Flexible mechanical arm self-adaptive variable impedance control method based on neural network

Abstract

The invention discloses a flexible mechanical arm self-adaptive variable impedance control method based on a neural network, relates to the technical field of flexible joint mechanical arm control, can make estimation compensation for model uncertainty by using the neural network, and can keep compliance when interacting with a person or an object so as to ensure the safety of personnel and equipment. In order to achieve the purpose, the technical scheme of the invention comprises the following steps: for a fourth-order nominal model of the two-degree-of-freedom flexible mechanical arm, singular perturbation is adopted to decompose the fourth-order nominal model into two second-order subsystems; designing a model uncertain part including friction force in a neural network estimation system, and training the neural network by using an improved optimal bounded ellipse algorithm; and aiming at unknown high-order angular velocities, designing an observer by using a training result of the neural network to observe so as to obtain observation values of the unknown high-order angular velocities. And designing a variable-stiffness impedance control controller for the slow subsystem, wherein the stiffness is adaptively adjusted according to the contact force. And designing a sliding mode controller for the fast subsystem, and finally giving an overall controller design.

Description

Technical Field

[0001] The present invention relates to the technical field of flexible joint mechanical arm control, and in particular to a flexible mechanical arm adaptive variable impedance control method based on a neural network. Background Art

[0002] Robotic arms have been widely used in manufacturing and assembly, and many are also used in daily life. The interaction between robots and humans is inevitable, so it is very important to achieve safe interaction between robots and humans. Flexible joint robots are generally driven by motors, which in turn drive joint movement. The structural design is inherently flexible, making them very suitable for products that frequently interact with humans, such as collaborative robots.

[0003] However, compared with traditional rigid manipulators, the existence of flexible joints also increases the complexity of the system and the difficulty of designing controllers. At the same time, flexible joint manipulators have strong nonlinear phenomena, and their system parameters often change during movement and grasping, which further increases the complexity of controller design. Commonly used control methods such as PID control are often prone to serious jitter in highly nonlinear and strongly coupled systems such as flexible joint manipulators, affecting the control performance of the manipulator. Therefore, how to design a suitable control strategy for flexible joint manipulators with unknown nonlinearities and variable system parameters, and achieve good control effects of the manipulator when only the output is measurable, is an urgent problem to be solved in the prior art. In addition, considering that in scenarios such as human-machine collaboration, the manipulator needs to interact with people or the environment. In order to ensure the safety of the interaction process, impedance control methods are often used. However, because the controller parameters of traditional fixed stiffness impedance control are fixed, in practical applications, either it can quickly follow the reference trajectory but the flexibility is poor, or it can show good flexibility but the performance of following the reference trajectory is poor.

[0004] Therefore, designing an impedance control method that can adaptively adjust the stiffness, so that the robot arm can follow the reference trajectory faster when there is no external force contact, and maintain better compliance characteristics when there is external force contact, so that the robot arm can better adapt to different working environments compared to traditional fixed impedance control, is another technical problem that needs to be urgently solved by existing methods. Summary of the invention

[0005] In view of this, the present invention provides a neural network-based adaptive variable impedance control method for a flexible robotic arm, which can adaptively adjust the stiffness, thereby enabling the robotic arm to follow the reference trajectory faster when there is no external force contact, and maintain better compliance characteristics when there is external force contact, allowing the robotic arm to better adapt to different working environments compared to traditional fixed impedance control.

[0006] To achieve the above object, the technical solution of the present invention is a method for adaptive variable impedance control of a flexible mechanical arm based on a neural network, comprising the following steps:

[0007] S1: For the fourth-order nominal model of the two-degree-of-freedom flexible joint robot, in order to simplify the controller design, the singular perturbation method is used to decompose it into two second-order subsystems: a fast subsystem and a slow subsystem.

[0008] S2: Design a neural network to estimate the friction in the system and the unmodeled parts of the model, and train the neural network using the improved optimal bounded ellipse algorithm.

[0009] S3: For unknown system states, an observer is designed based on the training results of the neural network to observe it.

