An Adaptive Tracking Control Method for a Dynamic Uncertainty System with Asymmetric Time Delay

Abstract

The present invention discloses an adaptive tracking control method for a dynamic uncertain system with asymmetric time delay, belonging to the technical field of teleoperation control. The method includes establishing a system dynamics model and a data operation structure, and designing a master-slave end control law and an adaptive update law, so that the actual force feedback information of the slave end can be provided to the master end in real time. The present invention uses a fuzzy neural network to approximate the uncertain terms in the model, and combines the backstepping method to design the slave end controller, so that the system position tracking error converges uniformly and the transparency of the system is improved. In terms of method, the present invention uses the idea of self-adaptation to update the weight parameters and tracking errors in the control law model in real time online, further shortening the adjustment time for the actual system to achieve stability. At the same time, the signal design of the control law avoids the dependence on the acceleration signal and the upper bound information of external disturbances during the neural network approximation process.

Description

Technical Field

[0001] The present invention relates to the technical field of teleoperation control, and particularly to an adaptive tracking control method for a dynamic uncertain system with asymmetric time delay. Background Art

[0002] A teleoperation robot system can maximize the safety of an operator when exploring an unknown environment and expand the operating ability of humans in an unknown dangerous environment. A typical teleoperation system refers to a robot control system in which a human is used as an operating end to remotely control a robot in a remote working environment by sending computer instructions locally or by manipulating an operating arm, so that the robot can complete a specified task in a certain manner. Compared with a fully automatic system, a teleoperation system can bidirectionally transmit control instructions and feedback information of the working environment between the master end and the slave end, which not only greatly improves the safety of the operator and the working efficiency of the robot, but also can avoid interference from an unknown environment through more precise control by the human operator, reduce the failure rate and damage rate of the mechanism, improve the completion efficiency of complex tasks, and make the system more flexible by the operator.

[0003] At present, a teleoperation robot system needs to solve two key problems: one is the time delay problem existing in the communication channels between the master and slave ends; the other is various uncertainty problems caused by the highly nonlinear internal and external models of the system. Researchers have proposed a variety of bilateral teleoperation control algorithms based on different ideas to overcome the influence of system time delay on stability, and at the same time, by combining with other controller designs, to solve the problems of model uncertainty and external interference existing in bilateral teleoperation control. However, there are still the following problems: 1) When realizing system stability, it is impossible to take into account system transparency, and it is often designed through passivity control theory, which makes the system overly conservative and leads to a decrease in transparency; 2) Some control laws always need to assume that the derivative of the time delay is bounded. Due to the randomness of the information transmission channel, in the framework of a continuous nonlinear system, the jitter time delay is rarely processed; 3) The realization of high transparency is based on the accurate solution of the parameters of the system dynamics model.

[0004] Therefore, how to provide a teleoperation control method to improve the transparency of the system, shorten the time, and avoid being interfered by the outside world is a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0005] For this reason, the present invention provides an adaptive tracking control method for a dynamic uncertain system with asymmetric time delay to solve the problem that it is impossible to take into account system transparency due to realizing system stability in the prior art.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] An adaptive tracking control method for a dynamic uncertain system with asymmetric time delay, comprising the following steps:

[0008] S1: Taking a teleoperation system including two n-degree-of-freedom robots as the object, under the condition of considering the joint friction of the robots, establish a system dynamics model and give the structural characteristics of such a nonlinear model;

[0009] S2: Using fuzzy logic and neural network structures, establish a data operation structure;

[0010] S3: Based on the backstepping method, define the position error signal and velocity error signal of the slave robot; according to the fuzzy neural network operation structure, design the slave control law; design the adaptive update laws of the fuzzy neural network weight parameters and error estimation of the slave robot, so that the fuzzy neural network can approximate the dynamics of the robot without relying on the acceleration signal and the upper bound information of external disturbances;

[0011] S4: Using the position time delay signal of the master robot, design a master fuzzy neural network control law with gravity compensation; design the adaptive update laws of the fuzzy neural network weight parameters and error estimation of the master robot, so that the actual force feedback information of the slave end can be provided to the master end in real time.

