409 B CN 110116409B
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陈正
黄方昊
宋伟
王滔
朱世强
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Zhejiang University ZJU
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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Abstract

The invention discloses a four-channel teleoperation bilateral control method based on a disturbance observer. A globally stable disturbance observer-based nonlinear sliding mode controller design method is provided by establishing a nonlinear system dynamic model of a bilateral teleoperation system, so that the main problems of nonlinearity, uncertainty, external interference and the like of the teleoperation system are solved. Aiming at the problem of nonlinearity of a bilateral teleoperation system, the invention designs a four-channel structure suitable for the nonlinear bilateral teleoperation system, and better system transparency is obtained through transmission of master end positions, operation torque of an operator, slave end positions and environment operation torque signals among communication channels. Aiming at the problems of uncertainty and external interference of a bilateral teleoperation system, the invention designs ideal track generators and a nonlinear sliding mode controller based on a disturbance observer at a master end and a slave end respectively, and guarantees the global stability of the system based on the Lyapunov theory.

Description

Four-channel teleoperation bilateral control method based on disturbance observer
Technical Field
The invention belongs to the field of teleoperation control, in particular to a four-channel teleoperation bilateral control method based on a disturbance observer, and aims to improve the transparency of a nonlinear teleoperation system.
Background
With the development of automation and robot technology, a remote operation technology of human-computer interaction is adopted, namely, an operator operates a master robot to realize motion control of a slave robot, so that remote operation is realized. In view of the characteristics of high telepresence and near real-time synchronous operation of the teleoperation technology, the teleoperation technology has wide application prospects in the fields of space exploration, underwater operation, nuclear environment monitoring, teleoperation and the like.
Transparency is widely studied as an important index of teleoperation systems. The four-channel structure is an effective method for improving the transparency of the teleoperation system, and ideal transparency conditions are obtained by matching impedance coefficients of a master end and a slave end. However, the existing four-channel structure is mostly used for the linear teleoperation system, and with the complication and refinement of the operation task, the linear teleoperation system based on the four-channel structure cannot well perform the operation task. Therefore, in order to deal with complex and fine operation tasks, the invention provides a four-channel teleoperation bilateral control method based on a disturbance observer, which considers the problems of nonlinearity, uncertainty, external interference and the like of a multi-degree-of-freedom master-slave robot, overcomes the influence of nonlinearity, uncertainty and external interference of the master-slave robot on the performance of a teleoperation system, and improves the transparency of the teleoperation system.
Disclosure of Invention
The invention aims to provide a four-channel teleoperation bilateral control method based on a disturbance observer, and aims to solve the technical problems of transparency, nonlinearity, uncertainty and the like of a traditional teleoperation system.
In order to achieve the purpose, the technical scheme of the invention comprises the following specific contents:
a four-channel teleoperation bilateral control method based on a disturbance observer comprises the following steps:
1) establishing a nonlinear system dynamics model of a bilateral teleoperation system, which comprises the following specific steps:
1-1) establishing a dynamic model of a master-slave robot
Figure BDA0002071134320000011
Figure BDA0002071134320000012
Wherein, thetam,
Figure BDA0002071134320000013
And thetas,
Figure BDA0002071134320000014
Indicating position, velocity and acceleration signals of the master and slave robots, Mm0And Ms0Representing the known mass inertia matrix, Cm0And Cs0Representing a known Coriolis force/centripetal force matrix, Gm0And Gs0Representing a known gravity matrix, dmAnd dsRepresenting external interference and model error, umAnd usRepresenting a control input, τhAnd τeIndicating the operator's operating torque or the ambient work torque.
The dynamic model of the master-slave robot has the following characteristics:
①
Figure BDA0002071134320000021
and
Figure BDA0002071134320000022
is an oblique symmetric matrix;
②
Figure BDA0002071134320000023
③
Figure BDA0002071134320000024
1-2) establishing a mass-spring-damping environmental dynamics model
Figure BDA0002071134320000025
Wherein M ise,Ce,GeRepresenting an environmental parameter.
