CN111427264B - A Neural Adaptive Fixed Time Control Method for Complex Telemanipulation Technology - Google Patents

Abstract

The invention provides a neural self-adaptive fixed time control method of complex teleoperation technology, which includes: firstly, kinematics and dynamics modeling are performed on the master-slave robot of the teleoperation system, and the tracking error is set; The control strategy of the operator's influence on the entire teleoperating system and the complex hybrid communication between master-slave robots; finally, a neural adaptive non-singular fixed-time control method is proposed, and combined with the kinematics and dynamics models, the complex teleoperating system is realized The fixed time stability of the master-slave robot's mutual position and trajectory tracking. The beneficial effects of the invention are: it is closer to reality; it has more engineering significance, considers the unavoidable communication time delay between master and slave robots, and the considered time delay is a more realistic mixed time delay; realizes fixed time tracking, The method of the present invention has a stronger ability to adapt to engineering requirements, and avoids the singularity of the controller. In addition, the neural network is applied to reduce the control gain, thereby reducing the control cost and control cost.

Description

A Neural Adaptive Fixed Time Control Method for Complex Telemanipulation Technology

technical field

The present invention relates to the technical field of industrial control, in particular to a neural self-adaptive fixed-time control method of complex teleoperation technology.

Background technique

Teleoperation is a multidisciplinary interdisciplinary subject, which integrates the fields of mechanics, electronics, information theory, automation theory and so on. It is worth noting that robotics was born from the combination of two technologies - teleoperation and CNC milling. With the rapid development of technology and industry, robotics and teleoperation technology have also developed rapidly. Due to the comprehensive development of industrial automation and the improvement of science and technology, the rapid update and progress of remote operation technology is meeting the needs of current industrial automation, and can also replace humans to complete high-risk and difficult tasks.

However, in the practical application of teleoperation technology, there will be various problems restricting its development. The most significant one is that the parameter uncertainty of the master-slave robot itself and the external disturbances in teleoperation technology will affect the teleoperation. The technical realization of the goal will also increase the control cost of the teleoperation technology; on the other hand, there is the time delay problem of the communication signal of the communication channel between the master and slave robots in the teleoperation technology, but these problems are unavoidable in practical engineering. of.

In addition, the general execution tasks of teleoperation technology are that multiple tasks are executed continuously. One problem is that if the person using this technology can predict the completion time of each task in advance, it will inevitably reduce the control cost of teleoperation technology, and For practical engineering applications, teleoperation technology that can predict the completion time of tasks has stronger adaptability and better completion efficiency. And the teleoperation system can better combine the status of people in this technology, which can make the whole technology more intelligent and improve the technology's ability to deal with emergencies, and we call this improvement of people's influence in the technology. Teleoperation technology is called HIL teleoperation technology, and HIL teleoperation technology can also better cope with complex real-world engineering applications.

Therefore, in the present invention, the HIL teleoperating system that considers disturbance and model parameter uncertainty and communication time delay is called a complex teleoperating system, and it is of great engineering significance to study the fixed time tracking control method to deal with the complex teleoperating system.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides a kind of neural adaptive non-singular fixed time control method of complex teleoperation technology, which mainly comprises the following steps:

S101: Model the kinematics and dynamics of the master-slave robot of the teleoperation system, and set the tracking error; wherein, the influence of the operator of the master robot on the master robot and the influence of environmental factors on the master robot are added to the established model. Influence from robots;

S102: Establish a control framework for the influence of the operator of the master robot on the entire teleoperation system and complex communication between the master and slave robots. The communication includes constant time delay, time-varying time delay and random time delay effects;

S103: Design a neural adaptive non-singular fixed-time control method, and combine the kinematics and dynamics models to realize bilateral fixed-time trajectory tracking control of a master-slave robot in a complex teleoperating system.

Further, in step S101, the specific steps of establishing a kinematics and dynamics model and setting the tracking error include:

S201: Establish the conventional kinematics and dynamics model of the teleoperating system, as shown in formula (1):

均为n×1的向量，它们分别为任务空间中的广义坐标和广义速 度；M_i(q_i)是n×n的矩阵，它是一个对称正定惯性矩阵；

是n×n的矩阵，它是包 含科氏力和离心力的矢量；g_i(q_i)是n×1的列向量，它的物理含义是重力转矩；d_i(t)是n× 1的列向量，它代表的是有界的输入扰动；τ_i(t)是n×1的列向量，它代表的是控制输入； h_i(q_i)代表的是关节空间坐标对于任务空间坐标的映射；J_i(q_i)＝θh_i(q_i)/θq_in×n的矩阵， 它表示雅克比矩阵；F_i是n×1的向量：F_m代表主机器人的操作员对主机器人的影响力，F_s代表环境因素对从机器人的影响以力；F_s是根据实际应用情况预先设定的值，且F_s＜f， 其中f是预设的有界常数；n代表遥操作系统中主从机器人的维度；In the above formula, i∈{m, s} represents the master robot and the slave robot respectively; q _i (t) is an n×1 column vector, which represents the angle of each joint of the robot; x _i and