[0012] Furthermore, establishing the dynamics model of the bilateral teleoperation system in S1 specifically includes the following steps:

[0013] S101: Establish the master robot model:

[0014]

[0015] Establish the slave robot model:

[0016]

[0017] where q i , are respectively the joint positions, velocities and accelerations of the master and slave robots; is the positive definite inertia matrix of the master and slave robots; are the Coriolis force and centrifugal force terms of the master and slave robots; is the gravity term of the master and slave robots; is the viscous friction force; is the Coulomb friction force, μ ci is the Coulomb friction coefficient; is the external disturbance with an upper bound; are the input torques of each joint of the master and slave robots; is the force applied by the operator on the master robot; is the environmental force received by the slave robot; is the Jacobian matrix; the subscript i ∈ {m, s} represents the master and slave manipulators;

[0018] S102: Establish the operator dynamics model:

[0019]

[0020] Establish the remote environment model:

[0021]

[0022] where M i , B i , are the mass matrix, damping matrix and stiffness matrix of the operator or remote environment, and the subscript i ∈ {h, e} represents the operator and the remote velocity vector, is the external force generated by the operator or remote environment;

[0023] S103: Integrate the operator dynamics model with the master robot model to obtain the master system dynamics model:

[0024]

[0025] Integrate the remote environment model with the slave robot model to obtain the slave system dynamics model:

[0026]

[0027] where,

[0028] The dynamic model of the above bilateral teleoperation system has the following structural characteristics:

[0029] 1) There is an inequality ||M i || ≤ b1 + b2||q i || + b3||q i || 2 , that is, the dynamic model uncertainty and external non - linear disturbance have upper bounds;

[0030] 2) where, is a skew - positive definite matrix.

[0031] Furthermore, in step S3, the backstepping method is used to process the position error reference signal to obtain the slave control law, and the backstepping method is used to process the velocity error signal and the fuzzy neural network is used to approximate the uncertain terms therein, so as to design the slave adaptive update law. The specific steps of step S3 are as follows:

[0032] S301: Define the following variables Taking the derivatives of variables x1 and x2, the following equations can be obtained:

[0033]

[0034]

[0035] The system output is selected as y = x1;

[0036] S302: Define the position error signal:

[0037]

[0038] Define the velocity error signal:

[0039]

[0040] Define the virtual control signal:

[0041]

[0042] Taking the derivatives of both sides of equations (16) and (17) with respect to time t and considering equation (18), it can be expressed as

[0043]

[0044] where

[0045] S303: Select the following Lyapunov equation:

[0046]

[0047] Taking the derivative of the Lyapunov equation (20) with respect to time t, we get

[0048]

[0049] Obviously, when the error signal z2 approaches zero, according to the Lyapunov stability criterion, the slave system will asymptotically converge. Design the following slave control law:

[0050]

[0051] where, is the error estimation adaptive update law, is the actual approximation value of the fuzzy neural network;

[0052] S304: Select the following Lyapunov equation:

[0053]

[0054] Then, take the derivative with respect to the relative time and obtain the following equation

[0055]

[0056] Substitute the end control law (22) into equation (24), and we can get

[0057]

[0058] Use the fuzzy neural network to approximate the uncertain term Ψ s , then we have

[0059]

[0060] where and the actual approximation value of the fuzzy neural network is

[0061] S305: Considering the estimation formula (26), equation (24) can be transformed into

[0062]

[0063] Furthermore, we can get

[0064]

[0065] where

[0066] S306: Design the adaptive update law of the fuzzy neural network weight parameters as

[0067]

[0068] where Γ s represents a diagonal positive definite constant matrix;

[0069] Design the adaptive update law of the estimation error to be selected as

[0070]

[0071] Furthermore, in equation (26), the fuzzy neural network is used to approximate the uncertain term Φ s , but the input variables of the fuzzy neural network include the acceleration signal. To avoid the many inconveniences brought by measuring the acceleration signal, an equivalent input variable without the acceleration signal is given. According to the master-end dynamics model, the master-end acceleration signal can be expressed as

[0072]

[0073] Replace the input variables of the slave-end system's fuzzy neural network with the following form that does not depend on the acceleration signal:

[0074]

[0075] Further, step S4 specifically includes the following steps:

[0076] S401: Define the time-delay signal of the main robot joint position

[0077]

