CN110340894B - Teleoperation system self-adaptive multilateral control method based on fuzzy logic - Google Patents

Abstract

Translated fromChinese

本发明公开了一种基于模糊逻辑的非线性遥操作系统的自适应多边控制方法。本发明基于模糊逻辑函数，估计了非线性环境动力学的非功率参数，并通过存在时延的通信通道传输回主端，进行主端环境力的重构；针对主从机器人存在的各种不确定性问题，本发明基于模糊逻辑系统，通过设计自适应率在线更新包含未知系统模型信息的非线性函数的参数；针对系统的位置追踪性能，本发明通过基于模糊逻辑系统的非线性自适应多边控制方法，当系统存在通信时延时，使从机器人准确地跟踪主机器人的轨迹信号；针对多机器人间的协同作业时作业力分配的问题，本发明通过设计多机器人的协同控制算法，实现了多个从机器人的作业力分配。

The invention discloses an adaptive multilateral control method based on a fuzzy logic nonlinear teleoperating system. Based on the fuzzy logic function, the invention estimates the non-power parameters of nonlinear environmental dynamics, and transmits it back to the main end through a communication channel with time delay to reconstruct the environmental force of the main end; To solve the deterministic problem, the present invention is based on a fuzzy logic system, and the parameters of the nonlinear function including the model information of the unknown system are updated online by designing the adaptive rate; for the position tracking performance of the system, the present invention adopts the nonlinear adaptive multilateral based on the fuzzy logic system. The control method enables the slave robot to accurately track the trajectory signal of the master robot when there is a time delay in communication in the system; for the problem of work force distribution during cooperative operation among multiple robots, the present invention realizes the multi-robot cooperative control algorithm by designing a multi-robot cooperative control algorithm. Work force distribution for multiple slave robots.

Description

Translated fromChinese

一种基于模糊逻辑的遥操作系统自适应多边控制方法An adaptive multilateral control method for teleoperating systems based on fuzzy logic

技术领域technical field

本发明属于遥操作控制领域，具体来说是一种基于模糊逻辑的遥操作系统自适应多边控制方法，同时保证非线性多边遥操作系统的稳定性、透明性和多从机器人的协同作业性能。The invention belongs to the field of teleoperation control, in particular to a fuzzy logic-based teleoperating system adaptive multilateral control method, which simultaneously ensures the stability and transparency of the nonlinear multilateral teleoperation system and the cooperative operation performance of multi-slave robots.

背景技术Background technique

随着机电技术的不断发展，机器人系统的研究越来越成为现阶段的热门课题，其中依靠人机交互的遥操作机器人技术已经取得了阶段性的进展，并在军事、工业和医疗领域有着广泛的应用。With the continuous development of electromechanical technology, the research on robotic systems has become a hot topic at this stage. Among them, the tele-operation robot technology relying on human-computer interaction has achieved staged progress, and has a wide range of applications in military, industrial and medical fields. Applications.

然而，随着作业任务往复杂、精细的方向发展，需要作业环境中存在多个具有多自由度的机器人进行协同作业，这类机器人往往存在非线性和各种不确定性；此外，随着协同作业机器人数量的增多，多机器人间的信号通信会使存在时延的通信通道中的信号传输变得更加复杂，甚至恶化遥操作系统的稳定性和透明性。However, with the development of complex and delicate tasks, multiple robots with multiple degrees of freedom are required to work collaboratively in the work environment. Such robots often have nonlinearities and various uncertainties; in addition, with the cooperation of With the increase of the number of working robots, the signal communication between multiple robots will make the signal transmission in the communication channel with delay more complicated, and even deteriorate the stability and transparency of the teleoperating system.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于提出一种基于模糊逻辑的遥操作系统自适应多边控制方法，以解决传统多边遥操作系统中的稳定性与透明性权衡，主从机器人的非线性和各种不确定性，以及多机器人的协同作业等技术问题。The purpose of the present invention is to propose an adaptive multilateral control method of teleoperating system based on fuzzy logic, so as to solve the trade-off between stability and transparency in traditional multilateral teleoperating system, nonlinearity and various uncertainties of master-slave robot, And technical problems such as multi-robot collaborative operation.

为实现上述目的，本发明的技术方案具体内容如下：To achieve the above object, the specific content of the technical scheme of the present invention is as follows:

一种基于模糊逻辑的遥操作系统自适应多边控制方法，包括以下步骤：An adaptive multilateral control method for teleoperating systems based on fuzzy logic, comprising the following steps:

(一)建立多边遥操作系统的非线性动力学模型。(1) Establish the nonlinear dynamic model of the multilateral teleoperating system.

