H-infinity fuzzy fault-tolerant control method based on multilateral teleoperation system

Abstract

The present invention discloses an H-infinity fuzzy fault-tolerant control method based on a multilateral teleoperation system. First, a nonlinear multilateral teleoperation system is modeled as a T-S fuzzy system with a communication time-varying delay. Then, according to the characteristics of partial failure of the actuator and multiple types of communication delays, an H-infinity fuzzy fault-tolerant architecture is established by using the method of a free weight matrix. The communication delay between the master and slave robots is asynchronous and time-varying. Then, by establishing a modally related Lyapunov-Krasovskii functional, sufficient conditions are obtained to make the closed-loop system not only stochastic mean square stable but also have specified H∞ noise suppression performance. Then, the nonlinearity of the matrix inequality under the sufficient condition is processed, and the controller gain is obtained using Matlab. The present invention has H∞ disturbance suppression performance while taking into account the random mean square stability of the system, and designs an asynchronous fault-tolerant controller so that the system can still maintain a respectable operating state when there is an actuator failure.

Description

Technical Field

[0001] The present invention relates to the technical field of fault-tolerant control, and in particular to a fault-tolerant control method for applying a TS fuzzy model to a multilateral teleoperation system with partial actuator failure and communication time-varying delay, and in particular to an H-infinity fuzzy fault-tolerant control method based on a multilateral teleoperation system. Background Art

[0002] In recent years, robot technology has developed rapidly. However, due to the limitations of current existing technologies, it is difficult for robots to complete many complex tasks autonomously. Therefore, in the face of complex tasks or environments that humans cannot reach, humans hope to combine their own consciousness with the strong execution power of the robot arm. When performing such tasks, the human operator controls the master robot arm at the master end, sends the command signal to the slave end, and then controls the slave robot arm to perform the task; at the same time, humans can perceive the slave environment through various sensors at the slave end, such as force sensors, tactile sensors, etc., to help humans make correct decisions at the master end. This technology is called teleoperation technology. Generally, a teleoperation system includes only one operator, one master robot arm and one slave robot arm. The task is completed by one robot arm at the slave end. This type of teleoperation system is a single-master single-slave teleoperation system. Many scholars have devoted themselves to the research of single-master single-slave teleoperation systems and have achieved certain research results. However, many complex tasks are difficult to complete with only a single robot arm at the slave end, and multiple robots need to cooperate with each other. For complex tasks at the remote end, multiple slave end robotic arms can cooperate with each other to complete them. Multiple operators can control the slave end robotic arms through multiple master end robotic arms at the master end to complete complex tasks through cooperation. This type of teleoperation system is called a multi-master-slave teleoperation system.

[0003] With the continuous development of science and technology, the control algorithm based on the single-master-slave teleoperation system has developed rapidly. However, the traditional single-master-slave teleoperation system has certain limitations when performing certain tasks and is not suitable for completing coordination tasks. The multi-master-multi-slave teleoperation system makes up for the shortcomings of the single-master-slave teleoperation system. When studying the control of the multi-master-multi-slave teleoperation system, it is necessary not only to ensure the control accuracy and stability of the teleoperation system, but also to ensure the coordination of the slave-end manipulator. How to ensure the stability and coordination of the multi-master-multi-slave teleoperation system has always been a difficult problem. In actual application, when the multi-master-multi-slave teleoperation system performs handling tasks, the slave-end manipulator is often disturbed, including the interference of internal parameters and the interference of the external environment, which will not only affect the effect of the master-slave trajectory tracking, but also affect the coordinated handling tasks.