[0078] Design the control law of the main robot with gravity compensation as

[0079]

[0080] Wherein,

[0081] S402: Considering the uncertainty of the gravity term in the dynamic model of the main robot The control law (34) of the main robot becomes

[0082]

[0083] Wherein, represents the uncertain term and friction force of the main robot system;

[0084] S403: Use the fuzzy neural network to online estimate the above uncertain term U m and obtain

[0085]

[0086] Wherein, X m represents the input quantity of the fuzzy neural network, represents the output quantity of the rule layer, ò m represents the optimal estimation error of the fuzzy neural network;

[0087] S404: Take the estimation of U m as

[0088]

[0089] Replace the uncertain term in formula (35) with the estimated value formula (37), then the main control law given in formula (34) can be rewritten as:

[0090]

[0091] Further, design the main adaptive update law with reference to the structure of the slave update law. The main adaptive update law of the fuzzy neural network weights is

[0092]

[0093] Among them, Γ m is a diagonal positive definite constant matrix;

[0094] The parameter main - end adaptive update law of the design error estimation term is selected as

[0095]

[0096] Furthermore, when performing model integration in step S103, the mapping relationship between the end - effector velocity in the operational space and the joint velocity in the joint - angle space is utilized:

[0097]

[0098] Its differential is:

[0099]

[0100] Among them, the Jacobian matrix of the robot joint velocity

[0101] Furthermore, the fuzzy neural network in step S2 includes a membership - function layer, a rule layer, and a fuzzy - logic layer. The membership - function layer represents the membership function of the input variable with rectangular - box nodes to distinguish the degree of fit of the input quantity x = [x1…x i …x n T with the classifier The rule layer represents the fuzzy - inference rule with circular nodes marked with Π, and the fuzzy - logic layer represents the output signal of the network with circular nodes marked with Σ.

[0102] Furthermore, establishing the data - operation structure in step S2 specifically includes the following steps:

[0103] S201: The membership - function layer selects the following Gaussian membership function as the membership function of the input quantity:

[0104]

[0105] Among them, c i and are respectively the mean value and the standard deviation of the Gaussian function;

[0106] S202: The rule layer passes the inference result to the fuzzy - logic layer, and the output of the rule layer can be expressed as:

[0107]

[0108] Among them, l k represents the k - th output of the rule layer, represents the weight value between the output layer and the rule layer; ​

[0109] S203: The output signal of the fuzzy logic layer is calculated as follows:

[0110]

[0111] According to the concept of the fuzzy function vector, the output of the fuzzy neural network can be summarized as

[0112]

[0113] where \(y = [y_1\ y_2\ \cdots\ y o \),

[0114] S204: According to the global approximation theory, for a nonlinear function \(U\) on any closed set, there exists an optimal approximation weight matrix \(w^*\) that satisfies the following form:

[0115]

[0116] where \(\delta(x(t))\) represents the bounded minimum approximation error.

[0117] The present invention has the following advantages:

[0118] The present invention solves the stability tracking problem of a nonlinear bilateral teleoperation system with asymmetric time delay and additional uncertainty problems. The present invention uses a fuzzy neural network to approximate the uncertain terms in the model and combines the backstepping method to design the slave controller, so that the system position tracking error converges uniformly and the transparency of the system is improved. The present invention uses the idea of self - adaptation in the method to update the weight parameters and tracking error in the control law model in real - time online, further shortening the adjustment time for the actual system to achieve stability. At the same time, the signal design of the control law avoids the dependence on the acceleration signal and the upper - bound information of external disturbances during the neural network approximation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0119] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only exemplary, and for those of ordinary skill in the art, without creative efforts, other implementation drawings can be obtained according to the provided drawings.

[0120] The structures, proportions, sizes, etc. shown in this specification are only used to match the content disclosed in the specification for those familiar with this technology to understand and read, and are not used to limit the implementation conditions of the present invention. Therefore, they do not have substantial technical significance. Any modification of the structure, change in the proportional relationship, or adjustment of the size, without affecting the effects that the present invention can produce and the purposes that can be achieved, should still fall within the scope covered by the technical content disclosed in the present invention.

