CN110253584B - Remote control-oriented discrete time-varying boundary bilateral control method - Google Patents

Remote control-oriented discrete time-varying boundary bilateral control method Download PDF

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CN110253584B
CN110253584B CN201910592144.3A CN201910592144A CN110253584B CN 110253584 B CN110253584 B CN 110253584B CN 201910592144 A CN201910592144 A CN 201910592144A CN 110253584 B CN110253584 B CN 110253584B
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bilateral
discrete time
joint angle
bilateral control
boundary
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CN110253584A (en
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马志强
黄攀峰
刘正雄
董刚奇
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Northwestern Polytechnical University
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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

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  • Automation & Control Theory (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
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Abstract

The invention belongs to the field of mechanical arm dynamics, and relates to a discrete time boundary bilateral control method facing remote control. The invention realizes the direct application of the state-bounded bilateral control method in a computer system, ensures bilateral synchronization and can also ensure the stable precision of the system through reasonable selection of parameters.

Description

Remote control-oriented discrete time-varying boundary bilateral control method
Technical Field
The invention belongs to the field of mechanical arm dynamics, and relates to a discrete time boundary bilateral control method for remote control.
Background
The remote control technology can support the robot to realize the migration of human behaviors in time and space under the condition of danger difficult to involve by human or cross-domain situation, for example, the robot can execute actions such as taking over and controlling task targets under underwater, toxic, nucleated and space environments. In consideration of the synchronization problem of the operation of the master end and the slave end in remote control, a high-synchronization finite state control method needs to be designed, so that the synchronization precision of the remote control is improved, and the reliability of the operation of the slave end is ensured. The currently and generally adopted method involves state-bounded, but a discrete time method suitable for an actual physical system is not available, the influence of sampling time on the control effect cannot be effectively solved, and then the bilateral control precision is reduced.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a discrete time variable boundary bilateral control method for remote control, which is used for realizing the direct application of a state-bounded bilateral control method in a computer system, so that the stability and the precision of the system can be ensured by reasonably selecting parameters while the bilateral synchronization is ensured.
Technical scheme
A discrete time boundary bilateral control method facing remote control is characterized by comprising the following steps:
step 1: discrete time remote control bilateral control system:
Figure BDA0002116418680000011
wherein, subscripts m and s respectively refer to a master end mechanical arm and a slave end mechanical arm which are remotely controlled, for convenience of description, i is equal to m, s is used for describing a subsequent variable, k represents a sampling time,
Figure BDA0002116418680000012
the joint cross-vector is represented by a joint cross-vector,
Figure BDA0002116418680000013
a matrix of positive definite moments of inertia is represented,
Figure BDA0002116418680000021
a matrix of the coriolis forces is represented,
Figure BDA0002116418680000022
is an unknown but bounded external disturbance,
Figure BDA0002116418680000023
representing the input force of a human operator,
Figure BDA0002116418680000024
which is representative of the environmental force,
Figure BDA0002116418680000025
representing the torque output by the mechanical arm;
converting the bilateral control model to obtain the following differential expression:
qi(k+1)＝qi(k)+δΔqi(k)
Δqi(k+1)＝Δqi(k)+δfi(k)+δgi(k)ui(k)+δdi(k)
wherein δ represents the sampling interval of the discrete time system, corresponding to the bilateral control model, obtaining:
Figure BDA0002116418680000026
Figure BDA0002116418680000027
di(k)＝-Bi(Δqi(k))
wherein, Fi(k) Respectively corresponding to the environment force and the input of an operator according to the situation;
step 2: for a predetermined state boundary, in combination with the value characteristics of the state deviation, the switching signals of the control law are designed:
synchronization error:
Figure BDA0002116418680000028
wherein the error of the master end is em(k) The slave error is es(k)，TmAnd TsRespectively, the multiplying power of the delay time of the master end and the slave end relative to the sampling interval. The joint angle of the bilateral robot arm is limited to
Figure BDA0002116418680000029