[0010] S4: For the slow subsystem, a variable stiffness impedance controller is designed to adaptively change the stiffness.

[0011] S5: Design a sliding mode controller for the fast subsystem and combine the controllers of the two subsystems according to the singular perturbation method to give the overall controller design.

[0012] Furthermore, in S1, for the fourth-order nominal model of the two-degree-of-freedom flexible joint manipulator, in order to simplify the controller design, the singular perturbation method is used to decompose it into two second-order subsystems: a fast subsystem and a slow subsystem, specifically:

[0013] Consider the following flexible joint robot model

[0014]

[0015] in, is the joint angle, is the driving motor angle, is the inertia matrix, are the Coriolis force and the centrifugal force, is gravity, is the external force torque, is the system friction, For systems with unmodeled dynamics, is the control quantity input, is the transmission ratio matrix of the motor and is a diagonal matrix, is the moment of inertia matrix of the motor rotor and is a diagonal matrix, is the elastic coefficient matrix of the joint elastic element and is a diagonal matrix; is the set of real numbers, with the superscript being the dimension.

[0016] The singular perturbation method is as follows: first rewrite the system model into state space form and take the following system state:

[0017]

[0018] where x 1 、x 2 ,y 1 ,y 2 There are four system states, 0<ε<<1 is the preset parameter, B 0 =ε 2 K; At the same time, the unmodeled dynamics of the system are combined with the friction and nonlinear terms of the system to form a lumped uncertainty Then the state space form is:

[0019]

[0020] where a 1 =D -1 B 0 , a 2 =(J -1 N -2 +D -1 )B 0 , b 1 =J -1 N -1 .

[0021] Since 0<ε<<1, the y in the system 1 ,y 2 Change speed ratio x 1 ,x 2 Fast, the system state has two different time scales, and the original fourth-order system is decomposed into two second-order subsystems using the singular perturbation method.

[0022] Let the new lumped uncertainty F * =D -1 F, uncertain compensation item and u=u a +u b ,u b is the tracking control item to be designed, where Yes F * The estimated value of , then (3) becomes (4)

[0023]

[0024] in

[0025] Let ε = 0, Get the system equilibrium point

[0026]

[0027] where u bsis the control component of the slow subsystem when ε = 0; Substitute y in (2) 1 , we get the slow subsystem as shown in equation (6):

[0028]

[0029] in

[0030] Defining new state variables Substituting it into (2), we get formula (7):

[0031]

[0032] Defining extended time variables And let ε = 0 in (4), and then give the fast subsystem as:

[0033]

[0034] in u bf is the control component of the slow-fast system when ε = 0 and satisfies u bs +u bf =u b .

[0035] Further, S2: design a neural network to estimate the friction in the system and the unmodeled part of the model, and train the neural network using the improved optimal bounded ellipse algorithm, specifically:

[0036] Consider the lumped uncertainty term F in the slow subsystem equation (5): * , design a neural network to estimate the lumped uncertainty F * :

[0037] F * =W *T Φ(Z)+∈ (9)

[0038] Φ(Z)=[φ(z 1 ),φ(z 2 ),…,φ(z N )] T (10)

[0039] Where ∈ is the estimation error, W * is the optimal weight from the hidden layer to the output layer of the neural network, Z = [z 1 , z 2 , …, z N ] T =Vx, is the neural network input, is the weight from the input layer to the hidden layer of the neural network, N is the number of nodes in the middle layer of the neural network, φ(z i ) is the neural network activation function.

[0040] The selected activation functions are as follows:

[0041]

[0042] where β t is the design parameter.

[0043] Using formula (9), formula (6) can be rewritten as:

[0044]

[0045] Furthermore, in S2, the following method is used to train the neural network to obtain the optimal weight W * , as follows:

[0046] First, in order to prevent noise interference, and because the angular velocity is unknown, a second-order filter is used Filter the left and right sides of equation (12) to obtain:

[0047]

[0048] where ω n is the second-order filter parameter, ζ is the damping ratio, the complex frequency s is the independent variable of the Laplace transform, and x 2f is x 2 The filter value of yes The filter value of C 1f It is C 1 The filter value, Φ f is the filtered value of Φ, ∈ f is the filtered value of ∈.