[0121] Figure 1 Schematic diagram of the adaptive tracking controller structure with an asymmetric time-delay system designed for the present invention;

[0122] Figure 2 Schematic diagram of the fuzzy logic structure of the controller designed for the present invention;

[0123] Figure 3 Schematic diagram of the simulation system of the controller designed for the present invention;

[0124] Figure 4 Position tracking simulation diagram of the controller designed for the present invention under the condition that the operator applies an alternating external force;

[0125] Figure 5 Position tracking error simulation diagram of the controller designed for the present invention under the condition that the operator applies an alternating external force;

[0126] Figure 6 Control torque tracking simulation diagram of the controller designed for the present invention under the condition that the operator applies an alternating external force;

[0127] Figure 7 Position tracking simulation diagram of the controller designed for the present invention under the condition of physical collision;

[0128] Figure 8 Control torque tracking simulation diagram of the controller designed for the present invention under the condition of physical collision;

[0129] Figure 9 Position tracking simulation diagram of the controller designed for the present invention and other two types of neural network controllers for circular trajectory tracking; Detailed implementation manners

[0130] The following specific embodiments illustrate the implementation manners of the present invention. Those familiar with this technology can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

[0131] An adaptive tracking control method for a dynamic uncertain system with asymmetric time delay, comprising the following steps:

[0132] S1: Taking a teleoperation system including two n-degree-of-freedom robots as the object, and establishing a system dynamics model under the condition of considering robot joint friction, specifically:

[0133] S101: Establishing the master robot model:

[0134]

[0135] Establishing the slave robot model:

[0136]

[0137] where q i , are respectively the joint positions, velocities and accelerations of the master and slave robots; is the positive definite inertia matrix of the master and slave robots, is the Coriolis force and centrifugal force terms of the master and slave robots, is the gravity term of the master and slave robots; is the viscous friction force; is the Coulomb friction force, μ ci is the Coulomb friction coefficient; is the external disturbance with an upper bound; The input torques of each joint of the master and slave robots; is the force exerted by the operator on the master robot; is the environmental force received by the slave robot; is the Jacobian matrix; the subscript i ∈ {m, s} represents the master and slave manipulators;

[0138] S102: Establishing the operator dynamics model:

[0139]

[0140] Establishing the remote environment model:

[0141]

[0142] where M i , B i , are the mass matrix, damping matrix and stiffness matrix of the operator or the remote environment, and the subscript i ∈ {h, e} represents the operator, remote velocity vector; is the external force generated by the operator or the remote environment;

[0143] S103: Integrate the operator dynamics model with the master robot model to obtain the master system dynamics model:

[0144]

[0145] Integrate the remote environment model with the slave robot model to obtain the slave system dynamics model:

[0146]

[0147] Among them,

[0148] When performing model integration, the mapping relationship between the end velocity in the workspace and the joint velocity in the joint angle space is utilized:

[0149]

[0150] Its differential is:

[0151]

[0152] Among them, the robot joint velocity Jacobian matrix

[0153] The above master-slave teleoperation system dynamics model has the following structural characteristics:

[0154] 1) There is an inequality ||M i || ≤ b1 + b2||q i || + b3||q i || 2 , that is to say, the dynamic model uncertainty and external non-linear disturbance have upper bounds;

[0155] 2) is a skew positive definite matrix.

[0156] The stability of the control algorithm needs to be proved under the condition of satisfying the above structural characteristics.

[0157] As Figure 2 shown, the fuzzy neural network includes a membership function layer, a rule layer, and a fuzzy logic layer. The membership function layer represents the membership function of the input variable with rectangular box nodes to distinguish the degree of fit between the input quantity x = [x1…x i …x n T and the classifier . The rule layer represents the fuzzy inference rule with circular nodes marked with Π, and the fuzzy logic layer represents the output signal of the network with circular nodes marked with Σ.