[0004] At the same time, in reality, the actuators of the system will inevitably have various problems, such as stuck, partial failure, offset failure, etc., and when the multi-master and multi-slave teleoperation system is operating, more components or parts are involved, so the frequency of failures is higher, and these failures will cause the performance of the system to degrade or even crash. It can be imagined that the more complex the components of the multi-master and multi-slave teleoperation system, the higher the failure rate. Therefore, there is an urgent need for a fault-tolerant system that can achieve one or more key components in a faulty state, and the system can still operate stably and safely. This system has a certain tolerance for failures. This type of control technology can enable the system to remain calm when a failure occurs and control the performance indicators within an ideal range. Therefore, the current research in the field of fault-tolerant control is also of great practical significance. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention proposes an H-infinity fuzzy fault-tolerant control method based on a multilateral teleoperation system, which can improve the stability of the control system and the dynamic performance indicators of the system, while taking into account the random mean square stability of the system and making the system have H∞ disturbance suppression performance, so that the system can still maintain an observable operating state when there are disturbances and actuator failures.

[0006] In order to solve the above technical problems, the technical solution of the present invention is:

[0007] An H-infinity fuzzy fault-tolerant control method based on a multilateral teleoperation system comprises the following steps:

[0008] S1. Simulate the multilateral teleoperation system through dynamic model;

[0009] S2. Setting the control torque so that the dynamic model has a gravity compensation effect;

[0010] S3, split the multi-master and multi-slave teleoperation system into an operating system consisting of two master robots and two slave robots, and obtain a new dynamic model;

[0011] S4. Design the controller according to the fault distribution of the actuators in the multilateral teleoperation system;

[0012] S5, simulate the multilateral teleoperation system with partial actuator failure through TS fuzzy control model;

[0013] S6, establishing a control law based on the time delay between the master and slave robots;

[0014] S7. Establish state equations of a multilateral teleoperation system based on fault distribution;

[0015] S8. Fault-tolerant control is achieved by selecting appropriate Lyapunov functions for the state equations of the multilateral teleoperation system;

[0016] S9, fault-tolerant control optimization, that is, designing the gain of the controller.

[0017] Preferably, the dynamic model is an Euler-Lagrange dynamic model, which is expressed as follows:

[0018]

[0019]

[0020] Where j = {m, s}, the subscript m represents the master robot, the subscript s represents the slave robot, and i = {1, ..., N} represents the serial number of the corresponding robot. Respectively represent the acceleration, velocity and displacement in the joint space; M ji (q ji )∈R n×n represents the inertia force matrix; represents the Coriolis effect and centrifugal effect; τ hi ∈R n and τ ei ∈R n represents the human operator force and environmental force; and τ ji ∈R n Represents the control torque of the master robot and the slave robot.

[0021] Preferably, in step S2, the gravity compensation is in the form of Thus we get:

[0022]

[0023] Preferably, in step S3, both the master robot and the slave robot have two degrees of freedom, and define x ji1 =q ji1 , x ji2 =q ji2 , And j = {m, s}, i = {1, ..., N}, so the dynamic model can be rewritten as:

[0024]

[0025] in:

[0026]

[0027]

[0028]

[0029]

[0030] Here, m ji1 Indicates the weight of the first connecting rod, m ji2 represents the weight of the second connecting rod, l i1 is the length of the first connecting rod, l i2 is the length of the second connecting rod. j = {m, s}, the subscript m represents the master robot, the subscript s represents the slave robot, and i = {1, ..., N} represents the serial number of the corresponding robot.

[0031] Preferably, in step S4, the controller is set to u F (t) = Mu(t), and the actuator fault distribution matrix M = diag{m1,m2,...,m p}satisfy

[0032]

[0033] When m a =1, it means that the actuator has no fault; when m a =0, it means the actuator is completely ineffective; when 0<m a When <1, it indicates that a partial failure has occurred in the actuator.