[0049] After filtering both sides of equation (9), we can obtain:

[0050]

[0051] in Yes F f The filter value of yes The i-th column of fi is∈ f The i-th column of .

[0052] Consider the following identification model:

[0053]

[0054] in It corresponds to The estimated value of .

[0055] Define identification error:

[0056]

[0057] The improved optimal bounded ellipse method is used to train the neural network, and its specific expression is as follows:

[0058]

[0059] in

[0060]

[0061] g i =g i0 r i r pi (20)

[0062]

[0063] in is the gain coefficient, satisfying λ i >1; is the upper bound of the neural network estimation error; is a symmetric positive definite matrix, YesP i To the lower bound p li I distance; is a fixed forgetting factor, satisfying 0<g i0 <1; and For ||P i ||Lower bound and upper bound, satisfying p li <p ui ,Q=Φ(Vx),Q f =Φ(Vx f ); Projection operator Given by:

[0064]

[0065] in is a parameter, r pi Given by:

[0066]

[0067] Further, S3: for unknown system states, an observer is designed based on the training results of the neural network to observe it, including an observer for the slow subsystem, specifically:

[0068] For unknown state x 2 , the dynamic equation of the slow subsystem is as follows:

[0069]

[0070] in

[0071] The total disturbance of the system ∈ x Expands to a new state variable x 3 , let v(t) denote x 3 The system equation becomes:

[0072]

[0073] Then design the neural network observer as shown below

[0074]

[0075] where β 0 is the bandwidth of the observer, β 1 =3β 0 , is x 1 The estimated value of is the state estimation error; using the neural network state observer (26), the unknown system state x is obtained 2 and the unknown total disturbance x 3 Estimated value of This prepares the conditions for the subsequent controller design.

[0076] Further, S3: for unknown system states, an observer is designed based on the training results of the neural network to observe it, and also includes an observer for the fast subsystem, specifically:

[0077] For unknown state y 2 , considering the fast subsystem dynamic equation of formula (8), the total disturbance of the system ∈ y Expanded into a new state variable y 3 , ι(t) represents y 3 Differentiating, the system equation becomes

[0078]

[0079] Then design the neural network observer as shown below

[0080]

[0081] where β 0 is the bandwidth of the observer, β 1 =3β0 Yes 1 The estimated value of is the state estimation error; using the neural network observer (28), we can get the unknown system state y 2 and the total disturbance y 3 Estimated value of as well as This prepares the conditions for the subsequent controller design.

[0082] Further, S4: for the slow subsystem, an adaptive variable impedance control controller is designed, specifically:

[0083] Consider the slow subsystem (12), and the reference trajectory x r , the error dynamic equation of the slow subsystem is written as follows:

[0084]

[0085] in For x r The second derivative of v1 and λ v2 , they satisfy:

[0086]

[0087] in To meet the impedance control parameters in the impedance relationship shown below:

[0088]

[0089] where e = x 1 -x r is the tracking error.

[0090] Using Lambda v1 Design the sliding surface s as shown below s :

[0091] s s =λ v1 e 1 +e 2 (33)

[0092] Using equations (32) and (33), a variable impedance controller is designed for the slow subsystem, and the expression is as follows:

[0093]

[0094] in |τ ext | is τ extThe absolute value of β s and α s is a constant matrix.

[0095] Furthermore, S5: for the fast subsystem, a sliding mode controller is designed, and the controllers of the two subsystems are merged according to the singular perturbation method, and the overall controller design is given, which is specifically:

[0096] Considering the fast subsystem (8), define the sliding surface s y as follows:

[0097] s y =λ y z 1 +y 2 (35)

[0098] in is the design parameter.

[0099] Then we can give s y About the time variable t ∈ The derivative of is:

[0100]

[0101] Then the fast subsystem controller can be designed as:

[0102]

[0103] in and These are controller parameters.