[0158] ​S2: Establish a data operation structure by using fuzzy logic and neural network structure, specifically as follows:

[0159] S201: The membership function layer selects the following Gaussian membership function as the membership function of the input quantity:

[0160]

[0161] where c i and are the mean value and standard deviation of the Gaussian function respectively;

[0162] S202: The rule layer transfers the inference result to the fuzzy logic layer, and the output of the rule layer can be expressed as:

[0163]

[0164] where, l k represents the k-th output of the rule layer, represents the weight value between the output layer and the rule layer;

[0165] S203: The output signal of the fuzzy logic layer is calculated according to the following method:

[0166]

[0167] According to the concept of the fuzzy function vector, the output of the fuzzy neural network can be summarized as

[0168]

[0169] where, y = [y1 y2 … y o ,

[0170] S204: According to the global approximation theory, for the nonlinear function U on any closed set, there exists an optimal approximation weight matrix w* that satisfies the following form:

[0171]

[0172] where, ò(x(t)) represents the bounded minimum approximation error.

[0173] Establish a fuzzy neural network operation structure to process the input signal and use it to online estimate the uncertain terms in the system dynamics model.

[0174] S3: Based on the backstepping method, define the position error signal and velocity error signal of the slave robot; according to the fuzzy neural network operation structure, design the slave control law; design the adaptive update laws for the weights of the fuzzy neural network of the slave robot and the error estimation, so that the fuzzy neural network can approximate the dynamics of the robot without relying on the acceleration signal and the upper bound information of external disturbances.

[0175] Use the backstepping method to process the position error reference signal to obtain the slave control law, use the backstepping method to process the velocity error signal and approximate the uncertain terms therein with the help of the fuzzy neural network, and thus design the slave adaptive update law, specifically:

[0176] S301: Define the following variables Taking the derivatives of variables x1 and x2, the following equalities can be obtained:

[0177]

[0178]

[0179] The system output is selected as y = x1;

[0180] S302: Define the position error signal:

[0181]

[0182] Define the velocity error signal:

[0183]

[0184] Define the virtual control signal:

[0185]

[0186] Taking the derivatives of both sides of equations (16) and (17) with respect to time t and considering equation (18), it can be expressed as

[0187]

[0188] where

[0189] S303: Select the following Lyapunov equation:

[0190]

[0191] Taking the derivative of the Lyapunov equation (20) with respect to time t, we get

[0192]

[0193] Obviously, when the error signal z2 approaches zero, according to the Lyapunov stability criterion, the slave system will asymptotically converge. The following slave control law is designed:

[0194]

[0195] where is the adaptive update law of the error estimate, is the actual approximation value of the fuzzy neural network;

[0196] S304: Select the following Lyapunov equation:

[0197]

[0198] Then, take the derivative with respect to relative time and obtain the following equation

[0199]

[0200] Substitute the slave control law (22) into equation (24), and we can get

[0201]

[0202] Utilize the fuzzy neural network to approximate the uncertain term Ψ s , then we have

[0203]

[0204] where and the actual approximation value of the fuzzy neural network is

[0205] S305: Considering the estimation equation (26), equation (24) can be transformed into

[0206]

[0207] Furthermore, we can get

[0208]

[0209] where

[0210] S306: Design the adaptive update law of the fuzzy neural network weight parameters as

[0211]

[0212] where Γ s represents a diagonal positive definite constant matrix;

[0213] Design the error estimate adaptive update law to be selected as

[0214]

[0215] In equation (26), a fuzzy neural network is used to approximate the uncertain term Φ s , however, the input variables of the fuzzy neural network include the acceleration signal. To avoid the many inconveniences brought by measuring the acceleration signal, an equivalent input variable without the acceleration signal is given. According to the master-side dynamic model, the master-side acceleration signal can be expressed as

[0216]

[0217] This indicates that the input variables of the fuzzy neural network of the slave-side system can be replaced with the following form that does not depend on the acceleration signal:

[0218]

[0219] S4: Using the position time-delay signal of the master-side robot, design a master-side fuzzy neural network control law with gravity compensation; design an adaptive update law for the weight parameters and error estimation of the master-side robot's fuzzy neural network, so that the actual force feedback information of the slave-side can be provided to the master-side in real time. Specifically:

[0220] S401: Define the joint position time-delay signal of the master-side robot

[0221]

[0222] Design the control law of the master-side robot with gravity compensation as

[0223]

[0224] where

[0225] S402: Considering the uncertainty of the gravity term in the master-side robot dynamic model the control law (34) of the master-side robot becomes

[0226]

[0227] where represents the uncertain term and friction force of the master-side robot system;