2) A sliding mode controller of a main robot is designed based on a disturbance observer, and the method specifically comprises the following steps:
2-1) designing a main-end ideal track generator as follows:
Figure BDA0002071134320000026
Figure BDA0002071134320000027
Figure BDA0002071134320000028
wherein avrg {. represents an average value of {. cndot. } -，kfmDenotes the scale parameter, Mdm,Cdm,GdmRepresenting the planning parameters.
By mixing thetasBy inputting equation (4), the reference trajectory θ can be obtainedmr,
Figure BDA0002071134320000029
Then selecting proper Mdm,Cdm,GdmEquations (5) and (6) can obtain the ideal trajectory θmd,
Figure BDA00020711343200000210
2-2) defining the sliding surface s of the master robot controllermThe following were used:
Figure BDA00020711343200000211
wherein e ism＝θm-θmd，λm＝diag{λm1,...,λmi,..., λ mw1,2, w denotes the number of degrees of freedom of the master robot.
2-3) calculating smThe first derivation of (A) is as follows:
Figure BDA00020711343200000212
2-4) designing a main controller according to the step (8) to ensure the progressive stability of the main robot, and designing a controller umComprises the following steps:
Figure BDA0002071134320000031
wherein the content of the first and second substances,
Figure BDA0002071134320000032
νm＝diag{νm1,...,νmi,...,νmw}，
Figure BDA0002071134320000033
νmi0>0。
in the controller (9), sat(s)m) Representing a saturation function to avoid chattering in a sliding mode controller, can be defined as:
Figure BDA0002071134320000034
wherein β represents a boundary layer;
Figure BDA0002071134320000035
represents a non-linear disturbance observer which can be defined as:
Figure BDA0002071134320000036
wherein the content of the first and second substances,
Figure BDA0002071134320000037
Hmthe reversible matrix is expressed and can be obtained by calculating a linear matrix inequality.
3) The sliding mode controller of the slave robot is designed based on a disturbance observer, and specifically comprises the following steps:
3-1) design the slave-end ideal trajectory generator as follows:
Figure BDA0002071134320000038
Figure BDA0002071134320000039
Figure BDA00020711343200000310
wherein avrg {. denotes the average value of, kfsDenotes the scale parameter, Mds,Cds,GdsRepresenting the planning parameters.
By mixing thetamInputting equation (12), a reference trajectory theta can be obtainedsr,
Figure BDA00020711343200000311
Then selecting proper Mds,Cds,GdsEquations (13) and (14) can obtain the ideal trajectory θsd,
Figure BDA00020711343200000312
3-2) defining a slip form surface s from the robot controllersThe following were used:
Figure BDA00020711343200000313
wherein e iss＝θs-θsd，λs＝diag{λs1,...,λsi,..., λ sw1,2, w denotes the number of degrees of freedom from the robot.
3-3) calculating ssThe first derivation of (A) is as follows:
Figure BDA0002071134320000041
3-4) designing a slave controller according to the step (16), ensuring the progressive stability of the slave robot, and designing a controller usComprises the following steps:
Figure BDA0002071134320000042
wherein the content of the first and second substances,
Figure BDA0002071134320000043
νs＝diag{νs1,...,νsi,...,νsw}，
Figure BDA0002071134320000044
νsi0>0。
in the controller (17), sat(s)s) Representing a saturation function to avoid chattering in a sliding mode controller, can be defined as:
Figure BDA0002071134320000045
wherein β represents a boundary layer;
Figure BDA0002071134320000046
represents a non-linear disturbance observer which can be defined as:
Figure BDA0002071134320000047
wherein the content of the first and second substances,
Figure BDA0002071134320000048
Hsthe reversible matrix is expressed and can be obtained by calculating a linear matrix inequality.