[0104] Using the singular perturbation method, the final overall controller design is:

[0105] u=u a +u bs +u bf (38)

[0106] in

[0107] Beneficial effects:

[0108] Beneficial effects:

[0109] 1. The present invention proposes an adaptive variable impedance control method for a flexible robotic arm based on a neural network, which can train the neural network when some system states are unknown, and realize real-time online estimation of unknown nonlinearities of the system. Based on the results of neural network training, the present invention designs a state observer for unknown high-order angular velocities. The designed observer can well obtain the observed values ​​of unknown quantities, so as to facilitate the subsequent design of the controller. Compared with the traditional fixed stiffness impedance control, the controller designed by the invention enables the robotic arm to follow the reference trajectory faster when there is no external force contact, and can maintain better compliance characteristics when there is external force contact, which can improve the adaptability of the control method to different working states and working scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 A flowchart of a method for adaptive variable impedance control of a flexible manipulator based on a neural network;

[0111] Figure 2 It is a block diagram of a neural network-based adaptive variable impedance control method for a flexible manipulator;

[0112] Figure 3 The control output and angle tracking curve diagram of the adaptive variable impedance control method based on neural network and other methods in the case of tracking reference sinusoidal signal;

[0113] Figure 4 The tracking error curve is a comparison between the adaptive variable impedance control method based on neural network and other methods when tracking a reference sinusoidal signal. DETAILED DESCRIPTION

[0114] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0115] The present invention provides a

[0116] like Figure 1 The flowchart of a method for adaptive variable impedance control of a flexible mechanical arm based on a neural network specifically includes:

[0117] S1: Decompose the nominal fourth-order model of the flexible joint robot using the singular perturbation method. Consider the following flexible joint robot model

[0118]

[0119] in, is the joint angle, is the driving motor angle, is the inertia matrix, are the Coriolis force and the centrifugal force, is gravity, is the external force torque, is the system friction, For systems with unmodeled dynamics, is the control quantity input. is the transmission ratio matrix of the motor and is a diagonal matrix, is the moment of inertia matrix of the motor rotor and is a diagonal matrix, is the elastic coefficient matrix of the joint elastic element and is a diagonal matrix.

[0120] Rewrite the system model into state space form and take the following system state:

[0121]

[0122] Among them, 0<ε<<1 is a parameter designed by humans, B 0 =ε 2 K. At the same time, consider combining the unmodeled dynamics of the system with the friction and nonlinear terms of the system to write the lumped uncertainty Then the state space form is:

[0123]

[0124] where a 1 =D -1 B 0 , a 2 =(J -1 N -2 +D -1 )B 0 , b 1 =J -1 N -1 .

[0125] Since 0<ε<<1, the y in the system 1 ,y 2 The change rate will be faster than x 1 ,x 2 Much faster, the system state has two different time scales, so the original fourth-order system can be decomposed into two second-order subsystems by using the singular perturbation method.

[0126] Let F * =D -1 F, and u=u a +u b ,in Yes F * The estimated value of , then (3) can be transformed into (4)

[0127]

[0128] in

[0129] Let ε = 0, The system equilibrium point can be obtained

[0130]

[0131] where u bs is the control component of the slow subsystem when ε = 0. Substitute y in (2) 1 , we can get the slow subsystem as shown in equation (6).

[0132]

[0133] in

[0134] Defining new state variables Substituting it into (2), we can obtain (7)

[0135]

[0136] Defining extended time variables And let ε = 0 in (4), and then give the fast subsystem as:

[0137]

[0138] in u bf is the control component of the slow-fast system when ε = 0 and satisfies u bs +u bf =u b .