[0034] Preferably, in step S5, the following is obtained:

[0035] Fuzzy system model of the master robot

[0036]

[0037] From the fuzzy system model of the robot

[0038]

[0039] Preferably, in step S6, the method for establishing the control law is:

[0040] S6-1. For the fuzzy system model of the main robot, select the following fuzzy logic controller:

[0041] The kth control rule:

[0042] IF i1 (t)isΨ ik1 and...and y ip (t)isΨ ikp ,

[0043]

[0044] where k = 1, 2, ..., L, Ψ ikp is the fuzzy setting, L is the number of IF-THEN rules, y i1(t),...,y ip (t) is a premise variable; it can be understood that the rule k is the kth rule interpreted by the IF-THEN statement.

[0045] S6-2, get the fuzzy control law of the main robot:

[0046]

[0047] S6-3, Similarly, we can get the fuzzy control law of the robot:

[0048]

[0049] Here, assuming that the state vector x mi (t) and x si (t) is measurable, and when i = 1, When i=2, And β i and is the dominant factor, where β i ∈(0,1),i={1,2}.

[0050] Preferably, in step S7, the state equation of the multilateral teleoperation system is:

[0051]

[0052]

[0053] Summarizing and sorting out, we can get:

[0054]

[0055] in:

[0056]

[0057]

[0058]

[0059] Define z i (t) is the controller output:

[0060]

[0061] Preferably, in step S8, the Lyapunov function is:

[0062]

[0063] Preferably, the fault-tolerant control optimization in step S9 includes:

[0064] One-time optimization

[0065] Give a suitable matrix and The controller gain is designed to be Then the closed-loop system described in step S7 is in H ∞ Mean square stability at interference attenuation level γ is obtained if there exists a positive definite matrix and a positive scalar γ and a matrix of appropriate dimensions Y mik ,Y sik , then the following inequality holds:

[0066]

[0067] here They are the linear matrix inequalities The elements within it are composed of the basic elements already stated, represents a linear matrix inequality;

[0068] Secondary Optimization

[0069] If there exists a positive definite matrix And positive scalar γ>0,σ a > 0, a = 1, 2, 3, ..., 16 and matrices with appropriate dimensions Y mik ,Y sik , then the closed-loop system described in step S7 is in H ∞ The mean square stability under the interference attenuation level γ is established, and the following inequality holds:

[0070]

[0071] here They are the elements in the linear matrix inequality Ω, which is composed of the basic elements already stated. Ω represents a linear matrix inequality.

[0072] The present invention has the following characteristics and beneficial effects:

[0073] By adopting the above technical solution and adding fault-tolerant control, the multi-master and multi-slave teleoperation system can realize one or more key components in a fault state during operation, and the system can still operate stably and safely. In addition, the multi-master and multi-slave teleoperation system has a wider range of applications and can realize more difficult operations. Ultimately, the operating system can improve the stability of the control system and the dynamic performance indicators of the system, while taking into account the random mean square stability of the system and the H∞ disturbance suppression performance of the system, so that the system can still maintain a considerable operating state when there are disturbances and actuator failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0075] Figure 1 , a schematic diagram of setting fuzzy rules in an embodiment of the present invention;

[0076] Figure 2 , a first degree of freedom displacement tracking trajectory diagram of a slave robot and a master robot in an embodiment of the present invention;

[0077] Figure 3 , a second degree of freedom displacement tracking trajectory diagram of a slave robot and a master robot in an embodiment of the present invention;

[0078] Figure 4 , a first degree of freedom displacement tracking trajectory diagram of the slave two robots and the master two robots in an embodiment of the present invention;

[0079] Figure 5 , a second degree of freedom displacement tracking trajectory diagram of the slave two robots and the master two robots in an embodiment of the present invention;

[0080] Figure 6 , first degree of freedom displacement tracking trajectory diagram from the first robot and from the second robot in the embodiment of the present invention;

[0081] Figure 7 , second degree of freedom displacement tracking trajectory diagram from the first robot and the second robot in the embodiment of the present invention;

[0082] Figure 8 , an environmental force fitting diagram from a robot in an embodiment of the present invention;

[0083] Fig. 9 , the environmental force fitting diagram of the two robots in the embodiment of the present invention;