(二)基于模糊逻辑系统的作业环境估计与主端环境重构。(2) Operating environment estimation and master-side environment reconstruction based on fuzzy logic system.

(三)基于模糊逻辑系统设计主机器人的自适应多边控制器。(3) Design the adaptive multilateral controller of the main robot based on the fuzzy logic system.

(四)基于模糊逻辑系统设计从机器人的自适应多边控制器。(4) The adaptive multilateral controller of slave robot is designed based on fuzzy logic system.

与现有技术相比，本发明具有如下有益效果：Compared with the prior art, the present invention has the following beneficial effects:

1、基于模糊逻辑系统，估计了非线性环境动力学的非功率参数，并通过存在时延的通信通道传输回主端，进行主端环境力的重构，从而避免了因功率信号在通信通道中的传输造成的遥操作系统的失稳问题，并为操作者提供准确的力反馈信息。1. Based on the fuzzy logic system, the non-power parameters of nonlinear environmental dynamics are estimated, and transmitted back to the main end through the communication channel with delay to reconstruct the environmental force of the main end, thereby avoiding the power signal in the communication channel. The instability problem of the teleoperating system caused by the transmission in the middle, and provide accurate force feedback information for the operator.

2、基于模糊逻辑系统，通过设计自适应率在线更新包含未知系统模型信息的非线性函数的参数，从而解决了主从机器人存在的各种不确定性问题。2. Based on the fuzzy logic system, the parameters of the nonlinear function containing the unknown system model information are updated online by designing the adaptive rate, thus solving the various uncertainties of the master-slave robot.

3、通过基于模糊逻辑系统的非线性自适应多边控制方法，当系统存在通信时延时，使从机器人准确地跟踪主机器人的轨迹信号，从而提升系统的位置追踪性能。3. Through the nonlinear adaptive multilateral control method based on fuzzy logic system, when there is a delay in communication in the system, the slave robot can accurately track the trajectory signal of the master robot, thereby improving the position tracking performance of the system.

4、通过设计多机器人的协同控制算法，实现了多个从机器人的作业力分配，从而提升了多个从机器人对作业任务的协同作业性能。4. By designing a multi-robot collaborative control algorithm, the work force distribution of multiple slave robots is realized, thereby improving the collaborative operation performance of multiple slave robots for work tasks.

5、通过设计李雅普诺夫函数，保证了非线性多边遥操作系统中所有信号的有界性，从而保住了系统的全局渐进稳定性；5. By designing the Lyapunov function, the boundedness of all signals in the nonlinear multilateral teleoperating system is guaranteed, thereby maintaining the global asymptotic stability of the system;

附图说明Description of drawings

图1是本发明提出的基于模糊逻辑系统的非线性遥操作系统的自适应多边控制框图。FIG. 1 is a block diagram of the adaptive multilateral control of the nonlinear teleoperating system based on the fuzzy logic system proposed by the present invention.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅用以解释本发明，并不用于限定本发明。此外，下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

现结合实施例、附图1对本发明作进一步描述：Now in conjunction with embodiment, accompanyingdrawing 1 the present invention is further described:

本发明的实施技术方案为：The technical implementation scheme of the present invention is:

1)建立多边遥操作系统的非线性动力学模型，具体为：1) Establish a nonlinear dynamic model of the multilateral teleoperating system, specifically:

1-1)建立主机器人、从机器人与作业环境的非线性动力学模型1-1) Establish the nonlinear dynamic model of the master robot, slave robot and working environment

其中，q_m,i,

和q_s,i,

表示第i个主从机器人位置、速度和加速度信号，x_m,i,

表示第i个主机器人的末端位置，x_s,o,

表示作业任务中抓取目标的质心位置，M_m,i和M_s表示质量惯性矩阵，C_m,i和C_s表示科氏力/向心力矩阵，G_m,i和G_s表示重力矩阵，D_m,i和D_s表示外干扰和建模误差，u_m,i和u_s表示控制输入，F_h,i表示第i个操作者的操作力，F_e表示从机器人与作业任务中的环境力，i＝1,2,....,n。Among them, q_m,i ,

and q_s,i ,

Indicates the position, velocity and acceleration signals of the i-th master-slave robot, x_m,i ,

represents the end position of the i-th master robot, x_s,o ,

Indicates the position of the center of mass of the grasping target in the task, M_{m, i} and M_s represent the mass inertia matrix, C_{m, i} and C_s represent the Coriolis force/centripetal force matrix, G_{m, i} and G_s represent the gravity matrix, D_{m, i} and D_s represent external disturbance and modeling error,_{um, i} and u_s represent the control input, F_{h, irepresent} the operating force of the ith operator, and Fe represent the environment from the robot and the task Force, i=1,2,....,n.