Both are n×1 vectors, which are the generalized coordinates and the generalized velocity in the task space respectively; M _i (q _i ) is an n×n matrix, which is a symmetric positive definite inertia matrix;

is an n×n matrix, which is a vector containing the Coriolis force and centrifugal force; g _i (q _i ) is an n×1 column vector whose physical meaning is gravitational torque; d _i (t) is n× 1 , which represents the bounded input perturbation; τ _i (t) is the n×1 column vector, which represents the control input; h _i (q _i ) represents the joint space coordinates for the task space coordinates The mapping of J _i (q _i ) = θhi (q _i )/θq _{i n} ×n matrix, which represents the Jacobian matrix; F _i is an n×1 vector: F _m represents the operator of the main robot to the main The influence of the robot, F _s represents the influence of environmental factors on the slave robot; F _s is a preset value according to the actual application, and F _s <f, where f is a preset bounded constant; n represents the remote The dimension of the master-slave robot in the operating system;

S202: Express the uncertainty of physical parameters contained in the master-slave manipulator as:

和g_i(q_i)均为动力学参数；M_0i(q_i)、

和g_0i(q_i)分别为对 应动力学参数的实际值的估计值；ΔM_i(q_i)、

和Δg_i(q_i)是对应动力学参数的不确 定项，也就是实际值与估计值的差值；In the above formula, M _i (q _i ),

and g _i (q _i ) are kinetic parameters; M _0i (q _i ),

and g _0i (q _i ) are estimates of the actual values of the corresponding kinetic parameters, respectively; ΔM _i (q _i ),

and Δg _i (q _i ) are the uncertainty terms of the corresponding kinetic parameters, that is, the difference between the actual value and the estimated value;

Defining the intermediate variable H _i , the formula (3) can be obtained:

S203: Combine the formula (1) and the formula (3) to obtain the system equation of the final kinematics and dynamic model of the master-slave robot of the teleoperated system, as shown in the formula (4):

In the above formula, the subscript i=m represents the relevant parameters of the master robot, and the subscript i=s represents the relevant parameters of the slave robot;

S204: According to the system equation (4) of the final kinematics and dynamics model, obtain the mathematical expression of the complex teleoperation system master-slave robot tracking each other to achieve the goal required by the teleoperation technology:

In the above formula, e _i is the tracking error of the master-slave robot, that is, _em is the tracking error of the master robot tracking the slave robot, _es is the tracking error of the slave robot tracking the master robot; T _i is the mixed time when the master-slave robot communicates Delay: _Tm is the time delay when the master robot communicates, and T _s is the time delay when the slave robot communicates.

Further, in step S101, the control strategy includes the following three situations:

Case 1: The main robot tracks the reference trajectory without being influenced by the operator: F _m = 0;

Case 2: The operator applies a spring-damping force to manipulate the main robot to move to the reference trajectory: F _m = -ξv; where ξ is the damping coefficient and v is the velocity;

Case 3: The operator applies a bounded force to change the reference trajectory of the main robot F _m =sup _t≥0 ||F _m || _∞ ≤c, where c is a bounded constant and is a preset value, sup _{t≥ 0} A represents the supremum of A within the domain of t ≥ 0.

Further, in step S102, the communication between the master and slave robots adopts mixed time delay communication, which includes constant time delay, time-varying time delay and random time delay, and the specific expression is shown in formula (6):

是随机时滞，T_i，3＝0.1random(1，1，[110])。Among them, T _i,1 is a constant delay, and satisfies 0≤T _i,1 ≤1; T _i,2 is a time-varying delay, and satisfies

is a random delay, T _i,3 = 0.1 random(1, 1, [110]).

Further, in step S103, the neural adaptive non-singular fixed-time controller includes a non-singular fixed-time sliding mode surface, a neural adaptive rate and a task space non-singular controller; specifically:

S301: Construct a non-singular fixed-time sliding mode surface based on a non-singular fixed-time sliding mode control algorithm, and the specific expression is shown in formula (7):

In the above formula, i∈{m, s} represents the master robot and the slave robot respectively; l ₁ , χ ₁ , l ₂ , χ ₂ are preset positive odd numbers, and these four parameters meet the conditions: l ₁ >χ ₁ , l ₂ <χ ₂ <2l ₂ ; α ₁ =diag[α ₁₁ ,...,α _1n ] and β ₁ =diag[β ₁₁ ,...,β _1n ] are positive definite matrices;

S302: Construct the neural adaptation rate based on the RBF neural network, as follows:

The RBF neural network expression is shown in formula (8):

是输入数据向量；

是RBF神经网络逼近误差；c_j∈R^c是第j个神经元的中心；σ_j表示第j个神经元的宽度；In the above formula, Wi ∈ R _n ^×b represents the weight matrix of n neurons;

is the input data vector;

is the RBF neural network approximation error; c _j ∈ R ^c is the center of the jth neuron; σ _j represents the width of the jth neuron;

The adaptive control method and the RBF neural network are combined to construct the adaptive rate of the neural network, as shown in formula (9):

In the above formula, Λ _i and λ _i are positive numbers pre-designed by ourselves; s _i is a non-singular fixed-time sliding mode surface.

