CN110262256B - Multilateral self-adaptive sliding mode control method of nonlinear teleoperation system - Google Patents

Multilateral self-adaptive sliding mode control method of nonlinear teleoperation system Download PDF

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CN110262256B
CN110262256B CN201910649003.0A CN201910649003A CN110262256B CN 110262256 B CN110262256 B CN 110262256B CN 201910649003 A CN201910649003 A CN 201910649003A CN 110262256 B CN110262256 B CN 110262256B
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陈正
黄方昊
宋伟
朱世强
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Zhejiang University ZJU
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Abstract

The invention discloses a multilateral self-adaptive sliding mode control method of a nonlinear teleoperation system. The method is based on a radial basis function, estimates the non-power environment parameters of the slave-end environment dynamics, and transmits the non-power environment parameters back to the main end through a communication channel to reconstruct the environment force of the main end; aiming at the problems of nonlinearity and various uncertainties of a master robot and a slave robot, the invention designs a track generator and a nonlinear adaptive sliding mode controller based on a radial basis function network at the master end and the slave end respectively, designs an adaptive rate for training a nonlinear function containing system modeling information on line, and ensures the stability and the accurate position tracking performance of the system; aiming at the problem of signal communication among multiple robots, the control force distribution of the multiple slave robots is realized by designing a cooperative force distribution algorithm, so that the cooperative operation performance of the multiple slave robots on the operation task is improved.

Description

Multilateral self-adaptive sliding mode control method of nonlinear teleoperation system
Technical Field
The invention belongs to the field of teleoperation control, and particularly relates to a multilateral self-adaptive sliding mode control method of a nonlinear teleoperation system, which can simultaneously ensure the stability and transparency of the nonlinear teleoperation system and the cooperative operation of multiple master and slave robots.
Background
With the development of complex and fine operation tasks, teleoperation technology relying on human-computer interaction is continuously used in industrial environments, in particular to the development of multilateral teleoperation technology relying on cooperative operation of multiple master-slave robots, namely, multiple operators operate multiple master robots at master ends to realize cooperative control of multiple slave robots and complete complex or fine operation tasks, and the teleoperation technology is widely applied to the fields of space exploration, deep sea sampling, telemedicine, safety detection and the like and is widely researched as an important support technology in the application field of robots.
However, the transmission of the signal in the communication channel inevitably generates communication delay, thereby affecting the accuracy of receiving the main robot command signal from the robot and deteriorating the stability and transparency of the teleoperation system. In addition, due to the complex or fine slave-end task requirement, multiple robots with multiple degrees of freedom are often required to perform cooperative operation, such robots often have nonlinearity and various uncertainties, signal transmission in a communication channel becomes more complex due to signal communication among multiple robots, and a traditional linear teleoperation system structure based on a passive theory and a four-channel structure cannot well achieve good control performance. Therefore, the problems of the stability and transparency of the teleoperation system due to the communication delay are balanced, and the nonlinearity, various uncertainties, signal communication among multiple robots and the like exist in a plurality of master and slave robots with multiple degrees of freedom.
Disclosure of Invention
The invention provides a multilateral self-adaptive sliding mode control method of a nonlinear teleoperation system, which aims to solve the technical problems of stability, transparency, nonlinearity, various uncertainties, multi-robot cooperative operation and the like of the traditional multilateral teleoperation system.
In order to achieve the purpose, the technical scheme of the invention comprises the following specific contents:
a multilateral adaptive sliding mode control method of a nonlinear teleoperation system comprises the following steps:
and (I) establishing a dynamic model of the nonlinear multilateral teleoperation system.
And (II) designing an adaptive sliding mode controller of the slave robot based on the radial basis function neural network.
And (III) estimating the working environment and reconstructing the main-end environment based on the radial basis function.
And (IV) designing an adaptive sliding mode controller of the main robot based on the radial basis function neural network.
Compared with the prior art, the invention has the following beneficial effects:
1. based on the radial basis function, the non-power environment parameters of the slave-end environment dynamics are estimated and transmitted back to the master end through the communication channel to reconstruct the environment force of the master end, so that the transmission of power signals in the communication channel is avoided, and accurate force feedback information is provided for an operator.
2. Based on a radial basis function, a nonlinear function containing system modeling information is trained on line by designing a self-adaptive rate, so that various uncertainties existing in a master robot and a slave robot of a multilateral teleoperation system are solved.
