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CN110253584B - A Discrete Time Variable Boundary Bilateral Control Method for Remote Control - Google Patents

A Discrete Time Variable Boundary Bilateral Control Method for Remote Control 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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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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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

一种面向远程操控的离散时间变边界双边控制方法A Discrete Time Variable Boundary Bilateral Control Method for Remote Control

技术领域technical field

本发明属于机械臂动力学领域，涉及一种面向远程操控的离散时间变边界双边控制方法。The invention belongs to the field of mechanical arm dynamics, and relates to a remote control-oriented discrete-time variable boundary bilateral control method.

背景技术Background technique

远程操控技术能够支持机器人在人类难以涉足的危险或者跨域情景下实现人类行为在时空上的迁移，如可在水下、有毒、有核及空间环境下执行对任务目标的接管和操控等动作。考虑到远程操控中主端和从端操作的同步问题，需要设计高同步的有限状态控制方法，一方面提升远程操控的同步精度，一方面保证从端操作的可靠性。当前普遍采用的方法有涉及状态有界，然而没有适用于实际物理系统的离散时间方法，无法有效化解采样时间对控制效果的影响，继而降低了双边控制精度。Remote control technology can support robots to realize the migration of human behavior in time and space in dangerous or cross-domain scenarios that are difficult for humans to enter, such as taking over and controlling mission targets in underwater, toxic, nuclear and space environments. . Considering the synchronization problem of master and slave operations in remote control, it is necessary to design a high-synchronization finite state control method to improve the synchronization accuracy of remote control and ensure the reliability of slave operations. The currently commonly used methods involve state bounded, but there is no discrete time method suitable for actual physical systems, which cannot effectively resolve the influence of sampling time on the control effect, thereby reducing the bilateral control accuracy.

发明内容SUMMARY OF THE INVENTION

要解决的技术问题technical problem to be solved

为了避免现有技术的不足之处，本发明提出一种面向远程操控的离散时间变边界双边控制方法使用该方法实现状态有界的双边控制方法在计算机系统中的直接应用，保证双边同步的同时，通过参数的合理选取还能确保系统的稳定精度。In order to avoid the deficiencies of the prior art, the present invention proposes a remote control-oriented discrete-time variable-boundary bilateral control method. This method is used to realize the direct application of the state-bounded bilateral control method in a computer system, and to ensure bilateral synchronization at the same time. , and the reasonable selection of parameters can also ensure the stability and accuracy of the system.

技术方案Technical solutions

一种面向远程操控的离散时间变边界双边控制方法，其特征在于步骤如下：A discrete-time variable boundary bilateral control method for remote control, characterized in that the steps are as follows:

步骤1：离散时间远程操控双边控制系统：Step 1: Discrete time remote control of bilateral control system:

Figure BDA0002116418680000011
Figure BDA0002116418680000011

其中，下标m和s分别指代远程操控的主端和从端机械臂，为了方便说明，用i＝m，s说明后续变量，k表示采样时刻，

Figure BDA0002116418680000012
表示关节交向量，
Figure BDA0002116418680000013
表示正定惯量矩阵，
Figure BDA0002116418680000021
表示科氏力矩阵，
Figure BDA0002116418680000022
是未知但有界的外部扰动，
Figure BDA0002116418680000023
表示人类操作人员的输入力，
Figure BDA0002116418680000024
表示环境力，
Figure BDA0002116418680000025
表示机械臂输出的力矩；Among them, the subscripts m and s refer to the master and slave manipulators of the remote control respectively. For the convenience of description, i=m, s is used to describe the subsequent variables, k is the sampling time,
Figure BDA0002116418680000012
represents the joint intersection vector,
Figure BDA0002116418680000013
represents the positive definite inertia matrix,
Figure BDA0002116418680000021
represents the Coriolis force matrix,
Figure BDA0002116418680000022
is an unknown but bounded external disturbance,
Figure BDA0002116418680000023
represents the input force of the human operator,
Figure BDA0002116418680000024
represents the environmental force,
Figure BDA0002116418680000025
Indicates the torque output by the robotic arm;