Further, the expression of the task space non-singular controller is shown in formula (10):

τ _i =τ _0i +τ _ei (10)

In the above formula,

η_i是预设的控制增 益，且

其中

in,

η _i is the preset control gain, and

in

Further, in step S103, the step that realizes the bilateral fixed time tracking control of the master-slave robot of complex teleoperation system is:

S401: Substitute the task space non-singular controller shown in formula (10) into the system equation of the final kinematics and dynamics model of the master-slave robot with a complex teleoperated system shown in formula (4) to form a closed-loop system, such as Formula (11) shows:

Convert equation (11) mathematically to:

S402: Combine the closed-loop system constructed in step S401 to construct a V function, that is, a Lyapunov function, as shown in formula (12):

V = V _m +V _s (12)

其中，

In the above formula,

in,

S403: (Through the previous conditions and the design of the V function, it can be obtained that the V function is positive definite) Derive the V function to obtain formula (13):

S404: Substitute the derivative of the fixed-time sliding mode surface into formula (13) to obtain formula (14):

S405: Through the fixed time criterion, it is obtained that the fixed time sliding mode surface and the first derivative of the V function are both fixed time convergence, and the V function is positive definite and the first derivative of the V function is negative definite, and then the neural adaptive fixed time is obtained. The complex teleoperating system of the control method can have a fixed-time convergence capability, and the teleoperating system can complete the fixed-time tracking control target, and the tracking upper bound time is as follows:

In the above formula, all parameters have nothing to do with the initial state of the teleoperating system, but are only related to the parameters of the neural adaptive non-singular fixed-time control method, and the parameters of the neural adaptive non-singular fixed-time control method are controlled by the operator. pre-setting.

The beneficial effects brought by the technical solution provided by the present invention are: the technical solution proposed by the present invention has the following advantages:

1) It is closer to reality, considering the parameter uncertainty and external disturbance in the master-slave robot model, making the designed control method more practical;

2) It has more engineering significance, considering the unavoidable communication time delay between master and slave robots, and the considered time delay is a more realistic hybrid time delay, while avoiding the possible singularity of the usual fixed-time controller. ;

3) The fixed time tracking is realized, so that the method of the present invention has a stronger ability to adapt to engineering requirements, and the neural network is applied, which reduces the tremor and thus reduces the control cost and control cost.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, in which:

Fig. 1 is the flow chart of the neural adaptive non-singular fixed time control method of a kind of complex teleoperation technology in the embodiment of the present invention;

Fig. 2 is a kind of neural self-adaptive fixed time control method of complex teleoperation technology in the embodiment of the present invention exemplifies the flow chart;

3 is a mechanical structure diagram of a master-slave robot in an embodiment of the present invention;

4 is a mixed time-delay diagram when a communication channel is established in a complex teleoperating system in an embodiment of the present invention;

5 is a position tracking diagram of a complex teleoperating system in an embodiment of the present invention;

6 is a position tracking diagram of a complex teleoperating system in an embodiment of the present invention;

7 is a position tracking error diagram of a complex teleoperating system in an embodiment of the present invention;

8 is a position tracking error diagram of a complex teleoperating system in an embodiment of the present invention;

Fig. 9 is the force exerting diagram of the operator in the complex teleoperating system in the embodiment of the present invention;

FIG. 10 is a diagram of trajectory tracking of a complex teleoperating system and a trajectory tracking diagram of an XY plane in an embodiment of the present invention.

Detailed ways

In order to have a clearer understanding of the technical features, objects and effects of the present invention, the specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

The embodiments of the present invention provide a neural adaptive non-singular fixed-time control method of complex teleoperation technology; provide bilateral fixed-time tracking of HIL teleoperation system considering parameter uncertainty and external disturbance and complex mixed time delay, And the control cost requirements of master-slave robot are satisfied by selecting appropriate control gain and neural adaptive rate parameters.

Please refer to Fig. 1, Fig. 1 is the flow chart of the neural adaptive non-singular fixed time control method of a kind of complex teleoperation technology in the embodiment of the present invention, specifically comprises the following steps:

S101: Model the kinematics and dynamics of the master-slave robot of the teleoperation system, and set the tracking error; wherein, the influence of the operator of the master robot on the master robot and the influence of environmental factors on the master robot are added to the established model. From the influence of robots to force;

S102: Establish a control strategy for the influence of the operator of the master robot on the entire teleoperating system and complex communication between the master and slave robots;

The teleoperating system under this strategy is called the human-in-the-loop teleoperating system, or HIL teleoperating system for short; then the control strategy is embodied in the following three situations:

Case 1: The main robot needs to track the reference trajectory without being affected by the operator, that is, the operator does not have any influence on the main robot; (F _m = 0)

Case 2: The operator applies the spring-damping force to manipulate the main robot to move to the reference trajectory, that is, the operator controls or influences the main robot in the form of spring-damping force, thereby indirectly affecting the entire teleoperating system to achieve the operator's desire. The purpose to be achieved; (F _m = -ξv, where ξ is the damping coefficient and v is the velocity)

Case 3: The operator applies a bounded force to change the reference trajectory of the main robot, that is, the operator applies a force to the main robot. The operator's force temporarily changes the motion trajectory of the master-slave robot in the entire teleoperation system, so that the teleoperation system can have a more intelligent response method because of the operator; (F _m =sup _t≥0 ||F _m || _∞ ≤c, where c is a bounded constant).