[0139] S2: Design a neural network to estimate the friction in the system and the unmodeled parts of the model, and train the neural network using the improved optimal bounded ellipse algorithm, specifically:

[0140] Consider the lumped uncertainty term F in the slow subsystem equation (5): * , design a neural network to estimate the lumped uncertainty

[0141] F * =W *T Φ(Z)+∈ (9)

[0142] Φ(Z)=[φ(z 1 ),φ(z 2 ),…,φ(z N )] T (10)

[0143] Where ∈ is the estimation error, W *is the optimal weight from the hidden layer to the output layer of the neural network, is the neural network input, is the weight from the input layer to the hidden layer of the neural network, Z = [z 1 , z 2 , …, z N ] T =Vx, N is the number of nodes in the middle layer of the neural network. i ) is the neural network activation function, and the activation function selected in the design of the present invention is as follows:

[0144]

[0145] where β t is the design parameter.

[0146] Using formula (9), formula (6) can be rewritten as:

[0147]

[0148] In order to train the neural network to obtain the optimal weight W * , the design of the present invention adopts the following method to train the neural network, which is as follows:

[0149] First, in order to prevent noise interference, and because the angular velocity is unknown, a second-order filter can be used Filter the left and right sides of equation (12) to obtain:

[0150]

[0151] where ω n is the second-order filter parameter, ξ is the damping ratio, x 2f is x 2 The filter value of yes The filter value of C 1f It is C 1 The filter value, Φ f is the filtered value of Φ, ∈ f is the filtered value of ∈.

[0152] After filtering both sides of equation (9), we can obtain:

[0153]

[0154] in Yes F f The filter value of yes The i-th column of fi is∈ f The i-th column of .

[0155] Consider the following identification model:

[0156]

[0157] in It corresponds to The estimated value of .

[0158] Define identification error:

[0159]

[0160] The improved optimal bounded ellipse method is used to train the neural network, and its specific expression is as follows:

[0161]

[0162] in

[0163]

[0164] g i =g i0 r i r pi (20)

[0165]

[0166] The gain coefficient needs to satisfy λ i >1, is the upper bound of the neural network estimation error, is a symmetric positive definite matrix, YesP i To the lower bound p li The distance of I, is a fixed forgetting factor that needs to satisfy 0<g i0 <1, and For ||P i ||Lower and upper bounds need to satisfy p li <p ui ,Q=Φ(Vx),Q f =φ(V xf ). Projection operator Given by:

[0167]

[0168] in is a parameter, r pi Given by:

[0169]

[0170] S3: For unknown system states, an observer is designed based on the training results of the neural network to observe them. Specifically:

[0171] For unknown state x 2 , consider the dynamic equation of the slow subsystem as follows:

[0172]

[0173] in

[0174] The total disturbance of the system ∈ x Expands to a new state variable x 3 , let v(t) denote x 3 The system equation becomes

[0175]

[0176] Then design the neural network observer as shown below

[0177]

[0178] where β 0 is the bandwidth of the observer, β 1 =3β 0 is x 1 The estimated value of is the state estimation error. Using the neural network state observer (26), we can get the unknown system state x 2 and the unknown total disturbance x 3 Estimated value of This prepares the conditions for the subsequent controller design.

[0179] For unknown state y 2 , considering the fast subsystem dynamic equation of formula (8), the total disturbance of the system ∈ y Expanded into a new state variable y 3 , let ι(t) denote y 3 The system equation becomes

[0180]

[0181] Then design the neural network observer as shown below

[0182]

[0183] where β 0 is the bandwidth of the observer, β 1 =3β0 , Yes 1 The estimated value of is the state estimation error. Using the neural network observer (28), we can get the unknown system state y 2 and the total disturbance y 3 Estimated value of as well as This prepares the conditions for the subsequent controller design.

[0184] S4: For the slow subsystem, design a controller capable of adaptive variable impedance control, specifically:

[0185] Consider the slow subsystem (12), and the reference trajectory x r , the error dynamic equation of the slow subsystem is written as follows:

[0186]

[0187] in For x r The second derivative of . Choose two positive real auxiliary variables λ v1 and λ v2 , they satisfy:

[0188]

[0189] in To meet the impedance control parameters in the impedance relationship shown below:

[0190]

[0191] where e = x 1 -x r is the tracking error.