[0084] Fig.10 , a fitting diagram of the operating force of the master robot in an embodiment of the present invention;

[0085] Fig.11 , the operating force fitting diagram of the main and second robots in the embodiment of the present invention. DETAILED DESCRIPTION

[0086] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0087] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0088] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0089] The present invention provides an H-infinity fuzzy fault-tolerant control method based on a multilateral teleoperation system, comprising the following steps:

[0090] S1. Simulate the multilateral teleoperation system through dynamic model;

[0091] S2. Setting the control torque so that the dynamic model has a gravity compensation effect;

[0092] S3, split the multi-master and multi-slave teleoperation system into an operating system consisting of two master robots and two slave robots, and obtain a new dynamic model;

[0093] S4. Design the controller according to the fault distribution of the actuators in the multilateral teleoperation system;

[0094] S5, simulate the multilateral teleoperation system with partial actuator failure through TS fuzzy control model;

[0095] S6, establishing a control law based on the time delay between the master and slave robots;

[0096] S7. Establish state equations of a multilateral teleoperation system based on fault distribution;

[0097] S8. Fault-tolerant control is achieved by selecting appropriate Lyapunov functions for the state equations of the multilateral teleoperation system;

[0098] S9, fault-tolerant control optimization, that is, designing the gain of the controller.

[0099] According to a further configuration of the present invention, the dynamic model is an Euler-Lagrange dynamic model, which is expressed as follows:

[0100]

[0101]

[0102] Where j = {m, s}, the subscript m represents the master robot, the subscript s represents the slave robot, and i = {1, ..., N} represents the serial number of the corresponding robot. Respectively represent the acceleration, velocity and displacement in the joint space; M ji (q ji )∈R n×n represents the inertia force matrix; represents the Coriolis effect and centrifugal effect; τ hi ∈R n and τ ei ∈R n represents the human operator force and environmental force; and τ ji ∈R n Represents the control torque of the master robot and the slave robot.

[0103] Furthermore, in step S2, the gravity compensation is in the form of Thus we get:

[0104]

[0105] It can be understood that by adding gravity compensation to optimize the torque controller, the collaboration between the master robot and the slave robot can be better.

[0106] In a further configuration of the present invention, in step S3, both the master robot and the slave robot have two degrees of freedom, and x is defined asji1 =q ji1 , x ji2 =q ji2 , And j = {m, s}, i = {1, ..., N}, so the dynamic model can be rewritten as:

[0107]

[0108] in:

[0109]

[0110]

[0111]

[0112]

[0113] Here, m ji1 Indicates the weight of the first connecting rod, m ji2 represents the weight of the second connecting rod, l i1 is the length of the first connecting rod, l i2 is the length of the second connecting rod. j = {m, s}, the subscript m represents the master robot, the subscript s represents the slave robot, and i = {1, ..., N} represents the serial number of the corresponding robot.

[0114] Furthermore, in step S4, the controller is set to u F (t) = Mu(t), and the actuator fault distribution matrix M = diag{m1,m2,...,m p}satisfy

[0115]

[0116] When m a =1, it means that the actuator has no fault; when m a =0, it means the actuator is completely ineffective; when 0<m a When <1, it indicates that a partial failure has occurred in the actuator.

[0117] It is understandable that when setting up the controller, it is necessary to consider partial failure of the actuator so that the controller has a fault-tolerant control effect.