The communication channel of the teleoperating system is established between the master-slave robot. The communication channel of the master-slave robot is far away, and wireless transmission is often used, so there must be communication interference and communication time lag, so the simultaneous occurrence of communication interference and communication time lag is The time delay of communication is often not constant, or it is a separate time delay situation, and the time delay must be complex and chaotic. Therefore, in the embodiment of the present invention, a mixed time delay communication is established, that is, at the same time in the delay Constant time delay, time-varying time delay and random time delay are considered; and the HIL teleoperating system with mixed time delay is defined as a complex teleoperating system.

S103: Design a neural adaptive non-singular fixed-time control method, and combine the kinematics and dynamics models to realize bilateral fixed-time trajectory tracking control of a master-slave robot in a complex teleoperating system.

In step S101, the specific steps of establishing a kinematic and dynamic model and setting the tracking error include:

S201: Establish the conventional kinematics and dynamics model of the teleoperating system, as shown in formula (1):

均为n×1的向量，它们分别为任务空间中的广义坐标和广义速 度；M_i(q_i)是n×n的矩阵，它是一个对称正定惯性矩阵；

是n×n的矩阵，它是包 含科氏力和离心力的矢量；g_i(q_i)是n×1的列向量，它的物理含义是重力转矩；d_i(t)是n× 1的列向量，它代表的是有界的输入扰动；τ_i(t)是n×1的列向量，它代表的是控制输入； h_i(q_i)代表的是关节空间坐标对于任务空间坐标的映射；

是n×n的矩 阵，它表示雅克比矩阵；F_i是n×1的向量：F_m代表主机器人的操作员对主机器人的影响力，F_s代表环境因素对从机器人的影响以力；F_s是根据实际应用情况预先设定的值，且F_s＜f，其中f是预设的有界常数；n代表遥操作系统中主从机器人的维度；In the above formula, i∈{m, s} represents the master robot and the slave robot respectively; q _i (t) is an n×1 column vector, which represents the angle of each joint of the robot; x _i and

Both are n×1 vectors, which are the generalized coordinates and the generalized velocity in the task space respectively; M _i (q _i ) is an n×n matrix, which is a symmetric positive definite inertia matrix;

is an n×n matrix, which is a vector containing the Coriolis force and centrifugal force; g _i (q _i ) is an n×1 column vector whose physical meaning is gravitational torque; d _i (t) is n× 1 , which represents the bounded input perturbation; τ _i (t) is the n×1 column vector, which represents the control input; h _i (q _i ) represents the joint space coordinates for the task space coordinates mapping;

is an n×n matrix, which represents the Jacobian matrix; F _i is an n×1 vector: F _m represents the influence of the operator of the master robot on the master robot, and F _s represents the influence of environmental factors on the slave robot; F _s is a preset value according to the actual application situation, and F _s <f, where f is a preset bounded constant; n represents the dimension of the master-slave robot in the teleoperating system;

S202: Express the uncertainty of physical parameters contained in the master-slave manipulator as:

和g_i(q_i)均为动力学参数；M_0i(q_i)、

和g_0i(q_i)分别为对 应动力学参数的实际值的估计值；ΔM_i(q_i)、

和Δg_i(q_i)是对应动力学参数的不确 定项，也就是实际值与估计值的差值；In the above formula, M _i (q _i ),

and g _i (q _i ) are kinetic parameters; M _0i (q _i ),

and g _0i (q _i ) are estimates of the actual values of the corresponding kinetic parameters, respectively; ΔM _i (q _i ),

and Δg _i (q _i ) are the uncertainty terms of the corresponding kinetic parameters, that is, the difference between the actual value and the estimated value;

Defining the intermediate variable H _i , the formula (3) can be obtained:

S203: Combine the formula (1) and the formula (3) to obtain the system equation of the final kinematics and dynamic model of the master-slave robot of the teleoperated system, as shown in the formula (4):

In the above formula, the subscript i=m represents the relevant parameters of the master robot, and the subscript i=s represents the relevant parameters of the slave robot;

S204: According to the system equation (4) of the final kinematics and dynamics model, obtain the mathematical expression that the master and slave robots of the teleoperation system track each other to achieve the goal required by the teleoperation technology:

In the above formula, e _i is the tracking error of the master-slave robot, that is, _em is the tracking error of the master robot tracking the slave robot, _es is the tracking error of the slave robot tracking the master robot; T _i is the mixed time when the master-slave robot communicates Delay: _Tm is the time delay when the master robot communicates, and T _s is the time delay when the slave robot communicates.

In step S102, the control strategy includes the following three situations:

Case 1: The main robot tracks the reference trajectory without being influenced by the operator: F _m = 0;

Case 2: The operator applies a spring-damping force to manipulate the main robot to move to the reference trajectory: F _m = -ξv; where ξ is the damping coefficient and v is the velocity;

Case 3: The operator applies a bounded force to change the reference trajectory of the main robot F _m =sup _t≥0 ||F _m || _∞ ≤c, where c is a bounded constant and is a preset value, sup _{t≥ 0} A represents the supremum of A within the domain of t ≥ 0.