[0192] Using Lambda v1 Design the sliding surface s as shown below s :

[0193] s s =λ v1 e 1 +e 2 (33)

[0194] Using equations (32) and (33), a variable impedance controller can be designed for the slow subsystem, which is expressed as follows:

[0195]

[0196] in |τ ext | is τ extThe absolute value of β s and α s is a constant matrix. It can be seen from equation (34) that the stiffness of the method in the present invention can be adaptively adjusted according to the external force of the robot arm interacting with the outside world. In this new variable impedance design method shown, when the robot arm is not in contact with an obstacle or a target object, the external force is 0, τ s =β s , at this time τ s s s =β s s s The controller has a high feedback gain, which can reduce the tracking error and ensure the tracking accuracy of the system. When the robot arm contacts an obstacle or target object, the external force is often large, τ s is infinitely close to 0, so τ s s s It is also infinitely close to 0. At this time, by selecting appropriate impedance parameters, the robot arm can show more compliance when interacting with the environment, reduce the contact force, and ensure the safety of equipment and personnel. In summary, the variable impedance control proposed in the present invention enables the robot arm to better follow the reference trajectory when it is not in contact with an obstacle or target object, and can show better compliance when it contacts an obstacle or target object.

[0197] S5: Design a sliding mode controller for the fast subsystem, and combine the controllers of the two subsystems according to the singular perturbation method to give the overall controller design, which is as follows:

[0198] Considering the fast subsystem (8), define the sliding surface s y as follows:

[0199] s y =λ y z 1 +y 2 (35)

[0200] in is the design parameter.

[0201] Then we can give s y About the time variable t ∈ The derivative of is:

[0202]

[0203] Then the fast subsystem controller can be designed as:

[0204]

[0205] in and These are controller parameters.

[0206] Using the singular perturbation method, the final overall controller design is:

[0207] u=u a +u bs +u bf (38)

[0208] in

[0209] Figure 2 This is a block diagram of an adaptive variable impedance control method for a flexible robotic arm based on a neural network, which describes the framework of the entire control system.

[0210] The technical solution disclosed in the present invention is simulated and verified as follows:

[0211] Step 1: Select the system parameters of the two-degree-of-freedom flexible joint robot and design the parameters of the controller.

[0212] The parameters in the robotic arm model are:

[0213]

[0214] Selection of singular perturbation decomposition parameters

[0215] ε=0.1

[0216] The design parameters of the variable stiffness controller are selected as follows:

[0217]

[0218] The parameters of the sliding mode controller are selected as follows:

[0219]

[0220] Step 2: Select the reference signal, design the sampling period and simulation duration.

[0221] The reference signal is x r1 =x r2 =sin(0.2πt)+0.1

[0222] At the same time, for both reference trajectories, b = 0.9 to place an obstacle to test the flexibility of the control algorithm. The sampling period is set to dt = 0.0001s, and the simulation duration is designed to be t stop =10s.

[0223] Step 3: Conduct simulation experiments to compare the adaptive variable impedance control method proposed in the present invention with the traditional impedance control method. Figure 3 , Figure 4 shown. Figure 3 The angle tracking curve is compared between the adaptive variable impedance control method and other methods when tracking a reference sinusoidal signal. Figure 4 The angle tracking error curve of the adaptive variable impedance control method compared with other methods when tracking a reference sinusoidal signal. It can be seen from the figure that compared with the traditional method, the method proposed in the present invention maintains sufficient compliance when encountering obstacles, can produce smaller impacts, and prevent the robot arm from contacting objects or people with excessive torque to cause safety problems.

[0224] Based on the above technical content, a neural network-based adaptive variable impedance control method for flexible manipulators can be obtained. The singular perturbation method is used to decompose complex systems, the neural network is used to estimate the lumped uncertainty in the system, the improved optimal bounded ellipse algorithm is used to train the neural network, and the improved variable stiffness impedance control is used to design the controller. The gradient vanishing and gradient exploding problems in traditional neural network training are solved, and a state observer is established to solve the problem of unmeasurable high-order angular velocity and the problem that fixed parameters in traditional impedance control cannot be applied to multiple scenarios and multiple working states.