3. By the aid of the nonlinear self-adaptive sliding mode control method based on the radial basis function neural network, the slave robot can accurately track the track signal of the master robot in real time, and when communication delay, nonlinearity and various uncertainties exist in the system, the position tracking performance of the system can be improved.
4. By designing the Lyapunov function, the boundedness of all signals in the nonlinear multilateral teleoperation system is guaranteed, and the stability of the system is further guaranteed.
5. By designing a cooperative force distribution algorithm, the control force distribution of the multiple slave robots is realized, so that the cooperative operation performance of the multiple slave robots on the operation tasks is improved.
Drawings
FIG. 1 is a multi-edge adaptive sliding mode control block diagram of a non-linear teleoperation system based on a radial basis function neural network, which is provided by the invention;
FIG. 2 is a functional block diagram of a radial basis function neural network proposed by 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:
1) establishing a dynamic model of a nonlinear multilateral teleoperation system, which specifically comprises the following steps:
1-1) establishing a dynamic model of multiple main robots and interaction between multiple auxiliary robots and the environment
Figure BDA0002134543530000021
Figure BDA0002134543530000022
Wherein the content of the first and second substances,
Figure BDA0002134543530000023
and
Figure BDA0002134543530000024
representing the ith master-slave robot position, velocity and acceleration signals,
Figure BDA0002134543530000031
indicating the end position of the ith main robot,
Figure BDA0002134543530000032
representing the position of the center of mass of the target object in the task, Dm,iAnd DsRepresenting the mass inertia matrix, Cm,iAnd CsRepresenting a Coriolis force/centripetal force matrix, Gm,iAnd GsRepresenting a gravity matrix, dm,iAnd dsRepresenting external interference and modeling error, um,iAnd usRepresenting a control input, Fh,iIndicates the operation force of the ith operator, FeDenotes the environmental forces from the robot and the work task, i 1, 2.
The above system has the following characteristics:
①
Figure BDA0002134543530000033
and
Figure BDA0002134543530000034
is an oblique symmetric matrix;
② the partial kinetic equations in equations (1) and (2) can be written in the form of the following linear equations:
Figure BDA0002134543530000035
Figure BDA0002134543530000036
wherein, Wm,iAnd WsAnd H represents a neural network matrix.
1-2) establishing a dynamic model of a work environment
Figure BDA0002134543530000037
Wherein, WeRepresenting unknown slave-end environment parameters.
2) The self-adaptive sliding mode controller of the slave robot is designed based on a radial basis function neural network, and specifically comprises the following steps:
2-1) position signal x of the main robot due to communication delay inevitably generated by signal transmission in the communication channelm,i(t) transmission via a communication channelPosition signal x with time delay obtained from slave endm,i(t-t (t)), the trajectory generator from the robot is designed as follows:
Figure BDA0002134543530000038
averaging position signals by input time delay
Figure BDA0002134543530000039
Outputting ideal trajectory signals for tracking from a robot
Figure BDA00021345435300000310
Wherein lo,iAnd T (t) is communication time delay of the system.
2-2) defining the slip form surface s of the slave robotsThe following were used:
Figure BDA00021345435300000311
wherein e iss＝xsd,o-xs,oIndicating the tracking error from the robot to the target object,
Figure BDA0002134543530000041
2-3) substituting the tracking error into (5) to obtain
Figure BDA0002134543530000042
Therefore, the temperature of the molten metal is controlled,
Figure BDA0002134543530000043
wherein the content of the first and second substances,
Figure BDA0002134543530000044
2-4) designing a slave controller according to the step (6), ensuring the stability of a slave terminal system, and designing a controller usComprises the following steps:
us＝σs+ksvss-Fe-κsNsat(ss) (7)
wherein k issv>0，ksN>0。
In the slave controller (7), sat(s)s) A sliding mode saturation function to avoid buffeting is presented which can be defined as:
Figure BDA0002134543530000045
wherein μ represents a boundary layer;
σsrepresenting a method for estimating a non-linear function zsMay be defined as:
Figure BDA0002134543530000046
wherein the content of the first and second substances,
Figure BDA0002134543530000047
in order to adapt the parameters to the application,
Figure BDA0002134543530000048
2-5) design of the Lyapunov function V of the slave terminal systemsComprises the following steps:
Figure BDA0002134543530000049
wherein the content of the first and second substances,
Figure BDA00021345435300000410
representing the estimation error of the radial basis function.