[0118] It is understandable that since M is an unknown matrix, we define:

[0119] and |G|≤R≤I, To reduce conservatism,

[0120] in:

[0121] Γ o =diag{m1,...,m p}, R = diag{r1,r2,...,r p}

[0122] G = diag{g1,g2,...,g p},|G|=diag{|g1|,|g2|,....,|g p |},

[0123] m a =m ao (1+g a ),|g a |≤r a ≤1,

[0124]

[0125]

[0126]

[0127] Specifically, in step S5, since the multilateral teleoperation system model with partial actuator failure is a typical nonlinear system, it is difficult to directly design a fault-tolerant controller on such a system, so the TS fuzzy control model is used to describe the nonlinear system;

[0128] The dynamic model of the main robot is written as follows in rule a:

[0129] IF i1 (t)isΨ ia1 and...and y ip (t)isΨ iap ,

[0130]

[0131] Among them, iap is the fuzzy setting, L is the number of IF-THEN rules, y i1 (t),...,y ip (t) is the premise variable; it can be understood that the rule a is the ath rule interpreted by the IF-THEN statement.

[0132] Thus, the fuzzy system of the master robot is obtained:

[0133]

[0134] in, y i (t) = [y i1 (t)y i2 (t)...y ip (t)].

[0135] The fuzzy system model of the master robot can be described as:

[0136]

[0137] By analogy, the fuzzy system model of the robot is:

[0138]

[0139] It can be understood that the time delay between each pair of master-slave robots is asymmetric and continuously differentiable, so it must satisfy:

[0140]

[0141]

[0142] where d m1 (t) and d m2 (t) represents the time delay between the master robot 1 and the slave robot 1, and between the master robot 2 and the slave robot 2. s1 (t) represents the time delay between slave robot 1 and each master robot, d s2 (t) is the communication delay from the 2nd robot to each master robot. And Here μ, is a positive scalar.

[0143] In step S6, the method for establishing the control law of the multilateral teleoperation system is as follows:

[0144] S6-1. For the fuzzy system model of the main robot, select the following fuzzy logic controller:

[0145] Control rule k:

[0146] IF i1 (t)isΨ ik1 and...and y ip (t)isΨ ikp ,

[0147]

[0148] where k = 1, 2, ..., L, where Ψ ikpis the fuzzy setting, L is the number of IF-THEN rules, y i1 (t),...,y ip (t) is a premise variable; it can be understood that the rule k is the kth rule interpreted by the IF-THEN statement.

[0149] S6-2, get the fuzzy control law of the main robot:

[0150]

[0151] S6-3, Similarly, we can get the fuzzy control law of the robot:

[0152]

[0153] Here, assuming that the state vector x mi (t) and x si (t) is measurable, and when i = 1, When i=2, And β i and is the dominant factor, where β i ∈(0,1),i={1,2}.

[0154] According to a further configuration of the present invention, in step S7, the state equation of the multilateral teleoperation system is:

[0155]

[0156]

[0157] Summarizing and sorting out, we can get:

[0158]

[0159] in:

[0160]

[0161]

[0162]

[0163] Define z i (t) is the controller output:

[0164]

[0165] It can be understood that by selecting a suitable Lyapunov function, the system can achieve fault-tolerant mean square uniform stability and have H∞ performance indicators;

[0166] Specifically, the Lyapunov function is:

[0167]

[0168] That is: given a suitable controller gain K mik ,K sik , k = 1, 2, ..., L, and the matrix The closed-loop system described in step S7 is ∞ The mean square stability under the interference attenuation level γ. If there exists a positive definite matrix P i >0,Q ji >0, W ji > 0, and a positive scalar γ and a matrix N of suitable dimension, the following inequality holds:

[0169]

[0170] in:

[0171]

[0172]

[0173]

[0174] Φ 12 =-Q ji +W ji -I,

[0175]

[0176]

[0177] Φ 44 =-(1-μ)Q ji ,Φ 45 =(1-μ)Q ji ,

[0178]

[0179] Among them, γ is the system can achieve H in the mean square sense ∞ The indicators of interference level, Φ1, Φ2, Φ3, Φ4, Φ5, are linear matrix inequalities The elements within it are composed of the basic elements already stated, represents a linear matrix inequality.