In this embodiment of the present invention, a teleoperating system that satisfies these three conditions is called a HIL teleoperating system.

In step S102, the communication between the master and slave robots adopts mixed time delay communication, which includes constant time delay, time-varying time delay and random time delay, and the specific expression is shown in formula (6):

T_i，3是随机时滞，通过T_i，3＝0.1random(1，1，[110])这个函数得到；Among them, T _i,1 is a constant delay, and satisfies 0≤T _i,1 ≤1; T _i,2 is a time-varying delay, and satisfies

T _i,3 is a random time delay, obtained by the function T _i,3 =0.1random(1,1,[110]);

In the embodiment of the present invention, the HIL teleoperating system with the above mixed time delay is defined as a complex teleoperating system.

In step S103, the neural adaptive non-singular fixed-time controller includes a non-singular fixed-time sliding mode surface, a neural adaptive rate, and a task space non-singular controller; specifically:

S301: Construct a non-singular fixed-time sliding mode surface based on a non-singular fixed-time sliding mode control algorithm, and the specific expression is shown in formula (7):

In the above formula, i∈{m, s} represents the master robot and the slave robot respectively; l ₁ , χ ₁ , l ₂ , χ ₂ are preset positive odd numbers, and these four parameters meet the conditions: l ₁ >χ ₁ , l ₂ <χ ₂ <2l ₂ ; α ₁ =diag[α ₁₁ ,...,α _1n ] and β ₁ =diag[β ₁₁ ,...,β _1n ] are positive definite matrices;

S302: Construct the neural adaptation rate based on the RBF neural network, as follows:

The RBF neural network expression is shown in formula (8):

代表主从机器人转置下的神经网络自 适应率；

是输入数据向量；

是RBF神经网络逼近误差(将公式(3) 中H_i所包含的三个未知量ΔM_i(q_i)、

和Δg_i(q_i)带入RBF神经网络表达式，采用 RBF神经网络逼近方法得到RBF神经网络的参数

无需具体计算出ΔM_i(q_i)、

和Δg_i(q_i)的具体值)；c_j∈R^c是第j个神经元的中心；σ_j表示第j个神经元的宽度；In the above formula, Wi ∈ R _n ^×b represents the weight matrix of n neurons;

Represents the neural network adaptation rate under the master-slave robot transposition ;

is the input data vector;

is the approximation error of the RBF neural network (the three unknown quantities ΔM _i (q _{i )} ,

and Δg _i (q _i ) are brought into the RBF neural network expression, and the RBF neural network approximation method is used to obtain the parameters of the RBF neural network

There is no need to specifically calculate ΔM _i (q _i ),

and Δg _i (q _i ); c _j ∈ R ^c is the center of the jth neuron; σ _j represents the width of the jth neuron;

The adaptive control method is used to optimize the application of the RBF neural network in the controller, and the adaptive rate of the neural network is constructed, as shown in formula (9):

In the above formula, Λ _i and λ _i are preset positive numbers; s _i is the non-singular fixed-time sliding mode surface designed in formula (7).

The expression of the task space non-singular controller is shown in Equation (10):

τ _i =τ _0i +τ _ei (10)

In the above formula,

η_i是由操作员预先 设定的控制增益，且需要满足

其中

in,

η _i is the control gain preset by the operator and needs to be satisfied

in

In step S103, the steps of realizing the fixed-time master-slave robot mutual tracking control of the complex teleoperation system are:

S401: Substitute the task space non-singular controller shown in formula (10) into the system equation of the final kinematics and dynamics model of the master-slave robot with a complex teleoperated system shown in formula (4) to form a closed-loop system, such as Formula (11) shows:

Convert equation (11) mathematically to:

S402: Combine the closed-loop system constructed in step S401 to construct a V function, that is, a Lyapunov function, as shown in formula (12):

V = V _m +V _s (12)

其中，

In the above formula,

in,

S403: (Through the previous conditions and the design of the V function, it can be obtained that the V function is positive definite) Derive the V function to obtain formula (13):

S404: Substitute the derivative of the non-singular fixed-time sliding mode surface into formula (13) to obtain formula (14):

And because of the fixed time criterion, the fixed time criterion is expressed as follows:

如果存在一个正定的连续函 数，如下：Fixed time criterion: (Consider a simple system

If there is a positive definite continuous function as follows:

In the above formula, α>0, β>0; m, n, p, q are positive odd numbers and satisfy m>n, p<q; then the origin is the timing stable equilibrium of the system, and the settling time function T ₁ is as follows :

S405: Through the fixed time criterion, it is obtained that the fixed time sliding mode surface and the first derivative of the V function are both fixed time convergence, and the V function is positive definite and the first derivative of the V function is negative definite, and then the neural adaptive non-singularity is obtained. The complex teleoperating system with fixed time control method can have fixed time convergence capability, the system can complete fixed time master-slave tracking, and the tracking upper bound time is as follows:

In the embodiment of the present invention, taking the robot shown in Figure 3 as an example, the technical solution proposed by the present invention is illustrated, with reference to the flow chart shown in Figure 2:

L1: Model the kinematics and dynamics of the master-slave robot, and set the tracking error;

Referring to Figure 3, the following parameter table can be obtained:

Table 1 Parameters of two-degree-of-freedom manipulators

Among them, l _i , q, r, and m are shown in Fig. 3, which represent the length, included angle, center of mass position, and mass of each robotic arm, respectively.