4) A master-slave robot-based sliding mode controller designs a Lyapunov function to ensure the global stability of a teleoperation system, and specifically comprises the following steps:
4-1) designing a global Lyapunov function V as follows:
V＝Vm+Vs+Vm0+Vs0(20)
wherein the content of the first and second substances,
Figure BDA0002071134320000049
Figure BDA00020711343200000410
4-2) when | | | sm||,||ssWhen | | ≦ β, the global lyapunov function V will converge to:
Figure BDA0002071134320000051
wherein the content of the first and second substances,
Figure BDA0002071134320000052
Figure BDA0002071134320000053
and
Figure BDA0002071134320000054
representing the observed error values of the master and slave observer.
Compared with the prior art, the invention has the following beneficial effects:
1. a disturbance observer is designed, and the anti-interference performance of the nonlinear bilateral teleoperation system is improved by observing and compensating model errors and external interference of the teleoperation system;
2. a saturation function is designed, so that the buffeting problem existing in the traditional sliding mode controller is solved;
2. the nonlinear sliding mode control method based on the disturbance observer can enable the slave robot to track the position signal of the master robot in real time, overcomes the influence of nonlinearity, uncertainty and external interference on the performance of the bilateral teleoperation system, and improves the transparency of the system;
4. and the Lyapunov function is utilized to ensure the boundedness of all signals, so that the stability and the convergence of the nonlinear bilateral teleoperation system are ensured.
Drawings
FIG. 1 is a block diagram of four-channel teleoperation bilateral control based on a disturbance observer according to the present invention;
fig. 2 is a graph of position tracking and force feedback for the master and slave robots according to the present invention.
Detailed Description
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. 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 will now be further described with reference to the following examples and drawings:
the implementation technical scheme of the invention is as follows:
establishing a nonlinear system dynamics model of a bilateral teleoperation system
The dynamic model of the master-slave robot is as follows:
Figure BDA0002071134320000055
Figure BDA0002071134320000056
wherein, thetam,
Figure BDA0002071134320000057
And thetas,
Figure BDA0002071134320000058
Indicating position, velocity and acceleration signals of the master and slave robots, Mm0And Ms0Representing the known mass inertia matrix, Cm0And Cs0Representing a known Coriolis force/centripetal force matrix, Gm0And Gs0Representing a known gravity matrix, dmAnd dsRepresenting external interference and model error, umAnd usRepresenting a control input, τhAnd τeIndicating the operator's operating torque or the ambient work torque.
The dynamic model of the master-slave robot has the following characteristics:
①
Figure BDA0002071134320000061
and
Figure BDA0002071134320000062
is an oblique symmetric matrix;
②
Figure BDA0002071134320000063
③
Figure BDA0002071134320000064
the environmental dynamics model based on mass-spring-damping is as follows:
Figure BDA0002071134320000065
wherein M ise,Ce,GeRepresenting an environmental parameter.
(II) designing sliding mode controller for designing main robot based on disturbance observer
The master-end ideal trajectory generator is designed as follows:
Figure BDA0002071134320000066
Figure BDA0002071134320000067
Figure BDA0002071134320000068
wherein avrg {. denotes the average value of, kfmDenotes the scale parameter, Mdm,Cdm,GdmRepresenting the planning parameters.
By mixing thetasBy inputting equation (4), the reference trajectory θ can be obtainedmr,
Figure BDA0002071134320000069
Then selecting the combinationSuitably Mdm,Cdm,GdmEquations (5) and (6) can obtain the ideal trajectory θmd,
Figure BDA00020711343200000610
Defining a slip form surface s for a master robotic controllermThe following were used:
Figure BDA00020711343200000611
wherein e ism＝θm-θmd，λm＝diag{λm1,...,λmi,..., λ mw1,2, w denotes the number of degrees of freedom of the master robot.