[0180] According to a further configuration of the present invention, the fault-tolerant control optimization in step S9 includes:

[0181] One-time optimization

[0182] Give a suitable matrix and The controller gain is designed to be Then the closed-loop system described in step S7 is in H ∞ Mean square stability at interference attenuation level γ is obtained if there exists a positive definite matrix and a positive scalar γ and a matrix of appropriate dimensions Y mik ,Y sik , then the following inequality holds:

[0183]

[0184] in:

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194] here They are the linear matrix inequalities The elements within it are composed of the basic elements already stated, represents a linear matrix inequality;

[0195] Secondary Optimization

[0196] If there exists a positive definite matrix And positive scalar γ>0,σ a > 0, a = 1, 2, 3, ..., 16 and matrices with appropriate dimensions Y mik ,Y sik , then the closed-loop system described in step S7 is in H ∞ The mean square stability under the interference attenuation level γ is established, and the following inequality holds:

[0197]

[0198] in:

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214]

[0215]

[0216]

[0217]

[0218]

[0219]

[0220]

[0221] here They are the elements in the linear matrix inequality Ω, which is composed of the basic elements already stated. Ω represents a linear matrix inequality.

[0222] In this embodiment, the effectiveness of the fault-tolerant control design method of the above technical solution is verified through specific examples:

[0223] First, the parameters and conditions of digital simulation are given: Assume that m j1 =1kg,m j2 =1kg,l j1 =1m,l j2 = 1m, and angle

[0224] Displacement q mi1 ,q mi2 ,q si1 ,q si2 , the activity limit range is [-π / 2π / 2]. The master and slave robots each have 9 rule fuzzy models. Here are the fuzzy rules of the master robot, and the rest are similar:

[0225] Rule 1 q m11 is about -π / 2and q m12 is about -π / 2.

[0226] Rule 2 q m11 is about -π / 2and q m12 is about 0.

[0227] Rule 3 q m11 is about -π / 2and q m12 is aboutπ / 2.

[0228] Rule 4 q m11 is about 0 and q m12 is about -π / 2.

[0229] Rule 5 q m11 is about 0 and q m12 is about 0.

[0230] Rule6 q m11 is about 0 and q m12 is aboutπ / 2.

[0231] Rule7 q m11 is aboutπ / 2and q m12 is about -π / 2.

[0232] Rule8 q m11is aboutπ / 2and q m12 is about 0.

[0233] Rule9 q m11 is aboutπ / 2and q m12 is aboutπ / 2.

[0234] The communication delay is set to: d m1 =0.5sin 2 (t),d m2 =0.7sin 2 (t),d s1 =0.6sin 2 (t),d s2 =0.4sin 2 (t)

[0235] The failure factor boundary is chosen as The corresponding probability is E{θ nsi (k)=1}=0.45,E{θ nmi (k)=1}=0.35,n=1,2,...,p, so the failure factor is:

[0236]

[0237] By performing secondary optimization in step S9, the gains of the fault-tolerant controller of the present invention can be obtained respectively:

[0238]

[0239]

[0240]

[0241]

[0242]

[0243]

[0244]

[0245]

[0246]

[0247]

[0248]

[0249]

[0250]

[0251]

[0252]

[0253]

[0254]

[0255]

[0256] Figure 1 is the fuzzy membership function setting, Figure 2 , Figure 3 , Figure 4 , Figure 5 The motion tracking trajectories of the master robot and the slave robot show the effectiveness of the remote control system control method studied in this invention. Figure 6 , Figure 7 The trajectory comparison of the slave robots shows that the two slave robots can achieve synchronous movement. Figure 8 , Fig. 9 , Fig.10 , Fig.11 is a force fitting diagram, from which it can be seen that the multilateral teleoperation system studied in the present invention has the performance of environmental force and operation force feedback tracking.