The end position of the two-degree-of-freedom manipulator can be easily obtained from Table 1:

x=[x ₁ x ₂ ]

其中雅克比矩阵J(q)可以计算得到，J(q)如下所示：where x ₁ =l ₁ cos(q ₁ )+l ₂ coS(q ₁ +q ₂ ), x ₂ =l ₁ sin(q ₁ )+l ₂ sin(q ₁ +q ₂ ), and

where the Jacobian matrix J(q) can be calculated, and J(q) is as follows:

J ₁₁ , J ₁₂ , J ₂₁ , J ₂₂ are:

J ₁₁ =-l1sin(q ₁ )-l ₂ sin(q ₁ +q ₂ )

J ₁₂ =-l ₂ sin(q ₁ +q ₂ )

J ₂₁ =l ₁ cos(q ₁ )+l ₂ cos(q ₁ +q ₂ )

J ₂₂ =l ₂ cos(q ₁ +q ₂ )

The next dynamics and kinematics modeling models are:

是n×1的向量，它们分别为任务空间中的广义坐标和广义速度；M_i(q_i) 是n×n的矩阵，它是一个对称正定惯性矩阵；

是n×n的矩阵，它是包含科氏力和 离心力的矢量；g_i(q_i)是n×1的列向量，它的物理含义是重力转矩；d_i(t)是n×1的列向 量，它代表的是有界的输入扰动；τ_i(t)是n×1的列向量，它代表的是控制输入；h_i(q_i)代 表的是关节空间坐标对于任务空间坐标的映射；

是n×n的矩阵，它表示 雅克比矩阵；F_i是n×1的向量，它代表主从机器人受到的操作者或者环境造成的力。where i∈{m, s} represents the master robot and the slave robot, respectively, where q _i (t) is an n×1 column vector, which represents the angle of each joint;

is an n×1 vector, which are the generalized coordinates and the generalized velocity in the task space, respectively; M _i (q _i ) is an n×n matrix, which is a symmetric positive definite inertia matrix;

is an n×n matrix, which is a vector containing the Coriolis force and centrifugal force; g _i (q _i ) is an n×1 column vector whose physical meaning is gravitational torque; d _i (t) is an n×1 , which represents the bounded input perturbation; τ _i (t) is the n×1 column vector, which represents the control input; h _i (q _i ) represents the joint space coordinates for the task space coordinates mapping;

is an n×n matrix, which represents the Jacobian matrix; F _i is an n×1 vector, which represents the force caused by the operator or the environment on the master-slave robot.

Since the robotic arm contains uncertainty of physical parameters, we express the uncertainty of parameters as:

M _i (q _i )=M _0i (q _i )+ΔM _i (q _i )

g _i (q _i )=g _0i (q _i )+Δg _i (q _i ),

和g_0i(q_i)是对于实际值的估计值，而ΔM_i(q_i)、

和Δg_i(q_i) 是不确定项，也就是估计值与实际值的差值。那么我们可以得到：where M _0i (q _i ),

and g _0i (q _i ) are estimates for the actual values, while ΔM _i (q _i ),

and Δg _i (q _i ) are the uncertainty terms, that is, the difference between the estimated value and the actual value. Then we can get:

Therefore, the system equations are retrieved:

where i∈{m, s} represent the master robot and the slave robot, respectively, and:

The mathematical expression for the master-slave robot to track each other to achieve the goal required by the teleoperation technology is:

Among them, T _i is the mixed time delay when the master-slave robot communicates.

L2: Referring to Figure 9, the operator's force is established; referring to Figure 4, the communication channel is established. The mixed delay includes constant delay, time-varying delay and random delay. The specific expressions of these three delays are as follows:

T_i，3是随 机时滞且它是通过T_i，3＝0.1random(1，1，[110])这个函数得到。Among them, T _i,1 is a constant delay and satisfies 0≤T _i,1 ≤1; T _i,2 is a time-varying delay and satisfies

T _i,3 is a random time delay and it is obtained by the function T _i,3 =0.1random(1,1,[110]).

L3: The target trajectory for trajectory tracking is set to:

L31: The mathematical expression of the sliding surface is as follows:

Among them, i∈{m, s} represents the master robot and the slave robot respectively, l ₁ , χ ₁ , l ₂ , χ ₂ are positive odd numbers, and these four parameters satisfy l ₁ >χ1, l ₂ <χ ₂ <2l ₂ , α ₁ =diag[α ₁₁ , . . . , α _1n ] and β ₁ =diag[β ₁₁ , . . . , β _1n ] are positive definite matrices. The adaptive rate of the neural network is designed as follows:

Among them, Λ _i and λ _i are parameters set by the operator in advance, and they need to be positive constants; s _i is the non-singular fixed-time sliding mode surface designed before.