Then, s is calculatedmThe first derivation of (A) is as follows:
Figure BDA00020711343200000612
designing a main controller according to the step (8) to ensure the progressive stability of the main robot, and designing a controller umComprises the following steps:
Figure BDA0002071134320000071
wherein the content of the first and second substances,
Figure BDA0002071134320000072
νm＝diag{νm1,...,νmi,...,νmw}，
Figure BDA0002071134320000073
νmi0>0。
in the controller (9), sat(s)m) Representing a saturation function to avoid chattering in a sliding mode controller, can be defined as:
Figure BDA0002071134320000074
wherein β represents a boundary layer;
Figure BDA0002071134320000075
represents a non-linear disturbance observer which can be defined as:
Figure BDA0002071134320000076
wherein the content of the first and second substances,
Figure BDA0002071134320000077
Hmthe reversible matrix is expressed and can be obtained by calculating a linear matrix inequality.
(III) designing a sliding mode controller of a slave robot based on a disturbance observer
The slave-end ideal trajectory generator is designed as follows:
Figure BDA0002071134320000078
Figure BDA0002071134320000079
Figure BDA00020711343200000710
wherein avrg {. denotes the average value of, kfsDenotes the scale parameter, Mds,Cds,GdsRepresenting the planning parameters.
By mixing thetamInputting equation (12), a reference trajectory theta can be obtainedsr,
Figure BDA00020711343200000711
Then selecting proper Mds,Cds,GdsEquations (13) and (14) can obtain the ideal trajectory θsd,
Figure BDA00020711343200000712
Defining a slip form surface s from a robot controllersThe following were used:
Figure BDA0002071134320000081
wherein e iss＝θs-θsd，λs＝diag{λs1,...,λsi,..., λ sw1,2, w denotes the number of degrees of freedom from the robot.
Then, s is calculatedsThe first derivation of (A) is as follows:
Figure BDA0002071134320000082
according to (16), a slave controller is designed, the progressive stability of the slave robot is ensured, and the designed controller usComprises the following steps:
Figure BDA0002071134320000083
wherein the content of the first and second substances,
Figure BDA0002071134320000084
νs＝diag{νs1,...,νsi,...,νsw}，
Figure BDA0002071134320000085
νsi0>0。
in the controller (17), sat(s)s) Representing a saturation function to avoid chattering in a sliding mode controller, can be defined as:
Figure BDA0002071134320000086
wherein β represents a boundary layer;
Figure BDA0002071134320000087
represents a non-linear disturbance observer which can be defined as:
Figure BDA0002071134320000088
wherein the content of the first and second substances,
Figure BDA0002071134320000089
Hsthe reversible matrix is expressed and can be obtained by calculating a linear matrix inequality.
(IV) designing Lyapunov function of sliding mode controller based on master-slave robot
The global lyapunov function V is designed as follows:
V＝Vm+Vs+Vm0+Vs0 (20)
wherein the content of the first and second substances,
Figure BDA00020711343200000810
Figure BDA00020711343200000811
when | | | sm||,||ssWhen | | ≦ β, the global lyapunov function V will converge to:
Figure BDA0002071134320000091
wherein the content of the first and second substances,
Figure BDA0002071134320000092
Figure BDA0002071134320000093
and
Figure BDA0002071134320000094
representing the observed error values of the master and slave observer.
Based on (21), sm,ss,
Figure BDA0002071134320000095
Is bounded, such that em,
Figure BDA0002071134320000096
es,
Figure BDA0002071134320000097
And um,usIs bounded. Therefore, all signals in the non-linear teleoperation system are bounded and the system is globally stable.
(V) carrying out simulation experiment verification
In order to verify the feasibility of the theory, a simulation experiment is carried out under MATLAB, and the simulation experiment verifies the effect of the four-channel teleoperation bilateral control method based on the disturbance observer.