Wherein q isij(k) The angular position representing the jth joint angle of the master or slave end robot arm,γ ij(k) the lower bound of the change in joint angle,
Figure BDA00021164186800000210
an upper bound for joint angle variation;
defining desired angular positions for respective joint angles
Figure BDA00021164186800000211
Also satisfies
Figure BDA00021164186800000212
Two positive variables are defined, satisfy
Figure BDA00021164186800000213
Defining bilateral synchronization errors
Figure BDA00021164186800000214
Defining a switching signal
Figure BDA0002116418680000031
Auxiliary symbols as defined below
Figure BDA0002116418680000032
And step 3: designing a discrete time bilateral control law, and controlling according to the discrete time bilateral control law:
ui(k)＝vi(k)+wi(k)
Figure BDA0002116418680000033
Figure BDA0002116418680000034
wherein, thetaiAnd
Figure BDA0002116418680000035
is a diagonal matrix with all non-zero elements being positive
Figure BDA0002116418680000036
The absolute value of the difference between the limit boundary of the state variable and the initial value should not be less than 1, thetaiChosen as the inverse of the sampling period.
Advantageous effects
The invention provides a discrete time boundary bilateral control method facing remote control, which is characterized in that a discrete time remote control bilateral control system is established, and for a preset state boundary, a switching signal of a control law is designed by combining the value characteristic of state deviation, and a discrete time bilateral control law is designed. The invention realizes the direct application of the state-bounded bilateral control method in a computer system, ensures bilateral synchronization and can also ensure the stable precision of the system through reasonable selection of parameters.
Detailed Description
The invention will now be further described with reference to the examples:
in order to solve the technical problems, the invention is realized by the following technical scheme:
a remote control-oriented discrete time reinforced change boundary bilateral control method comprises the following steps:
a) consider a discrete-time telemanipulation bilateral control system:
Figure BDA0002116418680000041
wherein, subscripts m and s respectively refer to a master end mechanical arm and a slave end mechanical arm which are remotely controlled, for convenience of description, i is equal to m, s is used for describing a subsequent variable, k represents a sampling time,
Figure BDA0002116418680000042
the joint cross-vector is represented by a joint cross-vector,
Figure BDA0002116418680000043
a matrix of positive definite moments of inertia is represented,
Figure BDA0002116418680000044
a matrix of the coriolis forces is represented,
Figure BDA0002116418680000045
is an unknown but bounded external disturbance,
Figure BDA0002116418680000046
representing the input force of a human operator,
Figure BDA0002116418680000047
which is representative of the environmental force,
Figure BDA0002116418680000048
indicating mechanical armThe torque of the output.
Converting the bilateral control model to obtain the following differential expression:
qi(k+1)＝qi(k)+δΔqi(k)
Δqi(k+1)＝Δqi(k)+δfi(k)+δgi(k)ui(k)+δdi(k)
wherein delta represents the sampling interval of the discrete time system, corresponding to the bilateral control model, and is easy to obtain
Figure BDA0002116418680000049
Figure BDA00021164186800000410
di(k)＝-Bi(Δqi(k))
Wherein, Fi(k) Respectively corresponding to the environment force and the input of an operator according to the situation;
b) for a predetermined state boundary, in combination with the value characteristics of the state deviation, the switching signals of the control law are designed:
designing a synchronization error:
em(k)＝qm(k)-qs(k-Ts)
es(k)＝qs(k)-qm(k-Tm)
wherein the error of the master end is em(k) The slave error is es(k)，TmAnd TsRespectively, the multiplying power of the delay time of the master end and the slave end relative to the sampling interval. The joint angle of the bilateral robot arm is limited to
Figure BDA00021164186800000411
Wherein q isij(k) An angular position representing the jth joint angle of the master or slave end robot arm, and similarly, a desired angular position of each joint angle
Figure BDA0002116418680000051
Also satisfies
Figure BDA0002116418680000052
Two positive variables are defined, satisfy
Figure BDA0002116418680000053
Figure BDA0002116418680000054
Defining bilateral synchronization errors
Figure BDA0002116418680000055
Defining a switching signal
Figure BDA0002116418680000056
Auxiliary symbols as defined below
Figure BDA0002116418680000057
Figure BDA0002116418680000058
ξij(k)＝hij(k)ηij(k)+(1-hij(k))ζij(k)
c) Designing a discrete time bilateral control law;
ui(k)＝vi(k)+wi(k)
Figure BDA0002116418680000059
Figure BDA00021164186800000510
wherein, thetaiAnd
Figure BDA00021164186800000511
is a diagonal matrix, all non-zero elements are positive,
Figure BDA00021164186800000512
in order to ensure the synchronization stability of the bilateral system, the absolute value of the difference between the limit boundary of the state variable and the initial value should not be less than 1, thetaiIt is proposed to choose the inverse of the sampling period.