将双边控制模型进行转换，获得如下的差分表达式：Transform the bilateral control model to obtain the following differential expression:

qi(k+1)＝qi(k)+δΔqi(k)q i (k+1)=q i (k)+δΔq i (k)

Δqi(k+1)＝Δqi(k)+δfi(k)+δgi(k)ui(k)+δdi(k)Δq i (k+1)=Δq i (k)+δf i (k)+δg i (k)u i (k)+δd i (k)

其中δ表示离散时间系统的采样间隔，对应双边控制模型，获得：where δ represents the sampling interval of the discrete-time system, corresponding to the bilateral control model, to obtain:

Figure BDA0002116418680000026
Figure BDA0002116418680000026

Figure BDA0002116418680000027
Figure BDA0002116418680000027

di(k)＝-Bi(Δqi(k))d i (k)=-B i (Δq i (k))

其中，Fi(k)依情况，分别对应环境力与操作人员的输入；Among them, F i (k) corresponds to the environmental force and the operator's input according to the situation;

步骤2：对于预定的状态边界，结合状态偏差的值特征，设计控制律的切换信号：Step 2: For the predetermined state boundary, design the switching signal of the control law in combination with the value characteristics of the state deviation:

同步误差：

Figure BDA0002116418680000028
Synchronization error:
Figure BDA0002116418680000028

其中，主端误差为em(k)，从端误差为es(k)，Tm和Ts分别表示主端和从端的延迟时间相对于采样间隔的倍率。双边机械臂的关节角限制为

Figure BDA0002116418680000029
其中qij(k)表示主端或者从端机械臂的第j个关节角的角位置，γ ij(k)关节角变化的下界，
Figure BDA00021164186800000210
关节角变化的上界；Among them, the master-side error is em ( k ), the slave-side error is es ( k ), and T m and T s represent the multiples of the delay time of the master and slave ends relative to the sampling interval, respectively. The joint angle of the bilateral manipulator is limited to
Figure BDA0002116418680000029
where q ij (k) represents the angular position of the jth joint angle of the master or slave arm, γ ij (k) is the lower bound of the joint angle change,
Figure BDA00021164186800000210
The upper bound of the joint angle change;

定义各个关节角的期望角位置

Figure BDA00021164186800000211
同样满足
Figure BDA00021164186800000212
Define the desired angular position for each joint angle
Figure BDA00021164186800000211
also satisfied
Figure BDA00021164186800000212

定义两个正数变量，满足

Figure BDA00021164186800000213
Define two positive variables such that
Figure BDA00021164186800000213

定义双边同步误差

Figure BDA00021164186800000214
Defining Bilateral Synchronization Error
Figure BDA00021164186800000214

定义切换信号

Figure BDA0002116418680000031
Define the toggle signal
Figure BDA0002116418680000031

定义如下的辅助符号

Figure BDA0002116418680000032
Auxiliary symbols are defined as follows
Figure BDA0002116418680000032

步骤3：设计离散时间双边控制律，并以此进行控制：Step 3: Design a discrete-time bilateral control law and control it accordingly:

ui(k)＝vi(k)+wi(k)u i (k)=vi (k)+ wi ( k)

Figure BDA0002116418680000033
Figure BDA0002116418680000033

Figure BDA0002116418680000034
Figure BDA0002116418680000034

其中，θi和

Figure BDA0002116418680000035
是对角矩阵，所有非零元素都为正where θi and
Figure BDA0002116418680000035
is a diagonal matrix, all nonzero elements are positive

Figure BDA0002116418680000036
Figure BDA0002116418680000036

状态变量的限制边界与初始值的差的绝对值应不小于1，θi选择为采样周期的倒数。The absolute value of the difference between the limit boundary of the state variable and the initial value should not be less than 1, and θ i is selected as the reciprocal of the sampling period.