The simulation parameters are selected as follows:
taking a main controller (9) and a disturbance observer (11), wherein lambdam＝diag{10,10}，νm＝diag{0.2,0.2}，β＝0.05，Mdm＝diag{4.0,4.0}，Cdm＝diag{0,0}，Gdm＝diag{4.9,4.9}*θmd，τfm＝0.025，Hm＝diag{0.28,0.38}。
Taking a slave controller (17) and a disturbance observer (19), whereins＝diag{10,10}，νs＝diag{0.2,0.2}，β＝0.05，Mds＝diag{4.0,4.0}，Cds＝diag{0,0}，Gds＝diag{5.8,5.8}*θsd，τfs＝0.025，Hs＝diag{0.28,0.38}。
Taking the environmental parameter as Me＝diag{-2.0,-2.0}，Ce＝diag{0,0}，Ge＝diag{-0.9,-0.9}*θs。
Taking the operating moment of an operator as tauh＝[-2 sin t 4 sin t]T。
Defining a master-slave robot as a mechanical arm with 2 degrees of freedom, and parameters are as follows:
Figure BDA0002071134320000098
Figure BDA0002071134320000099
Figure BDA00020711343200000910
where j is m, s represents the master robot and the slave robot, respectively, and g is 9.8m/s2。
Fig. 2 is a graph showing position tracking and force feedback of the master robot and the slave robot, and it can be seen from the graph that the slave robot can better track the position signal of the master robot, the operator can feel the force feedback signal, and an ideal tracking track is provided for the master robot through formula (6). Thus, the non-linear teleoperation system is transparent.

Claims (7)

1. The four-channel teleoperation bilateral control method based on the disturbance observer is characterized by comprising the following steps of:
1) establishing a nonlinear system dynamics model of a bilateral teleoperation system, which comprises the following specific steps:
1-1) establishing a dynamic model of a master-slave robot
Figure FDA0002718206600000011
Figure FDA0002718206600000012
Wherein, thetam,
Figure FDA0002718206600000013
Respectively representing position, velocity and acceleration signals, theta, of the main robots,
Figure FDA0002718206600000014
Respectively representing position, velocity and acceleration signals from the robot, Mm0And Ms0Representing the known mass inertia matrix, Cm0And Cs0Representing a known Coriolis force/centripetal force matrix, Gm0And Gs0Representing a known gravity matrix, dmAnd dsRepresenting external interference and model error, umAnd usRepresenting a control input, τhAnd τeRepresenting an operator's operating torque or an environmental work torque;
1-2) establishing a mass-spring-damping environmental dynamics model
Figure FDA0002718206600000015
Wherein M ise,Ce,GeRepresenting an environmental parameter;
2) a sliding mode controller of a main robot is designed based on a disturbance observer, and the method specifically comprises the following steps:
2-1) designing a main-end ideal track generator as follows:
Figure FDA0002718206600000016
Figure FDA0002718206600000017
Figure FDA0002718206600000018
wherein avrg {. denotes the average value of, kfmDenotes the scale parameter, Mdm,Cdm,GdmRepresenting a planning parameter;
by mixing thetasBy inputting equation (4), the reference trajectory θ can be obtainedmr,
Figure FDA0002718206600000019
Then selecting proper Mdm,Cdm,GdmEquations (5) and (6) can obtain the ideal trajectory θmd,
Figure FDA00027182066000000110
2-2) defining the sliding surface s of the master robot controllermThe following were used:
Figure FDA00027182066000000111
wherein e ism＝θm-θmd，λm＝diag{λm1,...,λmi,...,λmw1,2, w denotes the number of degrees of freedom of the master robot;
2-3) calculating smThe first derivation of (A) is as follows:
Figure FDA0002718206600000021
2-4) designing a controller according to the step (8) to ensure the progressive stability of the main robot, and designing a controller umComprises the following steps:
Figure FDA0002718206600000022
wherein the content of the first and second substances,
Figure FDA0002718206600000023
νm＝diag{νm1,...,νmi,...,νmw}，
Figure FDA0002718206600000024
νmi0>0，
Figure FDA0002718206600000025
representing a non-linear disturbance observer;
3) the sliding mode controller of the slave robot is designed based on a disturbance observer, and specifically comprises the following steps:
3-1) design the slave-end ideal trajectory generator as follows:
Figure FDA0002718206600000026