Based on Lyapunov function VsDesign WsThe self-adaptive rate is as follows:
Figure BDA00021345435300000411
wherein k iss>0,s>0。
2-6) according to the slave controller (7), for obtaining a control input u for each slave robots,iThe collaborative force allocation algorithm is designed as follows:
Figure BDA0002134543530000051
wherein the content of the first and second substances,
Figure BDA0002134543530000052
q represents the weight factor of the different job requirements, Fs *Representing internal forces of the respective slave robot and target object, and NsFs *＝0。
3) The method comprises the following steps of (1) estimating a working environment and reconstructing a main terminal environment based on a radial basis function, specifically:
3-1) writing the dynamic model (3) of the slave end working environment into the form of a radial basis function, then:
Figure BDA0002134543530000053
wherein x isewAnd
Figure BDA0002134543530000054
and (4) correlating.
3-2) definition of
Figure BDA0002134543530000055
For optimal estimation of the parameters of the environment, ΩeAnd Ωe0Respectively represent xewAnd WeThe online estimation of the slave-end working environment can be realized through the neural network tool box of MATLAB.
3-3) due to the existence of the communication time delay T (t), in order to avoid the influence of the transmission of the power signal in the communication channel on the stability of the multilateral teleoperation system, the non-power environmental parameter estimation value of the slave end
Figure BDA0002134543530000056
And transmitting the environment reconstruction force to the main end, so that the reconstruction environment force of the main end is:
Figure BDA0002134543530000057
wherein x isemwAnd
Figure BDA0002134543530000058
and (4) correlating.
4) The self-adaptive sliding mode controller of the main robot is designed based on a radial basis function neural network, and specifically comprises the following steps:
4-1) definition of xmd,iIs an ideal track signal of the main robot and meets the following conditions:
Figure BDA0002134543530000059
Figure BDA00021345435300000510
wherein, i is 1, 2., n,
Figure BDA00021345435300000511
Dd,Cd,Gdrepresenting the impedance coefficient of the main robot. By selecting proper impedance coefficients, (15) - (16) can generate a passive main robot ideal track xmd,i。
4-2) defining the slip form surface s of the main robotm,iThe following were used:
Figure BDA00021345435300000512
wherein e ism,i＝xmd,i-xm,iIndicating the tracking error of the main robot,
Figure BDA0002134543530000061
4-3) substituting the tracking error into (17) to obtain
Figure BDA0002134543530000062
Therefore, the temperature of the molten metal is controlled,
Figure BDA0002134543530000063
wherein the content of the first and second substances,
Figure BDA0002134543530000064
4-4) designing a main controller according to the (18) to ensure the stability of the main end subsystem, and designing a controller um,iComprises the following steps:
um,i＝σm,i+kmv,ism,i-Fh,i-κmN,isat(sm,i) (19)
wherein k ismv,i>0，kmN,i>0。
In the slave controller (19), sat(s)m) A sliding mode saturation function to avoid buffeting is presented which can be defined as:
Figure BDA0002134543530000065
wherein μ represents a boundary layer;
σm,irepresenting a method for estimating a non-linear function zm,iMay be defined as:
Figure BDA0002134543530000066
wherein the content of the first and second substances,
Figure BDA0002134543530000067
in order to adapt the parameters to the application,
Figure BDA0002134543530000068
4-5) designing Lyapunov function V of main terminal systemm,iComprises the following steps:
Figure BDA0002134543530000069
wherein the content of the first and second substances,
Figure BDA00021345435300000610
representing the estimation error of the radial basis function.
Based on Lyapunov function Vm,iDesign Wm,iThe self-adaptive rate is as follows:
Figure BDA00021345435300000611
wherein k ism,i>0,m,i>0。

Claims (7)

1. A multilateral adaptive sliding mode control method of a nonlinear teleoperation system is characterized by comprising the following steps:
1) establishing a dynamic model of a nonlinear multilateral teleoperation system, which specifically comprises the following steps:
1-1) establishing a dynamic model of multiple main robots and interaction between multiple auxiliary robots and the environment
Figure FDA0002590738560000011
Figure FDA0002590738560000012
Wherein q ism,i,
Figure FDA0002590738560000013
And q iss,i,
Figure FDA0002590738560000014
Representing the ith master-slave robot position, velocity and acceleration signals, xm,i,
Figure FDA0002590738560000015
Representing the terminal position, terminal velocity and terminal acceleration signals, x, of the ith main robots,o,
Figure FDA0002590738560000016
Representing the position of the center of mass, the speed of the center of mass and the acceleration of the center of mass of the target object in the task, Dm,iAnd DsRepresenting the mass inertia matrix, Cm,iAnd CsRepresenting a Coriolis force/centripetal force matrix, Gm,iAnd GsRepresenting a gravity matrix, dm,iAnd dsRepresenting external interference and modeling error, um,iAnd usRepresenting a control input, Fh,iIndicates the operation force of the ith operator, FeRepresents the environmental forces from the robot and the work task, i 1, 2.