上述系统具有如下特性：The above system has the following characteristics:

①0<M_m,i≤δ_m0,iI，0<M_s≤δ_s0I，其中，δ_m0,i,δ_s0>0表示单位矩阵I的缩放系数；①0<M_m,i ≤δ_m0,i I, 0<M_s ≤δ_s0 I, where δ_m0,i ,δ_s0 >0 represents the scaling factor of the identity matrix I;

②

和

为斜对称矩阵；②

and

is an obliquely symmetric matrix;

③公式(1)和(2)中的部分动力学方程可以写成如下线性方程的形式：③Part of the kinetic equations in equations (1) and (2) can be written in the form of the following linear equations:

其中，θ_m,i和θ_s表示主从机器人的模型未知参数，ζ表示模糊逻辑矩阵。Among them, θ_m,i and θ_s represent the unknown parameters of the master-slave robot model, and ζ represents the fuzzy logic matrix.

1-2)建立作业环境的非线性动力学模型1-2) Establish a nonlinear dynamic model of the working environment

其中，θ_e表示未知的非功率环境参数。where θ_e represents an unknown non-power environmental parameter.

2)基于模糊逻辑系统的作业环境估计与主端环境重构，具体为：2) Based on fuzzy logic system operating environment estimation and master-end environment reconstruction, specifically:

2-1)将从端作业环境的动力学模型(3)写成径向基神经网络函数的形式，则：2-1) Write the dynamic model (3) of the slave operating environment in the form of a radial basis neural network function, then:

F_e＝ζ^T(x_ew)θ_e (4)F_e =ζ^T (x_ew )θ_e (4)

其中，x_ew表示模糊逻辑函数的输入量，且与x_s,o,

相关。Among them, x_ew represents the input of the fuzzy logic function, and is the same as x_s,o ,

related.

2-2)定义

为环境的最优估计参数，Ω_e和Ω_e0分别表示x_ew和W_e的有界集，通过MATLAB的模糊逻辑工具箱能够实现从端作业环境的在线估计。2-2) Definition

For the optimal estimation parameters of the environment, Ω_e and Ω_e0 represent the bounded sets of x_ew and We respectively_, and the online estimation of the slave operating environment can be realized by the fuzzy logic toolbox of MATLAB.

2-3)由于通信时延T(t)的存在，为避免功率信号在通信通道间的传递影响多边遥操作系统的稳定性，将非功率环境参数估计值

传递到主端，从而得到主端的重构环境力为：2-3) Due to the existence of the communication delay T(t), in order to avoid the transmission of power signals between communication channels from affecting the stability of the multilateral teleoperating system, the estimated value of the non-power environment parameters is

Pass it to the master, so as to obtain the reconstructed environment force of the master as:

其中，x_emw表示模糊逻辑函数的输入量，且与x_md,i,

相关。Among them, x_emw represents the input of the fuzzy logic function, and is the same as x_md,i ,

related.

3)基于模糊逻辑系统设计主机器人的自适应多边控制器，具体为：3) Design the adaptive multilateral controller of the main robot based on the fuzzy logic system, specifically:

3-1)设计主机器人的理想轨迹生成器如下：3-1) The ideal trajectory generator for designing the master robot is as follows:

其中，i＝1,2,...,n，

M_d,C_d,G_d表示轨迹生成器的优化参数。通过选取适当的优化系数，(6)-(7)能够生成无源的主机器人理想轨迹信号x_md,i。Among them, i=1,2,...,n,

M_d , C_d , G_d represent the optimization parameters of the trajectory generator. By choosing appropriate optimization coefficients, (6)-(7) can generate the passive ideal trajectory signal x_md,i of the master robot.

3-2)定义x_m1,i＝x_m,i，

则第i个主机器人的非线性动力学模型(1)可改写为：3-2) Define x_m1,i =x_m,i ,

Then the nonlinear dynamic model (1) of the i-th master robot can be rewritten as:

3-3)定义第i个主机器人的跟踪误差为：3-3) Define the tracking error of the i-th master robot as:

其中，α_m1,i表示主机器人的虚拟跟踪量。Among them, α_m1,i represents the virtual tracking amount of the main robot.