有益效果beneficial effect

本发明提出的一种面向远程操控的离散时间变边界双边控制方法，建立离散时间远程操控双边控制系统，对于预定的状态边界，结合状态偏差的值特征，设计控制律的切换信号，设计离散时间双边控制律。本发明实现状态有界的双边控制方法在计算机系统中的直接应用，保证双边同步的同时，通过参数的合理选取还能确保系统的稳定精度。The present invention proposes a remote control-oriented discrete-time variable boundary bilateral control method. A discrete-time remote-control bilateral control system is established. For a predetermined state boundary, combined with the value characteristics of the state deviation, the switching signal of the control law is designed, and the discrete-time control system is designed. Bilateral control law. The invention realizes the direct application of the state-bounded bilateral control method in the computer system, ensures the bilateral synchronization, and also ensures the stable precision of the system through the reasonable selection of parameters.

具体实施方式Detailed ways

现结合实施例对本发明作进一步描述：Now in conjunction with embodiment, the present invention will be further described:

为了解决上述存在的技术问题，本发明是通过以下技术方案实现的：In order to solve the above-mentioned technical problems, the present invention is achieved through the following technical solutions:

一种面向远程操控的离散时间强化变化边界双边控制方法，其步骤包括：A discrete-time enhanced-change boundary bilateral control method oriented to remote control, the steps of which include:

a)考虑离散时间远程操控双边控制系统：a) Consider a discrete-time remote control bilateral control system:

Figure BDA0002116418680000041
Figure BDA0002116418680000041

其中，下标m和s分别指代远程操控的主端和从端机械臂，为了方便说明，用i＝m，s说明后续变量，k表示采样时刻，

Figure BDA0002116418680000042
表示关节交向量，
Figure BDA0002116418680000043
表示正定惯量矩阵，
Figure BDA0002116418680000044
表示科氏力矩阵，
Figure BDA0002116418680000045
是未知但有界的外部扰动，
Figure BDA0002116418680000046
表示人类操作人员的输入力，
Figure BDA0002116418680000047
表示环境力，
Figure BDA0002116418680000048
表示机械臂输出的力矩。Among them, the subscripts m and s refer to the master and slave manipulators of the remote control respectively. For the convenience of description, i=m, s is used to describe the subsequent variables, k is the sampling time,
Figure BDA0002116418680000042
represents the joint intersection vector,
Figure BDA0002116418680000043
represents the positive definite inertia matrix,
Figure BDA0002116418680000044
represents the Coriolis force matrix,
Figure BDA0002116418680000045
is an unknown but bounded external disturbance,
Figure BDA0002116418680000046
represents the input force of the human operator,
Figure BDA0002116418680000047
represents the environmental force,
Figure BDA0002116418680000048
Indicates the torque output by the robotic arm.

将双边控制模型进行转换，获得如下的差分表达式：Transform the bilateral control model to obtain the following differential expression:

qi(k+1)＝qi(k)+δΔqi(k)q i (k+1)=q i (k)+δΔq i (k)

Δqi(k+1)＝Δqi(k)+δfi(k)+δgi(k)ui(k)+δdi(k)Δq i (k+1)=Δq i (k)+δf i (k)+δg i (k)u i (k)+δd i (k)

其中δ表示离散时间系统的采样间隔，对应双边控制模型，容易获得where δ represents the sampling interval of the discrete-time system, corresponding to the bilateral control model, which is easy to obtain

Figure BDA0002116418680000049
Figure BDA0002116418680000049

Figure BDA00021164186800000410
Figure BDA00021164186800000410

di(k)＝-Bi(Δqi(k))d i (k)=-B i (Δq i (k))

其中，Fi(k)依情况，分别对应环境力与操作人员的输入；Among them, F i (k) corresponds to the environmental force and the operator's input according to the situation;

b)对于预定的状态边界，结合状态偏差的值特征，设计控制律的切换信号：b) For the predetermined state boundary, design the switching signal of the control law in combination with the value feature of the state deviation:

设计同步误差：Design synchronization error:

em(k)＝qm(k)-qs(k-Ts)e m (k)=q m (k)-q s (kT s )

es(k)＝qs(k)-qm(k-Tm)e s (k)=q s (k)-q m (kT m )