L32: Substitute the neural adaptive non-singular fixed-time control method into the complex teleoperating system to form a closed-loop system as follows:

Converting it mathematically again can change the above closed-loop system into the following form again:

L33: Combine the closed-loop system constructed in step S31 to construct a Lyapunov function (V function)

V=V _m +V _s ,

in

和

which satisfy

and

First, through the previous conditions and the design of the V function, it can be obtained that the V function is positive definite. At this time, the V function is derived to obtain the following form:

Substituting the sliding surface into the first derivative of the V function, the above formula can be re-expressed as:

And because of the fixed time criterion, the fixed time criterion is expressed as follows:

如果存在一个正定的连续函 数，如下：Fixed time criterion: (Consider a simple system

If there is a positive definite continuous function as follows:

Where α>0, β>0, m, n, p, q are positive odd numbers and satisfy m>n, p<q. Then the origin is the timed stable equilibrium of the system at this time, and the settling time function T ₁ is as follows:

q_s＝[0.5，1]^T，

L34: Given control parameters l ₁ =9, χ ₁ =7, l ₂ =5, χ ₂ =9, α ₁ =diag(1,1), β ₁ =diag(1,1), η _i =50 , Λ _m =2.47, Λ _i =1.32, λ _m =1.1, λ _s =0.8. Set the initial value of the system state (unit: rads/s): q _m = [0.5, 1] ^T ,

q _s = [0.5, 1] ^T ,

Figure 5 and Figure 6 represent the position tracking diagram of the complex teleoperating system; Figure 7 and Figure 8 represent the position tracking error diagram of the complex teleoperating system; Figure 9 represents the force diagram of the operator in the complex teleoperating system ; Figure 10 shows the trajectory tracking of the complex teleoperation system and the trajectory tracking diagram of the XY plane. The trajectories are perfectly coincident, which proves that the goal of the teleoperation technology is completed.

The beneficial effects of the present invention are:

1) It is closer to reality, considering the parameter uncertainty and external disturbance in the master-slave robot model, making the designed control method more practical;

2) It has more engineering significance, considering the unavoidable communication time delay between master and slave robots, and the considered time delay is a more realistic hybrid time delay, while avoiding the possible singularity of the usual fixed-time controller. ;

3) The fixed time tracking is realized, so that the method of the present invention has a stronger ability to adapt to engineering requirements, and the neural network is applied, which reduces the tremor and thus reduces the control cost and control cost.

The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

Claims (5)

1. A neural self-adaptive nonsingular fixed time control method of a complex teleoperation technology is characterized by comprising the following steps of: the method comprises the following steps:

s101: performing kinematics and dynamics modeling on a master robot and a slave robot of a teleoperation system, and setting a tracking error; wherein, the influence of the operator of the master robot on the master robot and the influence of environmental factors on the slave robot are added into the established model;

s102: establishing a control strategy for the influence of an operator of the main robot on the whole teleoperation system and complex information communication between the main robot and the auxiliary robot, wherein the communication comprises the influence of constant time lag, time-varying time lag and random time lag;

s103: designing a neural self-adaptive nonsingular fixed time control method, and combining the kinematics and the dynamics model to realize fixed time bilateral trajectory tracking control of a master robot and a slave robot in a teleoperation system;

in step S103, the neural adaptive fixed-time controller includes a fixed-time nonsingular sliding-mode surface, a neural adaptive rate, and a nonsingular task space controller; the method specifically comprises the following steps:

s301: constructing a nonsingular fixed time sliding mode surface based on a nonsingular fixed time sliding mode control algorithm, wherein a specific expression is shown as a formula (7):

in the above formula, i ∈ { m, s } represents the master robot and the slave robot respectively; l₁，χ₁，l₂，χ₂Is a preset positive odd number, and the four parameters meet the condition: l₁＞χ₁，l₂＜χ₂＜2l₂；α₁＝diag[α₁₁，…，α_1n]And beta₁＝diag[β₁₁，…，β_1n]Is a positive definite matrix;

s302: the neural self-adaptive rate is constructed based on the RBF neural network, and the method specifically comprises the following steps:

the RBF neural network expression is shown in formula (8):

in the above formula, W_i∈R^n×bA weight matrix representing n neurons;

representing the self-adaptive rate of the neural network under transposition;

is an input data vector;

is an RBF neural network approximation error; c. C_j∈R^cIs the center of the jth neuron; sigma_jRepresents the width of the jth neuron; n is consistent with the robot dimension n in the system;

combining the self-adaptive control method with the RBF neural network to construct the self-adaptive rate of the neural network, as shown in formula (9):

in the above formula, Λ_iAnd λ_iIs a positive number designed in advance; s_iIs a fixed time sliding mode surface;

s303: the expression for constructing the nonsingular task space controller is shown in formula (10):