The above system has the following characteristics:
①
Figure FDA0002590738560000017
and
Figure FDA0002590738560000018
is an oblique symmetric matrix;
② the partial kinetic equations in equations (1) and (2) can be written in the form of the following linear equations:
Figure FDA0002590738560000019
Figure FDA00025907385600000110
wherein, Wm,iAnd WsRepresenting uncertain parameters of a master robot and a slave robot, and H represents a neural network matrix;
1-2) establishing a dynamic model of a work environment
Figure FDA00025907385600000111
Wherein, WeRepresenting unknown slave-end environment parameters;
2) the self-adaptive sliding mode controller of the slave robot is designed based on a radial basis function neural network, and specifically comprises the following steps:
2-1) designing a trajectory generator of the slave robot to output ideal trajectory, ideal velocity and acceleration signals x for tracking from the robotsd,o(t),
Figure FDA00025907385600000112
2-2) defining the slip form surface s of the slave robotsThe following were used:
Figure FDA00025907385600000113
wherein e iss＝xsd，o-xs，oIndicating the tracking error from the robot to the target object,
Figure FDA0002590738560000021
expressing the sliding mode surface adjusting parameters;
2-3) substituting the tracking error into (5) to obtain
Figure FDA0002590738560000022
Therefore, the temperature of the molten metal is controlled,
Figure FDA0002590738560000023
wherein the content of the first and second substances,
Figure FDA0002590738560000024
representing unknown system dynamics parameters of the slave robot;
2-4) designing a slave controller according to the step (6), ensuring the stability of a slave terminal system, and designing a controller usComprises the following steps:
us＝σs+ksvss-Fe-κsNsat(ss) (7)
wherein k issv>0 and ksN>0 represents a performance tuning parameter, σ, from the controller performancesRepresenting a method for estimating a non-linear function zsA radial basis function of;
2-5) design of the Lyapunov function V of the slave terminal systemsComprises the following steps:
Figure FDA0002590738560000025
wherein the content of the first and second substances,
Figure FDA0002590738560000026
representing an estimation error of the radial basis function;
2-6) based on the Lyapunov function VsDesign WsThe self-adaptive rate is as follows:
Figure FDA0002590738560000027
wherein k iss>0 ands>0 denotes a learning speed adjustment parameter of the adaptation rate,
Figure FDA0002590738560000028
representing the radial basis function σsThe input of (1);
2-7) according to the slave controller (7), for obtaining a control input u for each slave robots,iDesigning a cooperation force distribution algorithm;
3) the method comprises the following steps of (1) estimating a working environment and reconstructing a main terminal environment based on a radial basis function, specifically:
3-1) writing the dynamic model (3) of the slave end working environment into the form of a radial basis function, then:
Figure FDA0002590738560000029
wherein，xewRepresents the input of a neural network function, and is associated with xs,o,
Figure FDA00025907385600000210
Correlation;
3-2) definition of
Figure FDA00025907385600000211
For optimal estimation of the parameters of the environment, ΩeAnd Ωe0Respectively represent xewAnd WeThe bounded set of (2) realizes online estimation of the slave-end working environment through a neural network toolbox of MATLAB;
3-3) due to the existence of the communication time delay T (t), in order to avoid the influence of the transmission of the power signal in the communication channel on the stability of the multilateral teleoperation system, the non-power environmental parameter estimation value of the slave end
Figure FDA0002590738560000031
And transmitting the environment reconstruction force to the main end, so that the reconstruction environment force of the main end is:
Figure FDA0002590738560000032
wherein x isemwRepresents the input of a neural network function, and is associated with xmd,i,
Figure FDA0002590738560000033
Correlation;
4) the self-adaptive sliding mode controller of the main robot is designed based on a radial basis function neural network, and specifically comprises the following steps:
4-1) definition of xmd,iIs an ideal track signal of the main robot and meets the following conditions:
Figure FDA0002590738560000034
Figure FDA0002590738560000035
wherein, i is 1, 2., n,