其中，主端误差为em(k)，从端误差为es(k)，Tm和Ts分别表示主端和从端的延迟时间相对于采样间隔的倍率。双边机械臂的关节角限制为

Figure BDA00021164186800000411
其中qij(k)表示主端或者从端机械臂的第j个关节角的角位置，类似地，定义各个关节角的期望角位置
Figure BDA0002116418680000051
同样满足
Figure BDA0002116418680000052
定义两个正数变量，满足Among them, the master-side error is em ( k ), the slave-side error is es ( k ), and T m and T s represent the multiples of the delay time of the master and slave ends relative to the sampling interval, respectively. The joint angle of the bilateral manipulator is limited to
Figure BDA00021164186800000411
where q ij (k) represents the angular position of the jth joint angle of the master or slave arm, and similarly, defines the desired angular position of each joint angle
Figure BDA0002116418680000051
also satisfied
Figure BDA0002116418680000052
Define two positive variables such that

Figure BDA0002116418680000053
Figure BDA0002116418680000053

Figure BDA0002116418680000054
Figure BDA0002116418680000054

定义双边同步误差Defining Bilateral Synchronization Error

Figure BDA0002116418680000055
Figure BDA0002116418680000055

定义切换信号Define the toggle signal

Figure BDA0002116418680000056
Figure BDA0002116418680000056

定义如下的辅助符号Auxiliary symbols are defined as follows

Figure BDA0002116418680000057
Figure BDA0002116418680000057

Figure BDA0002116418680000058
Figure BDA0002116418680000058

ξij(k)＝hij(k)ηij(k)+(1-hij(k))ζij(k)ξ ij (k)=h ij (k)η ij (k)+(1-h ij (k))ζ ij (k)

c)设计离散时间双边控制律；c) Design discrete-time bilateral control law;

ui(k)＝vi(k)+wi(k)u i (k)=vi (k)+ wi ( k)

Figure BDA0002116418680000059
Figure BDA0002116418680000059

Figure BDA00021164186800000510
Figure BDA00021164186800000510

其中，θi和

Figure BDA00021164186800000511
是对角矩阵，所有非零元素都为正，where θi and
Figure BDA00021164186800000511
is a diagonal matrix, all non-zero elements are positive,

Figure BDA00021164186800000512
Figure BDA00021164186800000512

为了保证双边系统的同步稳定，状态变量的限制边界与初始值的差的绝对值应不小于1，θi建议选择为采样周期的倒数。In order to ensure the synchronization and 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, and θ i is recommended to be selected as the reciprocal of the sampling period.

Claims (1)