[0228] S403: Use a fuzzy neural network to perform online estimation of the above dynamic uncertainty terms and obtain m where X

[0229]

[0230] where X m represents the input quantity of the fuzzy neural network, Represents the output of the rule layer, ò m Represents the optimal estimation error of the fuzzy neural network;

[0231] S404: Take U m The estimate of is

[0232]

[0233] Replace the uncertain term in Equation (35) with the estimated value in Equation (37), then the master - end control law given in Equation (34) can be rewritten as:

[0234]

[0235] Design the master - end adaptive update law of the fuzzy neural network weights by referring to the structure of the slave - end update law. The master - end adaptive update law of the fuzzy neural network weights is designed as

[0236]

[0237] where, Γ m Is a diagonal positive definite constant matrix;

[0238] The master - end adaptive update law of the design error estimation term parameters is selected as

[0239]

[0240] As Figure 1 shown, d1, d2 represent the time - delay signals, and there are only speed and position signals in the communication network. Through the design of the bilateral controller, the present invention can weaken the influence of time - delay and solve certain uncertainty problems, meeting the requirements of system stable control.

[0241] As Figure 1 shown, the present invention is a simulation study on the master - slave ends of a dynamic uncertain control system achieving tracking stability under the condition of asymmetric time - delay in the communication link. The specific operation steps are as follows:

[0242] Step 1: Establish the dynamic model of the teleoperation system:

[0243] The present invention uses two identical two - degree - of - freedom robotic arms as the simulation objects of the teleoperation system, as Figure 3 shown.

[0244] Master - end system model:

[0245] Slave - end system model:

[0246] The specific expressions of each matrix and vector in the master - slave end system model are as follows:

[0247]

[0248]

[0249]

[0250] where: s i = sin(θ i ), c i = cos(θ i );

[0251] The friction model is as follows:

[0252]

[0253] The parameters of the robotic arm are as follows:

[0254] m1 = 20.34 kg; m2 = 17.68 kg; l1 = l2 = 0.511 m; μ f1 = 3.1, μ f2 = 3.6, μ c1 = 4.2, μ c2 = 4.5

[0255] The system delay parameters are as follows:

[0256] d1 = 1.2 s, d2 = 1.6 s

[0257] Step 2: Establish the controller as:

[0258] The master controller:

[0259] The slave controller:

[0260] where

[0261] The adaptive update law for the weights of the fuzzy neural network is designed as:

[0262] For the master:

[0263] For the slave:

[0264] where

[0265] The adaptive update law for the tracking error is designed as

[0266] For the master:

[0267] For the slave:

[0268] The parameter selection is as follows:

[0269] k p =-10.7, k d =8.2, k p =-10.7, λ1=λ2=5, b=4, c=[-2,-1.5,-1.0,-0.5,0,0.5,1.0,1.5,2.0]; initial position q m =[π / 2 -π / 2] T ,q s =[π / 2 -π / 2] T , initial velocity

[0270] In order to better verify the effectiveness and advancement of the algorithm of the present invention, three different tests are designed in the simulation experiment: 1) Tracking experiment under alternating external force, the initial operator applies a force of The test time is 50s; 2) Collision and recovery test, the initial operator applied force is The experimental time is 50s. At t∈[15,20], a wall is added to block the slave robot arm d s =[-80-80]; 3) Comparison test with other types of neural networks, the comparison object 1 is the PD-neural network controller, the parameter is k p =diag{5,5},k mv =diag{25,25}, k sv =diag{1.0,1.0}, Γ=diag{3.5,3.5}, the comparison object 2 is the RBF neural network controller, the parameter is k mv =diag{40,40},k mv =diag{40,40},Γ m =diag{2.5,2.5},Γ s =diag{3.5,3.5}, the three controllers perform circle tracking operation, and the operator applies a force of The experimental time is 40s.

[0271] The effects of the present invention are further described with reference to the accompanying drawings:

[0272] pass Figures 4-6 It can be seen that under the initial conditions and parameter settings given in the description, the slave end in the teleoperation system can track the master end according to the desired motion trajectory and complete the teleoperation motion. Within 15 seconds, the motion trajectory tracking of each manipulator on the master and slave ends converges, and the tracking error is small, with good trajectory tracking performance, and the control torque generated by the designed controller satisfies the boundedness.