3-4)定义(8)中的第一个子系统的李雅普诺夫函数V_m1,i如下：3-4) Define the Lyapunov function V_m1,i of the first subsystem in (8) as follows:

通过选取虚拟跟踪量α_m1,i为

则By selecting the virtual tracking amount α_{m1, i} is

but

3-5)定义(8)中的第二个子系统的李雅普诺夫函数V_m2,i如下：3-5) Define the Lyapunov function V_m2,i of the second subsystem in (8) as follows:

3-6)基于(8)和(9)，可得z_m2,i的导数为3-6) Based on (8) and (9), the derivative of z_m2,i can be obtained as

于是，可得V_m2,i的导数为Therefore, the derivative of V_m2,i can be obtained as

其中，

表示未知主机器人系统动力学函数。in,

represents the unknown master robot system dynamics function.

3-7)根据(14)设计主控制器，保证主端子系统的稳定性，设计的控制器u_m,i为：3-7) Design the main controller according to (14) to ensure the stability of the main terminal system. The designed controller_um,i is:

u_m,i＝-μ_m2,iz_m2,i-z_m1,i-Φ_m,i-F_h,i (15)u_m,i =-μ_m2,i z_m2,i -z_m1,i -Φ_m,i -F_h,i (15)

其中，μ_m2,i>0表示主控制器性能调整参数。Among them, μ_m2,i >0 represents the main controller performance adjustment parameter.

在从控制器(15)中，Φ_m,i表示一种用于估计η_m,i的模糊逻辑函数，可定义为：In the slave controller (15), Φ_m,i represents a fuzzy logic function for estimating η_m,i , which can be defined as:

其中，θ_m,i表示未知的主机器人系统动力学参数，

表示模糊逻辑函数的输入量，

表示第j个局部模糊逻辑函数。where θ_m,i represents the unknown dynamic parameters of the main robot system,

represents the input quantity of the fuzzy logic function,

represents the jth local fuzzy logic function.

3-8)设计主端系统的李雅普诺夫函数V_m,i为：3-8) Design the Lyapunov function V_m,i of the master-end system as:

其中，γ_m,i>0表示李雅普诺夫函数V_m,i的系数，

表示模糊逻辑函数的估计误差，

表示最优估计参数。。where γ_m,i >0 represents the coefficient of the Lyapunov function V_m,i ,

represents the estimation error of the fuzzy logic function,

represents the optimal estimated parameter. .

基于李雅普诺夫函数V_m,i设计θ_m,i的自适应率为：Based on the Lyapunov function V_m,i, the design adaptive rate of θ_m,i is:

其中，k_m,i>0和Γ_m,i>0表示自适应率的性能调节参数。where k_m,i >0 and Γ_m,i >0 represent the performance tuning parameters of the adaptation rate.

4)基于模糊逻辑系统设计从机器人的自适应多边控制器，具体为：4) Design the adaptive multilateral controller of the slave robot based on the fuzzy logic system, specifically:

4-1)由于信号在通信通道的传输会不可避免地产生通信时延，主机器人的位置信号x_m,i(t)通过通信通道传输到从端得到时延的位置信号x_m,i(t-T(t))，设计从机器人的理想轨迹生成器为H_f(s)＝1/(o_fs+1)²，其中，o_f表示时间常数，通过输入时延的平均位置信号

能够输出理想的从机器人跟踪轨迹x_sd,o(t),

其中，l_o,i表示抓取目标与机器人末端位置间的关系转换，T(t)为系统的通信时延。4-1) Since the transmission of the signal in the communication channel will inevitably generate a communication delay, the position signal x_m,i (t) of the master robot is transmitted to the slave through the communication channel to obtain the delayed position signal x_m,i ( tT(_t )), the ideal trajectory generator of the design slave robot is H_f (s)=1/(of s₊ 1)² , where of represents the time constant, the average position signal through the input time delay

Able to output ideal slave robot tracking trajectory x_sd,o (t),

Among them, l_o,i represents the relationship conversion between the grasping target and the end position of the robot, and T(t) is the communication delay of the system.

4-2)定义x_s1＝x_s,o，

则非线性动力学模型(2)可改写为：4-2) Define x_s1 =x_s,o ,

Then the nonlinear dynamic model (2) can be rewritten as:

4-3)定义从机器人与抓取目标的跟踪误差为：4-3) Define the tracking error between the slave robot and the grab target as:

其中，α_s1表示从机器人的虚拟跟踪量。Among them, α_s1 represents the virtual tracking amount of the slave robot.