1.一种面向远程操控的离散时间变边界双边控制方法，其特征在于步骤如下：1. a discrete time variable boundary bilateral control method for remote control, is characterized in that step is as follows: 步骤1：离散时间远程操控双边控制系统：Step 1: Discrete time remote control of bilateral control system:
Figure FDA0003424104990000011
Figure FDA0003424104990000011
 其中，下标m和s分别指代远程操控的主端和从端机械臂，为了方便说明，用i＝m，s说明后续变量，k表示采样时刻，
Figure FDA0003424104990000012
表示关节角向量，
Figure FDA0003424104990000013
表示正定惯量矩阵，
Figure FDA0003424104990000014
表示科氏力矩阵，
Figure FDA0003424104990000015
是未知但有界的外部扰动，
Figure FDA0003424104990000016
表示人类操作人员的输入力，
Figure FDA0003424104990000017
表示环境力，
Figure FDA0003424104990000018
表示机械臂输出的力矩；Among them, the subscripts m and s refer to the master and slave manipulators of the remote control respectively. For the convenience of description, i=m, s is used to describe the subsequent variables, k is the sampling time,
Figure FDA0003424104990000012
represents the joint angle vector,
Figure FDA0003424104990000013
represents the positive definite inertia matrix,
Figure FDA0003424104990000014
represents the Coriolis force matrix,
Figure FDA0003424104990000015
is an unknown but bounded external disturbance,
Figure FDA0003424104990000016
represents the input force of the human operator,
Figure FDA0003424104990000017
represents the environmental force,
Figure FDA0003424104990000018
Indicates the torque output by the robotic arm; 将双边控制模型进行转换，获得如下的差分表达式：Transform the bilateral control model to obtain the following differential expression: qi(k+1)＝qi(k)+δ△qi(k)q i (k+1)=q i (k)+δΔq i (k) △qi(k+1)＝△qi(k)+δfi(k)+δgi(k)ui(k)+δdi(k)Δq i (k+1)=Δq i (k)+δf i (k)+δg i (k)u i (k)+δd i (k) 其中δ表示离散时间系统的采样间隔，对应双边控制模型，获得：where δ represents the sampling interval of the discrete-time system, corresponding to the bilateral control model, to obtain:
Figure FDA0003424104990000019
Figure FDA0003424104990000019
Figure FDA00034241049900000110
Figure FDA00034241049900000110
 di(k)＝-Bi(△qi(k))d i (k)＝-B i (△q i (k)) 其中，Fi(k)依情况，分别对应环境力与操作人员的输入；Among them, F i (k) corresponds to the environmental force and the operator's input according to the situation; 步骤2：对于预定的状态边界，结合状态偏差的值特征，设计控制律的切换信号：Step 2: For the predetermined state boundary, design the switching signal of the control law in combination with the value characteristics of the state deviation: 同步误差：
Figure FDA00034241049900000111
Synchronization error:
Figure FDA00034241049900000111
 其中，主端误差为em(k)，从端误差为es(k)，Tm和Ts分别表示主端和从端的延迟时间相对于采样间隔的倍率；双边机械臂的关节角限制为
Figure FDA0003424104990000021
其中qij(k)表示主端或者从端机械臂的第j个关节角的角位置，γ ij(k)关节角变化的下界，
Figure FDA0003424104990000022
关节角变化的上界；Among them, the error of the master end is em (k), the error of the slave end is es (k), T m and T s represent the multiples of the delay time of the master end and the slave end relative to the sampling interval, respectively; the joint angle limit of the bilateral manipulator for
Figure FDA0003424104990000021
where q ij (k) represents the angular position of the jth joint angle of the master or slave arm, γ ij (k) is the lower bound of the joint angle change,
Figure FDA0003424104990000022
The upper bound of the joint angle change; 定义各个关节角的期望角位置
Figure FDA0003424104990000023
同样满足
Figure FDA0003424104990000024
Define the desired angular position for each joint angle
Figure FDA0003424104990000023
also satisfied
Figure FDA0003424104990000024
 定义两个正数变量，满足
Figure FDA0003424104990000025
Define two positive variables such that
Figure FDA0003424104990000025
 定义双边同步误差
Figure FDA0003424104990000026
Defining Bilateral Synchronization Error
Figure FDA0003424104990000026
 定义切换信号
Figure FDA0003424104990000027
Define the toggle signal
Figure FDA0003424104990000027
 定义如下的辅助符号
Figure FDA0003424104990000028
Auxiliary symbols are defined as follows
Figure FDA0003424104990000028
 步骤3：设计离散时间双边控制律，并以此进行控制：Step 3: Design a discrete-time bilateral control law and control it accordingly: ui(k)＝vi(k)+wi(k)u i (k)=vi (k)+ wi ( k)
Figure FDA0003424104990000029
Figure FDA0003424104990000029
Figure FDA00034241049900000210
Figure FDA00034241049900000210
 其中，θi和
Figure FDA00034241049900000211
是对角矩阵，所有非零元素都为正where θi and
Figure FDA00034241049900000211
is a diagonal matrix, all nonzero elements are positive
Figure FDA00034241049900000212
Figure FDA00034241049900000212
 状态变量的限制边界与初始值的差的绝对值应不小于1，θi选择为采样周期的倒数。The absolute value of the difference between the limit boundary of the state variable and the initial value should not be less than 1, and θ i is selected as the reciprocal of the sampling period.
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