[0273] pass Figures 7-8It can be seen that at 15 s, a physical collision occurred on the slave manipulator. Then, the control torque of the master system updated the physical collision of the environment, and the value suddenly increased, realizing the force feedback performance of the operator. When the physical collision was released at 25 s, after rapid decay oscillation, the slave manipulator continued to complete its tracking task, and the experiment showed the recovery ability and robustness of the designed controller from the physical collision.

[0274] Through Figure 9 It can be seen that although all three controllers can achieve asymptotic stable control under asymmetric time delay and uncertainty conditions, compared with the other two types of controllers, the teleoperation system using the controller designed by the present invention has better precise operation ability. Therefore, under fixed asymmetric time delay, various nonlinear and uncertainty conditions, the superiority of the designed controller in position tracking has been proved.

[0275] Although the present invention has been described in detail with general descriptions and specific embodiments above, based on the present invention, some modifications or improvements can be made, which are obvious to those skilled in the art. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of the present invention claimed.

Claims

1. An adaptive tracking control method for a dynamic uncertain system with asymmetric time delay, characterized in that, It includes the following steps: S1: Taking a teleoperation system with two n-degree-of-freedom robots as the object, under the condition of considering the joint friction of the robots, establish a system dynamics model and give the structural characteristics of such a nonlinear model; S2: Using fuzzy logic and neural network structure, establish a data operation structure; S3: Based on the backstepping method, define the position error signal and velocity error signal of the slave robot; According to the fuzzy neural network operation structure, design the slave control law; Design the adaptive update law of the fuzzy neural network weight parameters and error estimation of the slave robot, so that the fuzzy neural network can approximate the dynamics of the robot without relying on the acceleration signal and the upper bound information of external disturbances; S4: Using the position time-delay signal of the master robot, design the master fuzzy neural network control law with gravity compensation; Design the adaptive update law of the fuzzy neural network weight parameters and error estimation of the master robot, so that the actual force feedback information of the slave can be provided to the master in real time; The fuzzy neural network in the step S2 includes a membership function layer, a rule layer, and a fuzzy logic layer. The membership function layer uses rectangular box nodes to represent the membership functions of input variables to distinguish the input quantity x = [x1…x i x n T The degree of fit with the classifier . The rule layer uses circular nodes marked with Π to represent fuzzy inference rules, and the fuzzy logic layer uses circular nodes marked with Σ to represent the output signals of the network;​ The establishment of the data operation structure in step S2 specifically includes the following steps: S201: The membership function layer selects the following Gaussian membership function as the membership function of the input quantity: where c i and are the mean and standard deviation of the Gaussian function, respectively; S202: The rule layer transmits the inference result to the fuzzy logic layer, and the output of the rule layer can be expressed as: where, l k represents the k-th output of the rule layer, represents the weight between the output layer and the rule layer; According to the concept of the fuzzy function vector, the output of the fuzzy neural network can be summarized as where y = [y1 y2y o , S204: According to the global approximation theory, for any nonlinear function U on a closed set, there exists an optimal approximation weight matrix w* that satisfies the following form: Among them, ò(x(t)) represents the bounded minimum approximation error.

2. The adaptive tracking control method for a dynamic uncertain system with asymmetric time delay as claimed in claim 1, wherein The establishment of the dynamics model of the bilateral teleoperation system in S1 specifically includes the following steps: S101: Establish the master robot model: Establish the slave robot model: where q i , are the joint positions, velocities, and accelerations of the master and slave robots, respectively; is the positive definite inertia matrix of the master and slave robots; is the Coriolis and centrifugal force terms of the master and slave robots; is the gravity term of the master and slave robots; is the viscous friction force; is the Coulomb friction force, μ ci is the Coulomb friction coefficient; is the external disturbance with an upper bound; is the input torque of each joint of the master and slave robots; is the force applied by the operator to the master robot; is the environmental force received by the slave robot; is the Jacobian matrix; the subscript i ∈ {m, s} represents the master and slave manipulators; S102: Establish the operator dynamics model: Establish the remote environment model: where, M i , B i , are the mass matrix, damping matrix, and stiffness matrix of the operator or the remote environment, the subscript i ∈ {h, e} represents the operator and the remote velocity vector, f i * ∈ L ∞ is the external force generated by the operator or the remote environment; S103: Integrate the operator dynamics model with the master robot model to obtain the master system dynamics model: Integrate the remote environment model with the slave robot model to obtain the slave system dynamics model: Among them, The dynamics model of the above bilateral teleoperation system has the following structural characteristics: 1) There exists an inequality ||M i || ≤ b1 + b2||q i || + b3||q i || 2 , that is, there is an upper bound for the uncertainty of the dynamic model and external nonlinear disturbances; 2) Among them, is a skew positive definite matrix.