Figure FDA0002590738560000036
Dd,Cd,Gdrepresenting the impedance coefficient of the main robot; by selecting impedance coefficients, (15) - (16) can generate a passive main robot ideal track xmd,i；
4-2) defining the slip form surface s of the main robotm,iThe following were used:
Figure FDA0002590738560000037
wherein e ism,i＝xmd,i-xm,iIndicating the tracking error of the main robot,
Figure FDA0002590738560000038
expressing the sliding mode surface adjusting parameters;
4-3) substituting the tracking error into (17) to obtain
Figure FDA0002590738560000039
Therefore, the temperature of the molten metal is controlled,
Figure FDA00025907385600000310
wherein the content of the first and second substances,
Figure FDA00025907385600000311
representing unknown system dynamics parameters of the master robot;
4-4) designing a main controller according to the (18) to ensure the stability of the main end subsystem, and designing a controller um,iComprises the following steps:
um,i＝σm,i+kmv,ism,i-Fh,i-κmN,isat(sm,i) (19)
wherein k ismv,i>0 and kmN,i>0 indicates performance adjustment of the master controller performanceParameter, σm,iRepresenting a method for estimating a non-linear function zm,iA radial basis function of;
4-5) designing Lyapunov function V of main terminal systemm,iComprises the following steps:
Figure FDA0002590738560000041
wherein the content of the first and second substances,
Figure FDA0002590738560000042
representing an estimation error of the radial basis function;
4-6) based on the Lyapunov function Vm,iDesign Wm,iThe self-adaptive rate is as follows:
Figure FDA0002590738560000043
wherein k ism,i>0 andm,i>0 denotes a learning speed adjustment parameter of the adaptation rate,
Figure FDA0002590738560000044
representing the radial basis function σm,iIs input.
2. The multilateral adaptive sliding mode control method according to claim 1, wherein in step 2-1), the position signal x of the main robot is generated due to the communication delay inevitably generated by the transmission of the signal in the communication channelm,i(t) transmitting the time-delayed position signal x to the slave end via a communication channelm,i(t-t (t)), the trajectory generator from the robot is designed as follows:
Figure FDA0002590738560000045
wherein, tfRepresents a time constant; averaging position signals by input time delay
Figure FDA0002590738560000046
Outputting ideal trajectory, ideal velocity and ideal acceleration signals x for tracking from the robotsd,o(t),
Figure FDA0002590738560000047
Wherein lo，iAnd T (t) is communication time delay of the system.
3. The multilateral adaptive sliding mode control method according to claim 1, wherein in the step 2-4), sat(s)s) A sliding mode saturation function to avoid buffeting is expressed, defined as:
Figure FDA0002590738560000048
where μ denotes the boundary layer, sgn(s)s) Representing a symbolic function.
4. The multilateral adaptive sliding mode control method according to claim 1, wherein σ in step 2-4), σsIs defined as:
Figure FDA0002590738560000049
wherein the content of the first and second substances,
Figure FDA0002590738560000051
is an adaptive parameter.
5. Multilateral adaptive sliding mode control method according to claim 1, characterized in that in step 2-7), for obtaining the control input u of each slave robot according to the slave controller (7)s,iThe collaborative force allocation algorithm is designed as follows:
Figure FDA0002590738560000052
wherein the content of the first and second substances,
Figure FDA0002590738560000053
represents a distribution coefficient, and
Figure FDA0002590738560000054
Θ represents the weighting factors for different job requirements,
Figure FDA0002590738560000055
represents the internal forces of each slave robot and the target object, and
Figure FDA0002590738560000056
6. the multilateral adaptive sliding mode control method according to claim 1, wherein in step 4-4), sat(s)m,i) A sliding mode saturation function to avoid buffeting is expressed, defined as:
Figure FDA0002590738560000057
where μ denotes the boundary layer, sgn(s)m,i) Representing a symbolic function.
7. The multilateral adaptive sliding mode control method according to claim 1, wherein σ in step 4-4), σm,iIs defined as:
Figure FDA0002590738560000058
wherein the content of the first and second substances,
Figure FDA0002590738560000059
is an adaptive parameter.
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