[0257] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. An H-infinity fuzzy fault-tolerant control method based on a multilateral teleoperation system, characterized in that: The steps include: S1. Simulate the multilateral teleoperation system through dynamic model; The dynamic model is the Euler-Lagrange dynamic model, which is expressed as follows: Where j = {m, s}, the subscript m represents the master robot, the subscript s represents the slave robot, and i = {1, ..., N} represents the serial number of the corresponding robot. Respectively represent the acceleration, velocity and displacement in the joint space; represents the inertia force matrix; represents the Coriolis effect and the centrifugal effect; and represents human operator forces and environmental forces; and Represents the control torque of the master robot and the slave robot; S2. Set the control torque so that the dynamic model has the effect of gravity compensation. The form of gravity compensation is: Thus we get: S3, split the multi-master and multi-slave teleoperation system into an operating system consisting of two master robots and two slave robots, and obtain a new dynamic model; The master robot and the slave robot both have two degrees of freedom, and define x ji1 =q ji1 , x ji2 =q ji2 , And j = {m, s}, i = {1, ..., N}, so the dynamic model can be rewritten as: in: Here, m ji1 Indicates the weight of the first connecting rod, m ji2 represents the weight of the second connecting rod, l i1 is the length of the first connecting rod, l i2 is the length of the second link, j = {m, s}, the subscript m represents the master robot, the subscript s represents the slave robot, and i = {1, ..., N} represents the serial number of the corresponding robot; S4. Design the controller according to the fault distribution of the actuators in the multilateral teleoperation system; The controller is set to u F (t) = Mu(t), and the actuator fault distribution matrix M = diag{m1,m2,...,mp} satisfies When m a =1, it means that the actuator has no fault; when m a =0, it means the actuator is completely ineffective; when 0<m a When <1, it indicates that the actuator has a partial failure; S5. The TS fuzzy control model is used to simulate the multilateral teleoperation system with partial actuator failure, and the following results are obtained: Fuzzy system model of the master robot: From the fuzzy system model of the robot: S6, establishing a control law based on the time delay between the master and slave robots; The method for establishing the control law is: S6-1. For the fuzzy system model of the main robot, select the following fuzzy logic controller: The kth control rule: IF y i1 (t)isΨ ik1 and...and y ip (t)isΨ ikp , where k = 1, 2, ..., L, Ψ ikp is the fuzzy setting, L is the number of IF-THEN rules, y i1 (t),...,y ip (t) is the premise variable; S6-2, get the fuzzy control law of the main robot: S6-3, Similarly, we can get the fuzzy control law of the robot: Here, assuming that the state vector x mi (t) and x si (t) is measurable, and when i = 1, When i=2, And β i and is the dominant factor, where β i ∈(0,1),i={1,2} S7. Establish state equations of a multilateral teleoperation system based on fault distribution; The state equation of the multilateral teleoperation system is: Summarizing and sorting out, we can get: in: Define z i (t) is the controller output: S8. Fault-tolerant control is achieved by selecting appropriate Lyapunov functions for the state equations of the multilateral teleoperation system; S9, fault-tolerant control optimization, that is, designing the controller gain, The fault-tolerant control optimization includes: One-time optimization Give a suitable matrix and The controller gain is designed to be Then the closed-loop system described in step S7 is in H ∞ Mean square stability at interference attenuation level γ is obtained if there exists a positive definite matrix and a positive scalar γ and a matrix of appropriate dimensions Then the following inequality holds: here They are the linear matrix inequalities The elements within it are composed of the basic elements already stated, represents a linear matrix inequality; Secondary Optimization If there exists a positive definite matrix And positive scalar γ>0,σ a > 0, a = 1, 2, 3, ..., 16 and matrices with appropriate dimensions Then the closed-loop system described in step S7 is in H ∞ The mean square stability under the interference attenuation level γ is established, and the following inequality holds: here They are the elements in the linear matrix inequality Ω, which is composed of the basic elements already stated. Ω represents a linear matrix inequality.

2. The H-infinity fuzzy fault-tolerant control method based on a multilateral teleoperation system according to claim 1 is characterized in that: In step S8, the Lyapunov function is:

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