3. The adaptive tracking control method for a dynamic uncertain system with asymmetric time delay as described in claim 2, characterized in that, In step S3, the backstepping method is used to process the position error reference signal to obtain the slave control law, and the backstepping method is used to process the velocity error signal and approximate the uncertain terms with the help of the fuzzy neural network, so as to design the slave adaptive update law. The specific steps of step S3 are as follows: S301: Define the following variables Taking the derivatives of variables x1 and x2, the following equations can be obtained: The system output is selected as y = x1; S302: Define the position error signal: Define the velocity error signal: Define the virtual control signal: Taking the derivative of both sides of Equation (16) and Equation (17) with respect to time t and considering Equation (18), it can be expressed as Among them S303: Select the following Lyapunov equation: Taking the derivative of the Lyapunov equation (20) with respect to time t, we get Obviously, when the error signal z2 approaches zero, according to the Lyapunov stability criterion, the slave system will converge asymptotically. Design the following slave control law: Among them, is the adaptive update law for error estimation, is the actual approximation value of the fuzzy neural network; S304: Select the following Lyapunov equation: Then, take its derivative with respect to relative time and get the following equation Substituting the slave control law (22) into Equation (24), we can get Approximating the uncertain term Ψ using a fuzzy neural network s , then we have Among them, and the actual approximation value of the fuzzy neural network is S305: Considering the estimation formula (26), formula (24) can be transformed into Furthermore, it can be obtained that Among them, S306: Design the adaptive update law of the weights of the fuzzy neural network as where, Γ s represents a diagonally positive definite constant matrix; Design the adaptive update law of the error estimation to be 4. The adaptive tracking control method for a dynamic uncertain system with asymmetric time delay as described in claim 3, wherein In equation (26), a fuzzy neural network is used to approximate the uncertain term Φ s , but the input variables of the fuzzy neural network include acceleration signals. To avoid the many inconveniences brought about by measuring acceleration signals, an equivalent input variable without acceleration signals is given. According to the master dynamics model, the master acceleration signal can be expressed as Replace the input variables of the fuzzy neural network in the slave system with the following form that does not depend on the acceleration signal:

5. The adaptive tracking control method for a dynamic uncertain system with asymmetric time delay as claimed in claim 2, wherein The step S4 specifically includes the following steps: S401: Define the time-delay signal of the joint position of the master robot Design the control law of the master robot with gravity compensation as Among them, S402: Considering the uncertainty of the gravity term in the dynamic model of the master robot The control law (34) of the master robot becomes Among them, represents the uncertainties and frictional forces of the master robot system; S403: Online estimation is performed on the above uncertain term U using a fuzzy neural network m to obtain Among them, X m represents the input quantity of the fuzzy neural network, represents the output quantity of the rule layer, ò m represents the optimal estimation error of the fuzzy neural network; S404: Obtain U m The estimate of Replace the uncertain term in formula (35) with the estimated value formula (37), then the master control law given in formula (34) can be rewritten as:

6. The adaptive tracking control method for a dynamic uncertain system with asymmetric time delay according to claim 3, characterized in that, Design the master adaptive update law with reference to the structure of the slave update law. The master adaptive update law of the weights of the fuzzy neural network is where, Γ m is a diagonal positive definite constant matrix; Design the master adaptive update law of the parameters of the error estimation term to be 7. The adaptive tracking control method for a dynamic uncertain system with asymmetric time delay as claimed in claim 2, wherein When performing model integration in the step S103, the mapping relationship between the end velocity in the workspace and the joint velocity in the joint angle space is utilized: Its differential is: Among them, the robot joint velocity Jacobian matrix

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