[0225] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for adaptive variable impedance control of a flexible manipulator based on a neural network, characterized in that: The steps include: S1: For the fourth-order nominal model of the two-degree-of-freedom flexible joint robot, in order to simplify the controller design, the singular perturbation method is used to decompose it into two second-order subsystems: a fast subsystem and a slow subsystem; S2: Design a neural network to estimate the friction in the system and the unmodeled parts of the model, and train the neural network using the improved optimal bounded ellipse algorithm; S3: For unknown system states, an observer is designed based on the training results of the neural network to observe them; S4: Design a variable stiffness impedance controller that adaptively changes stiffness for the slow subsystem; S5: Design a sliding mode controller for the fast subsystem and combine the controllers of the two subsystems according to the singular perturbation method to give the overall controller design.

2. A method for adaptive variable impedance control of a flexible manipulator neural network based on output feedback as claimed in claim 1, characterized in that: In S1, for the fourth-order nominal model of the two-degree-of-freedom flexible joint manipulator, in order to simplify the controller design, the singular perturbation method is used to decompose it into two second-order subsystems, a fast subsystem and a slow subsystem, specifically: Consider the following flexible joint robot model in, is the joint angle, is the driving motor angle, is the inertia matrix, are the Coriolis force and the centrifugal force, is gravity, is the external force torque, is the system friction, For systems with unmodeled dynamics, is the control quantity input, is the transmission ratio matrix of the motor and is a diagonal matrix, is the moment of inertia matrix of the motor rotor and is a diagonal matrix, is the elastic coefficient matrix of the joint elastic element and is a diagonal matrix; is the set of real numbers, and its superscript is the dimension; The singular perturbation method is as follows: first rewrite the system model into state space form and take the following system state: Among them, x1, x2, y1, y2 are four system states, 0<ε<<1 is the preset parameter, B0=ε 2 K; At the same time, the unmodeled dynamics of the system are combined with the friction and nonlinear terms of the system to form a lumped uncertainty Then the state space form is: Where a1=D -1 B0, a2 = (J -1 N -2 +D -1 )B0,b1=J -1 N -1 ; Because 0<ε<<1, the change speed of y1, y2 in the system is faster than that of x1, x2, and the system state has two different time scales. The original fourth-order system is decomposed into two second-order subsystems using the singular perturbation method; Let the new lumped uncertainty F * =D -1 F, uncertain compensation item and u=u a +u b ,u b is the tracking control item to be designed, where Yes F * The estimated value of , then (3) becomes (4) in Let ε = 0, Get the system equilibrium point where u bs is the control component of the slow subsystem when ε = 0; Substituting y1 in (2), we get the slow subsystem shown in equation (6): in Defining new state variables Substituting it into (2), we get formula (7): Defining extended time variables And let ε = 0 in (4), and then give the fast subsystem as: in u bf is the control component of the slow-fast system when ε = 0, and satisfies u bs +u bf =u b .