Claims (1)

1. A discrete time boundary bilateral control method facing remote control is characterized by comprising the following steps:
step 1: discrete time remote control bilateral control system:
Figure FDA0003424104990000011
wherein, subscripts m and s respectively refer to a master end mechanical arm and a slave end mechanical arm which are remotely controlled, for convenience of description, i is equal to m, s is used for describing a subsequent variable, k represents a sampling time,
Figure FDA0003424104990000012
a vector of the joint angle is represented,
Figure FDA0003424104990000013
a matrix of positive definite moments of inertia is represented,
Figure FDA0003424104990000014
a matrix of the coriolis forces is represented,
Figure FDA0003424104990000015
is an unknown but bounded external disturbance,
Figure FDA0003424104990000016
representing the input force of a human operator,
Figure FDA0003424104990000017
which is representative of the environmental force,
Figure FDA0003424104990000018
representing the torque output by the mechanical arm;
converting the bilateral control model to obtain the following differential expression:
qi(k+1)＝qi(k)+δ△qi(k)
△qi(k+1)＝△qi(k)+δfi(k)+δgi(k)ui(k)+δdi(k)
wherein δ represents the sampling interval of the discrete time system, corresponding to the bilateral control model, obtaining:
Figure FDA0003424104990000019
Figure FDA00034241049900000110
di(k)＝-Bi(△qi(k))
wherein, Fi(k) Respectively corresponding to the environment force and the input of an operator according to the situation;
step 2: for a predetermined state boundary, in combination with the value characteristics of the state deviation, the switching signals of the control law are designed:
synchronization error:
Figure FDA00034241049900000111
wherein the error of the master end is em(k) The slave error is es(k)，TmAnd TsRespectively representing the multiplying power of the delay time of the master end and the delay time of the slave end relative to the sampling interval; the joint angle of the bilateral robot arm is limited to
Figure FDA0003424104990000021
Wherein q isij(k) The angular position representing the jth joint angle of the master or slave end robot arm,γ ij(k) the lower bound of the change in joint angle,
Figure FDA0003424104990000022
an upper bound for joint angle variation;
defining desired angular positions for respective joint angles
Figure FDA0003424104990000023
Also satisfies
Figure FDA0003424104990000024
Two positive variables are defined, satisfy
Figure FDA0003424104990000025
Defining bilateral synchronization errors
Figure FDA0003424104990000026
Defining a switching signal
Figure FDA0003424104990000027
Auxiliary symbols as defined below
Figure FDA0003424104990000028
And step 3: designing a discrete time bilateral control law, and controlling according to the discrete time bilateral control law:
ui(k)＝vi(k)+wi(k)
Figure FDA0003424104990000029
Figure FDA00034241049900000210
wherein, thetaiAnd
Figure FDA00034241049900000211
is a diagonal matrix with all non-zero elements being positive
Figure FDA00034241049900000212
The absolute value of the difference between the limit boundary of the state variable and the initial value should not be less than 1, thetaiChosen as the inverse of the sampling period.
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Citations (4)

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Publication number Priority date Publication date Assignee Title
JP2002318602A (en) * 2001-02-19 2002-10-31 Komatsu Ltd Device and method for controlling discrete time sliding mode for process system having dead time
CN107422639A (en) * 2017-07-13 2017-12-01 西北工业大学 A kind of bilateral teleoperation control method based on time delay estimadon
CN108646569A (en) * 2018-07-09 2018-10-12 燕山大学 The control method of remote control system under discrete-time state
CN108803344A (en) * 2018-07-25 2018-11-13 西北工业大学 A kind of symmetrical forecast Control Algorithm of robot bilateral teleoperation based on Mode-switch

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002318602A (en) * 2001-02-19 2002-10-31 Komatsu Ltd Device and method for controlling discrete time sliding mode for process system having dead time
CN107422639A (en) * 2017-07-13 2017-12-01 西北工业大学 A kind of bilateral teleoperation control method based on time delay estimadon
CN108646569A (en) * 2018-07-09 2018-10-12 燕山大学 The control method of remote control system under discrete-time state
CN108803344A (en) * 2018-07-25 2018-11-13 西北工业大学 A kind of symmetrical forecast Control Algorithm of robot bilateral teleoperation based on Mode-switch

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
一种基于共享控制的双臂协同遥操作控制方法;黄攀峰 等;《宇航学报》;20180131;104-110 *

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