4-4)定义(19)中的第一个子系统的李雅普诺夫函数V_s1如下：4-4) Define the Lyapunov function V_s1 of the first subsystem in (19) as follows:

通过选取虚拟跟踪量α_s1为

则By selecting the virtual tracking amount α_s1 as

but

4-5)定义(19)中的第二个子系统的李雅普诺夫V_s2如下：4-5) The Lyapunov V_s2 of the second subsystem in (19) is defined as follows:

4-6)基于(19)和(20)，可得z_s2的导数为4-6) Based on (19) and (20), the derivative of z_s2 can be obtained as

于是，可得V_s2的导数为Therefore, the derivative of V_s2 can be obtained as

其中，

表示未知从机器人系统动力学函数。in,

represents the unknown slave robot system dynamics function.

4-7)根据(25)设计从控制器，保证从端子系统的稳定性，设计的控制器u_s为：4-7) Design the slave controller according to (25) to ensure the stability of the slave terminal system. The designed controller u_s is:

u_s＝-μ_s2z_s2-z_s1-Φ_s+F_e (26)u_s = -μ_s2 z_s2 -z_s1 -Φ_s +F_e (26)

其中，μ_s2>0表示从控制器性能调整参数。Among them, μ_s2 > 0 means to adjust the parameters from the controller performance.

在从控制器(26)中，Φ_s表示一种用于估计η_s的模糊逻辑函数，可定义为：In the slave controller (26), Φ_s represents a fuzzy logic function for estimating η_s , which can be defined as:

其中，θ_s表示未知的从机器人系统动力学参数，

表示模糊逻辑函数的输入量，

表示第j个局部模糊逻辑函数。where θ_s represents the unknown dynamic parameters of the slave robot system,

represents the input quantity of the fuzzy logic function,

represents the jth local fuzzy logic function.

4-8)设计从端系统的李雅普诺夫函数V_s为：4-8) Design the Lyapunov function V_s of the slave system as:

其中，γ_s>0表示李雅普诺夫函数V_s的系数，

表示模糊逻辑函数的估计误差，

表示最优估计参数。where γ_s >0 represents the coefficient of the Lyapunov function V_s ,

represents the estimation error of the fuzzy logic function,

represents the optimal estimated parameter.

基于李雅普诺夫函数V_s设计θ_s的自适应率为：The adaptive rate of designing θ_s based on the Lyapunov function V_s is:

其中，k_s>0和Γ_s>0表示自适应率的性能调节参数。where k_s >0 and Γ_s >0 represent the performance tuning parameters of the adaptation rate.

4-9)根据从控制器(26)，为得到每个从机器人的控制输入u_s,i，设计多机器人的协同控制算法如下：4-9) According to the slave controller (26), in order to obtain the control input u_s,i of each slave robot, the cooperative control algorithm of multiple robots is designed as follows:

其中，

表示分配系数，且

W表示不同作业需求的权重系数，

表示各个从机器人与抓取目标的内部力，且

in,

represents the distribution coefficient, and

W represents the weight coefficient of different job requirements,

represents the internal force of each slave robot and grasping target, and

Claims (4)

Translated fromChinese

1.一种基于模糊逻辑的遥操作系统自适应多边控制方法，其特征在于，包括以下步骤：1. a teleoperating system adaptive multilateral control method based on fuzzy logic, is characterized in that, comprises the following steps:1)建立多边遥操作系统的非线性动力学模型，具体为：1) Establish a nonlinear dynamic model of the multilateral teleoperating system, specifically:1-1)建立主机器人、从机器人与作业环境的非线性动力学模型1-1) Establish the nonlinear dynamic model of the master robot, slave robot and working environment

其中，q_m,i,

和q_s,i,

表示第i个主从机器人位置、速度和加速度信号，x_m,i,

表示第i个主机器人的末端位置、末端速度和末端加速度，x_s,o,

表示作业任务中抓取目标的质心位置、质心速度和质心加速度，M_m,i和M_s表示质量惯性矩阵，C_m,i和C_s表示科氏力/向心力矩阵，G_m,i和G_s表示重力矩阵，D_m,i和D_s表示外干扰和建模误差，u_m,i和u_s表示控制输入，F_h,i表示第i个操作者的操作力，F_e表示从机器人与作业任务中的环境力，i＝1,2,....,n；Among them, q_m,i ,

and q_s,i ,

Indicates the position, velocity and acceleration signals of the i-th master-slave robot, x_m,i ,

represents the end position, end velocity and end acceleration of the i-th master robot, x_s,o ,