τ_i＝τ_0i+τ_ei (10)

in the above formula, the first and second carbon atoms are,

wherein,

η_iis a preset control gain, and

wherein

2. The neural adaptive nonsingular fixed time control method of the complex teleoperation technology according to claim 1, characterized in that: in step S101, the specific steps of establishing a kinematic and kinetic model and setting a tracking error include:

s201: establishing a conventional kinematic and dynamic model of the teleoperation system, as shown in formula (1):

in the above formula, i ∈ { m, s } represents the master robot and the slave robot respectively; q. q.s_i(t) is an n x 1 column vector representing the angle of each joint of the robot; x is the number of_iAnd

the vectors are n multiplied by 1 vectors which are generalized coordinates and generalized speeds in the task space respectively; m_i(q_i) Is an n x n matrix which is a symmetric positive definite inertia matrix;

is an n x n matrix, which is a vector containing coriolis forces and centrifugal forces; g_i(q_i) Is a column vector of n x 1, whose physical meaning is gravity torque; d_i(t) is an n x 1 column vector, which represents a bounded input perturbation; tau is_i(t) is an n × 1 column vector, which represents the control input; h is_i(q_i) Representing the mapping of joint space coordinates to task space coordinates;

is an n x n matrix, which represents the Jacobian matrix,

is represented by J_i(q_i) Transposing; f_iIs an n × 1 vector: f_mRepresenting the influence of the operator of the main robot on the main robot, F_sRepresenting the influence of environmental factors on the slave robot; f_sIs a value preset according to the actual application, and F_s< f, where f is a preset bounded constant; n represents the dimension of a master robot and a slave robot in the teleoperation system;

s202: the uncertainty of the physical parameters contained in the master-slave mechanical arm is represented as:

in the above formula, M_i(q_i)、

And g_i(q_i) Are all kinetic parameters; m_0i(q_i)、

And g_0i(q_i) Respectively corresponding to kinetic parametersAn estimated value of the actual value; Δ M_i(q_i)、

And Δ g_i(q_i) Is an uncertainty term corresponding to the kinetic parameter, i.e. the difference between the actual value and the estimated value;

defining intermediate variable H_iObtaining the formula (3):

s203: and (3) combining the formula (1) and the formula (3) to obtain a system equation of a final kinematics and dynamics model of the master-slave robot of the teleoperation system, as shown in the formula (4):

in the above formula, when the subscript i is m, the subscript i represents the relevant parameters of the master robot, and when the subscript i is s, the subscript i represents the relevant parameters of the slave robot;

s204: and obtaining a mathematical expression of the teleoperation system for mutually tracking the master robot and the slave robot to achieve the target required by the teleoperation technology according to the system equation (4) of the final kinematics and dynamics model, wherein the mathematical expression comprises the following steps:

in the above formula, e_iAs tracking error of master-slave robots, i.e. e_mTracking error of slave robot for master robot, e_sTracking the tracking error of the master robot for the slave robot; t is_iIs the mixed time lag of master-slave robot communication: t is_mTime lag, T, for communication of the host robot_sIs the time lag when communicating from the robot.

3. The neural adaptive nonsingular fixed time control method of the complex teleoperation technology according to claim 2, characterized in that: in step S101, the control strategy includes the following three cases:

the first condition is as follows: the main robot tracks the reference trajectory without being affected by the operator: f_m＝0；

Case two: the operator applies spring-damping force to maneuver the main robot to the reference trajectory: f_m- ξ v; where ξ is the damping coefficient and v is the velocity;

case three: the operator applies a bounded force to change the reference trajectory F of the main robot_m＝sup_t≥0||F_m||_∞C is a bounded constant, a preset value, sup_t≥0A represents the supremum of A in the domain where t ≧ 0.

4. A neural adaptive nonsingular fixed time control method of a complex teleoperation technique according to claim 3, characterized in that: in step S102, the communication between the master and slave robots is a hybrid time lag communication, which includes a constant time lag, a time-varying time lag, and a random time lag, and the specific expression is as shown in formula (6):

wherein, T_i，1Is constantly stagnant and satisfies 0. ltoreq. T_i，1≤1；T_i，2Is time-varying and time-lag, and satisfies

T_i，3Is a random time lag, T_i，3＝0.1random(1，1，[1 10])。

5. The neural adaptive nonsingular fixed time control method of the complex teleoperation technology according to claim 4, characterized in that: in step S103, the steps of implementing fixed time tracking control of the master-slave robot of the complex teleoperation system are:

s401: substituting the task space controller shown in formula (10) into the system equation of the final kinematics and dynamics model of the master-slave robot of the teleoperation system shown in formula (4) to form a closed-loop system, as shown in formula (11):

mathematically converting equation (11) to:

s402: in conjunction with the closed-loop system constructed in step S401, a V function, i.e., a lyapunov function, is constructed, as shown in equation (12):

V＝V_m+V_s (12)

in the above formula, the first and second carbon atoms are,

wherein,

s403: the V function is derived to obtain equation (13):

s404: substituting the derivative of the fixed-time sliding-mode surface into equation (13) to obtain equation (14):

s405: according to the fixed time criterion, the fixed time sliding mode surface and the first derivative of the V function are both fixed time convergence, the V function is positively determined, and the first derivative of the V function is negatively determined, so that the complex teleoperation system applying the neural self-adaptive fixed time control method has fixed time convergence capability, the teleoperation system can complete a fixed time tracking control target, and the tracking upper bound time is as follows:

in the above formula, all parameters are independent of the initial value of the teleoperation system state, and only related to the neural adaptive fixed time controller parameters, and the neural adaptive fixed time controller parameters are preset by an operator.

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