Figure FDA0002718206600000027
Figure FDA0002718206600000028
wherein avrg {. denotes the average value of, kfsDenotes the scale parameter, Mds,Cds,GdsRepresenting a planning parameter;
by mixing thetamInputting equation (12), a reference trajectory theta can be obtainedsr,
Figure FDA0002718206600000029
Then selecting proper Mds,Cds,GdsEquations (13) and (14) can obtain the ideal trajectory θsd,
Figure FDA00027182066000000210
3-2) defining a slip form surface s from the robot controllersThe following were used:
Figure FDA00027182066000000211
wherein e iss＝θs-θsd，λs＝diag{λs1,...,λsi,...,λsw1,2, w denotes the number of degrees of freedom from the robot;
3-3) calculating ssThe first derivation of (A) is as follows:
Figure FDA00027182066000000212
3-4) designing a controller according to (16) to ensure the gradual stability of the slave robot, and designing a controller usComprises the following steps:
Figure FDA0002718206600000031
wherein the content of the first and second substances,
Figure FDA0002718206600000032
νs＝diag{νs1,...,νsi,...,νsw}，
Figure FDA0002718206600000033
Figure FDA0002718206600000034
representing a non-linear disturbance observer;
4) designing a Lyapunov function of a sliding mode controller based on a master robot and a slave robot, which specifically comprises the following steps:
4-1) designing a global Lyapunov function V to ensure the global stability of the nonlinear teleoperation system;
4-2) when | | | sm||≤β,||ssWhen | is less than or equal to β, V will converge to:
Figure FDA0002718206600000035
wherein the content of the first and second substances,
Figure FDA0002718206600000036
Figure FDA0002718206600000037
and
Figure FDA0002718206600000038
representing the observed error values of the master and slave observer.
2. The four-channel teleoperation bilateral control method based on the disturbance observer according to claim 1, wherein in the step 1-1), the dynamic model of the master-slave robot has the following characteristics:
①
Figure FDA0002718206600000039
and
Figure FDA00027182066000000310
is an oblique symmetric matrix;
②
Figure FDA00027182066000000311
③
Figure FDA00027182066000000312
3. the four-channel teleoperation bilateral control method based on the disturbance observer according to claim 1, wherein in the step 2-4), sat(s)m) A saturation function is shown that avoids buffeting for sliding mode controllers,is defined as:
Figure FDA00027182066000000313
wherein β represents a boundary layer.
4. The four-channel teleoperation bilateral control method based on the disturbance observer according to claim 1, wherein in the step 2-4),
Figure FDA00027182066000000314
represents a non-linear disturbance observer defined as:
Figure FDA00027182066000000315
wherein the content of the first and second substances,
Figure FDA00027182066000000316
Hmthe reversible matrix of the main end is expressed and can be obtained by calculation of a linear matrix inequality.
5. The four-channel teleoperation bilateral control method based on the disturbance observer according to claim 1, wherein in the step 3-4), sat(s)s) A saturation function for avoiding buffeting of a sliding mode controller is represented, defined as:
Figure FDA0002718206600000041
wherein β represents a boundary layer.
6. The four-channel teleoperation bilateral control method based on the disturbance observer according to claim 1, wherein in the step 3-4),
Figure FDA0002718206600000042
represents a non-linear disturbance observer defined as:
Figure FDA0002718206600000043
wherein the content of the first and second substances,
Figure FDA0002718206600000044
Hsthe representation is a reversible matrix from the end, and can be obtained by linear matrix inequality calculation.
7. The four-channel teleoperation bilateral control method based on the disturbance observer according to claim 1, wherein in the step 4-1), the designed global lyapunov function V is as follows:
V＝Vm+Vs+Vm0+Vs0 (20)
wherein the content of the first and second substances,
Figure FDA0002718206600000045
Figure FDA0002718206600000046
Hmrepresenting the primary invertible matrix, HsRepresenting a slave-reversible matrix.
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