Indicates the centroid position, centroid velocity and centroid acceleration of the grasping target in the task, M_m,i and M_s indicate the mass inertia matrix, C_m,i and C_s indicate the Coriolis force/centripetal force matrix, G_m,i and G_s represents the gravity matrix, D_m,i and D_s represent the external disturbance and modeling error,_um,i and u_s represent the control input, F_{h,irepresents} the operating force of the ith operator, and Fe represents the slave robot and the environmental force in the task, i=1,2,....,n;上述系统具有如下特性：The above system has the following characteristics:①0<M_m,i≤δ_m0,iI，0<M_s≤δ_s0I，其中，δ_m0,i,δ_s0>0表示单位矩阵I的缩放系数；①0<M_m,i ≤δ_m0,i I, 0<M_s ≤δ_s0 I, where δ_m0,i ,δ_s0 >0 represents the scaling factor of the identity matrix I;②

和

为斜对称矩阵；②

and

is an obliquely symmetric matrix;③公式(1)和(2)中的部分动力学方程可以写成如下线性方程的形式：③Part of the kinetic equations in equations (1) and (2) can be written in the form of the following linear equations:

其中，θ_m,i和θ_s表示主从机器人的模型未知参数，ζ表示模糊逻辑矩阵；Among them, θ_m,i and θ_s represent the unknown parameters of the master-slave robot model, and ζ represents the fuzzy logic matrix;1-2)建立从端作业环境的非线性动力学模型1-2) Establish a nonlinear dynamic model of the slave operating environment

其中，θ_e表示未知的非功率环境参数；Among them, θ_e represents the unknown non-power environmental parameters;2)基于模糊逻辑系统的作业环境估计与主端环境重构，具体为：2) Operating environment estimation and master-end environment reconstruction based on fuzzy logic system, specifically:2-1)将从端作业环境的非线性动力学模型(3)写成径向基神经网络函数的形式，则：2-1) Write the nonlinear dynamic model (3) of the slave operating environment in the form of a radial basis neural network function, then:F_e＝ζ^T(x_ew)θ_e (4)F_e =ζ^T (x_ew )θ_e (4)其中，x_ew表示模糊逻辑函数的输入量；Among them, x_ew represents the input quantity of the fuzzy logic function;2-2)定义

为环境的最优估计参数，Ω_e和Ω_e0分别表示x_ew和θ_e的有界集，通过MATLAB的模糊逻辑工具箱实现从端作业环境的在线估计；2-2) Definition

are the optimal estimation parameters of the environment, Ω_e and Ω_e0 represent the bounded sets of x_ew and θ_e respectively, and the online estimation of the slave operating environment is realized by the fuzzy logic toolbox of MATLAB;2-3)进行主端的环境力重构；2-3) Carry out the environmental force reconstruction of the main end;3)基于模糊逻辑系统设计主机器人的自适应多边控制器，具体为：3) Design the adaptive multilateral controller of the main robot based on the fuzzy logic system, specifically:3-1)设计主机器人的理想轨迹生成器生成无源的主机器人理想轨迹信号x_md,i；设计的主机器人的理想轨迹生成器如下：3-1) Design the ideal trajectory generator of the main robot to generate a passive ideal trajectory signal x_md,i of the main robot; the ideal trajectory generator of the designed main robot is as follows:

其中，i＝1,2,...,n，

M_d,C_d,G_d表示轨迹生成器的优化参数；Among them, i=1,2,...,n,

M_d , C_d , G_d represent the optimization parameters of the trajectory generator;3-2)定义x_m1,i＝x_m,i，

则第i个主机器人的非线性动力学模型(1)可改写为：3-2) Define x_m1,i =x_m,i ,

Then the nonlinear dynamic model (1) of the i-th master robot can be rewritten as:

3-3)定义第i个主机器人的跟踪误差为：3-3) Define the tracking error of the i-th master robot as:

其中，α_m1,i表示主机器人的虚拟跟踪量；Among them, α_m1,i represents the virtual tracking amount of the main robot;3-4)定义(8)中的第一个子系统的李雅普诺夫函数V_m1,i如下：3-4) Define the Lyapunov function V_m1,i of the first subsystem in (8) as follows:

通过选取虚拟跟踪量α_m1,i，则By selecting the virtual tracking amount α_m1,i , then

3-5)定义(8)中的第二个子系统的李雅普诺夫函数V_m2,i如下：3-5) Define the Lyapunov function V_m2,i of the second subsystem in (8) as follows:

3-6)基于(8)和(9)，可得z_m2,i的导数为3-6) Based on (8) and (9), the derivative of z_m2,i can be obtained as

于是，可得V_m2,i的导数为Therefore, the derivative of V_m2,i can be obtained as

其中，

表示未知主机器人系统动力学函数，μ_m1,i>0表示虚拟跟踪量的调节参数；in,

represents the unknown master robot system dynamics function, μ_{m1, i} > 0 represents the adjustment parameter of the virtual tracking amount;3-7)根据(14)设计主控制器，保证主端子系统的稳定性，设计的控制器u_m,i为：3-7) Design the main controller according to (14) to ensure the stability of the main terminal system. The designed controller_um,i is:u_m,i＝-μ_m2,iz_m2,i-z_m1,i-Φ_m,i-F_h,i (15)u_m,i =-μ_m2,i z_m2,i -z_m1,i -Φ_m,i -F_h,i (15)其中，μ_m2,i>0表示主控制器性能调整参数；Among them, μ_m2,i >0 represents the performance adjustment parameter of the main controller;在从控制器(15)中，Φ_m,i表示一种用于估计η_m,i的模糊逻辑函数，定义为：In the slave controller (15), Φ_m,i represents a fuzzy logic function for estimating η_m,i , defined as:

其中，θ_m,i表示未知的主机器人系统动力学参数，

表示模糊逻辑函数的输入量，

表示第j个局部模糊逻辑函数；where θ_m,i represents the unknown dynamic parameters of the main robot system,

represents the input quantity of the fuzzy logic function,

represents the jth local fuzzy logic function;3-8)设计主端系统的李雅普诺夫函数V_m,i为：3-8) Design the Lyapunov function V_m,i of the master-end system as:

其中，γ_m,i>0表示李雅普诺夫函数V_m,i的系数，

表示模糊逻辑函数的估计误差，

表示最优估计参数；where γ_m,i >0 represents the coefficient of the Lyapunov function V_m,i ,

represents the estimation error of the fuzzy logic function,

represents the optimal estimated parameter;基于李雅普诺夫函数V_m,i设计θ_m,i的自适应率为：Based on the Lyapunov function V_m,i, the design adaptive rate of θ_m,i is:

其中，k_m,i>0和Γ_m,i>0表示自适应率的性能调节参数；Among them, k_m,i >0 and Γ_m,i >0 represent the performance adjustment parameters of the adaptation rate;4)基于模糊逻辑系统设计从机器人的自适应多边控制器，具体为：4) Design the adaptive multilateral controller of the slave robot based on the fuzzy logic system, specifically:4-1)由于信号在通信通道的传输会不可避免地产生通信时延，主机器人的位置信号x_m,i(t)通过通信通道传输到从端得到时延的位置信号x_m,i(t-T(t))，设计从机器人的理想轨迹生成器为H_f(s)＝1/(o_fs+1)²，其中，o_f表示时间常数，通过输入时延的平均位置信号

能够输出理想的从机器人跟踪轨迹x_sd,o(t),

其中，l_o,i表示抓取目标与机器人末端位置间的关系转换，T(t)为系统的通信时延；4-1) Since the transmission of the signal in the communication channel will inevitably generate a communication delay, the position signal x_m,i (t) of the master robot is transmitted to the slave through the communication channel to obtain the delayed position signal x_m,i ( tT(_t )), the ideal trajectory generator of the design slave robot is H_f (s)=1/(of s₊ 1)² , where of represents the time constant, the average position signal through the input time delay

Able to output ideal slave robot tracking trajectory x_sd,o (t),

Among them, l_o,i represents the relationship conversion between the grasping target and the end position of the robot, and T(t) is the communication delay of the system;4-2)定义x_s1＝x_s,o，

则非线性动力学模型(2)可改写为：4-2) Define x_s1 =x_s,o ,

Then the nonlinear dynamic model (2) can be rewritten as:

4-3)定义从机器人与抓取目标的跟踪误差为：4-3) Define the tracking error between the slave robot and the grab target as:

其中，α_s1表示从机器人的虚拟跟踪量；Among them, α_s1 represents the virtual tracking amount of the slave robot;4-4)定义(19)中的第一个子系统的李雅普诺夫函数V_s1如下：4-4) Define the Lyapunov function V_s1 of the first subsystem in (19) as follows:

通过选取虚拟跟踪量α_s1，则By selecting the virtual tracking amount α_s1 , then

4-5)定义(19)中的第二个子系统的李雅普诺夫V_s2如下：4-5) The Lyapunov V_s2 of the second subsystem in (19) is defined as follows:

4-6)基于(19)和(20)，可得z_s2的导数为4-6) Based on (19) and (20), the derivative of z_s2 can be obtained as

于是，可得V_s2的导数为Therefore, the derivative of V_s2 can be obtained as

其中，

表示未知从机器人系统动力学函数；in,

represents the unknown slave robot system dynamics function;4-7)根据(25)设计从控制器，保证从端子系统的稳定性，设计的控制器u_s为：4-7) Design the slave controller according to (25) to ensure the stability of the slave terminal system. The designed controller u_s is:u_s＝-μ_s2z_s2-z_s1-Φ_s+F_e (26)u_s = -μ_s2 z_s2 -z_s1 -Φ_s +F_e (26)其中，μ_s2>0表示从控制器性能调整参数；Among them, μ_s2 >0 indicates that the parameter is adjusted from the performance of the controller;在从控制器(26)中，Φ_s表示一种用于估计η_s的模糊逻辑函数，定义为：In the slave controller (26), Φ_s represents a fuzzy logic function for estimating η_s , defined as:

其中，θ_s表示未知的从机器人系统动力学参数，

表示模糊逻辑函数的输入量，

表示第j个局部模糊逻辑函数；where θ_s represents the unknown dynamic parameters of the slave robot system,

represents the input quantity of the fuzzy logic function,

represents the jth local fuzzy logic function;4-8)设计从端系统的李雅普诺夫函数V_s为：4-8) Design the Lyapunov function V_s of the slave system as:

其中，γ_s>0表示李雅普诺夫函数V_s的系数，

表示模糊逻辑函数的估计误差，

表示最优估计参数；where γ_s >0 represents the coefficient of the Lyapunov function V_s ,

represents the estimation error of the fuzzy logic function,

represents the optimal estimated parameter;基于李雅普诺夫函数V_s设计θ_s的自适应率为：The adaptive rate of designing θ_s based on the Lyapunov function V_s is:

其中，k_s>0和Γ_s>0表示自适应率的性能调节参数；where k_s >0 and Γ_s >0 represent the performance tuning parameters of the adaptation rate;4-9)根据从控制器(26)，为得到每个从机器人的控制输入u_s,i，设计多机器人的协同控制算法，所述的协同控制算法如下：4-9) According to the slave controller (26), in order to obtain the control input u_s,i of each slave robot, a cooperative control algorithm of multiple robots is designed, and the cooperative control algorithm is as follows:

其中，

表示分配系数，且

W表示不同作业需求的权重系数，

表示各个从机器人与抓取目标的内部力，且

in,

is the distribution coefficient, and

W represents the weight coefficient of different job requirements,

represents the internal force of each slave robot and grasping target, and

2.根据权利要求1所述的一种基于模糊逻辑的遥操作系统自适应多边控制方法，其特征在于，所述步骤2-3)中，由于通信时延T(t)的存在，为避免功率信号在通信通道间的传递影响多边遥操作系统的稳定性，将非功率环境参数估计值

传递到主端，从而得到主端的重构环境力为：2. a kind of teleoperating system adaptive multilateral control method based on fuzzy logic according to claim 1, is characterized in that, in described step 2-3), due to the existence of communication time delay T (t), in order to avoid The transmission of power signals between communication channels affects the stability of the multilateral teleoperating system, and the estimated values of non-power environmental parameters are

Pass it to the master, so as to obtain the reconstructed environment force of the master as:

其中，x_emw表示模糊逻辑函数的输入量。Among them, x_emw represents the input quantity of the fuzzy logic function.3.根据权利要求1所述的一种基于模糊逻辑的遥操作系统自适应多边控制方法，其特征在于，所述步骤3-4)中，选取的虚拟跟踪量α_m1,i为

3. a kind of teleoperating system adaptive multilateral control method based on fuzzy logic according to claim 1, is characterized in that, in described step 3-4), the virtual tracking quantity α_{m1 that chooses, i} is.

4.根据权利要求1所述的一种基于模糊逻辑的遥操作系统自适应多边控制方法，其特征在于，所述步骤4-4)中，选取的虚拟跟踪量α_s1为

其中，μ_s1>0表示虚拟跟踪量的调节参数。4. a kind of teleoperating system adaptive multilateral control method based on fuzzy logic according to claim 1, is characterized in that, in described step 4-4), the virtual tracking amount α_s1 selected is

Among them, μ_s1 >0 represents the adjustment parameter of the virtual tracking quantity.

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