3. The method for adaptive variable impedance control of a flexible manipulator neural network based on output feedback as claimed in claim 1, characterized in that: S2: Designing a neural network to estimate the friction in the system and the unmodeled part of the model, and training the neural network with an improved optimal bounded ellipse algorithm, specifically: Consider the lumped uncertainty term F in the slow subsystem equation (5): * , design a neural network to estimate the lumped uncertainty F * : F * =In *T Φ(Z)+∈ (9) Φ(Z)=[φ(z1),φ(z2),…,φ(z N )] T (10) Where ∈ is the estimation error, W * is the optimal weight from the hidden layer to the output layer of the neural network, Z = [z1, z2, ..., z N ] T =Vx, is the neural network input, is the weight from the input layer to the hidden layer of the neural network, N is the number of nodes in the middle layer of the neural network, φ(z i ) is the neural network activation function; The selected activation functions are as follows: where β t is the design parameter; Using formula (9), formula (6) can be rewritten as: 。 4. The method for adaptive variable impedance control of a flexible manipulator neural network based on output feedback as claimed in claim 3, characterized in that: In S2, the following method is used to train the neural network to obtain the optimal weight W * , as follows: First, in order to prevent noise interference, and because the angular velocity is unknown, a second-order filter is used Filter the left and right sides of equation (12) to obtain: where ω n is the second-order filter parameter, ζ is the damping ratio, the complex frequency s is the independent variable of the Laplace transform, and x 2f is the filtered value of x2, yes The filter value of C 1f is the filter value of C1, Φ f is the filtered value of Φ, ∈ f is the filtered value of ∈; After filtering both sides of equation (9), we can obtain: in Yes F f The filter value of yes The i-th column of fi is∈ f The i-th column of Consider the following identification model: in It corresponds to An estimated value of Define identification error: The improved optimal bounded ellipse method is used to train the neural network, and its specific expression is as follows: in g i =g i0 r i r pi (20) in is the gain coefficient, satisfying λ i >1; is the upper bound of the neural network estimation error; is a symmetric positive definite matrix, YesP i To the lower bound p li I distance; is a fixed forgetting factor, satisfying 0<g i0 <1; and For ||P i ||Lower bound and upper bound, satisfying p li <p ui ,Q=Φ(Vx),Q f =Φ(Vx f ); Projection operator Given by: in is a parameter, r pi Given by:

5. A method for adaptive variable impedance control of a flexible manipulator neural network based on output feedback as claimed in any one of claims 1 to 4, characterized in that: S3: For unknown system states, an observer is designed based on the training results of the neural network to observe the unknown system states, including an observer for the slow subsystem, specifically: For the unknown state x2, the dynamic equation of the slow subsystem is as follows: in The total disturbance of the system ∈ x Expanded into a new state variable x3, let v(t) represent the differential of x3, then the system equation becomes: Then design the neural network observer as shown below Where β0 is the bandwidth of the observer, β1 = 3β0, is the estimated value of x1, is the state estimation error; using the neural network state observer (26), we get the estimated values ​​of the unknown system state x2 and the unknown total disturbance x3 This prepares the conditions for the subsequent controller design.

6. The method for adaptive variable impedance control of a flexible manipulator neural network based on output feedback as claimed in claim 5, characterized in that: S3: for unknown system states, an observer is designed based on the training results of the neural network to observe the unknown system states, and also includes an observer for the fast subsystem, specifically: For the unknown state y2, consider the fast subsystem dynamic equation of formula (8), and transform the total disturbance of the system ∈ y Expanded into a new state variable y3, ι(t) represents the differential of y3, the system equation becomes Then design the neural network observer as shown below Where β0 is the bandwidth of the observer, β1 = 3β0, is the estimated value of z1, is the state estimation error; using the neural network observer (28), we can get the estimated values ​​of the unknown system state y2 and the total disturbance y3 as well as This prepares the conditions for the subsequent controller design.

7. The method for adaptive variable impedance control of a flexible manipulator neural network based on output feedback as claimed in claim 5, characterized in that: S4: Design an adaptive variable impedance control controller for the slow subsystem, specifically: Consider the slow subsystem (12), and the reference trajectory x r , the error dynamic equation of the slow subsystem is written as follows: in For x r The second derivative of v1 and λ v2 , they satisfy: in To meet the impedance control parameters in the impedance relationship shown below: where e = x1-x r is the tracking error; Using Lambda v1 Design the sliding surface s as shown below s : s s =λ v1 e1+e2 (33) Using equations (32) and (33), a variable impedance controller is designed for the slow subsystem, and the expression is as follows: in |τ ext | is τ ext The absolute value of β s and α s is a constant matrix.

8. The method for adaptive variable impedance control of a flexible manipulator neural network based on output feedback as claimed in claim 6, characterized in that: S5: Design a sliding mode controller for the fast subsystem, and combine the controllers of the two subsystems according to the singular perturbation method to give the overall controller design, which is specifically: Considering the fast subsystem (8), define the sliding surface s y as follows: s y =λ y z1+y2 (35) in is the design parameter; Then we can give s y About the time variable t ∈ The derivative of is: Then the fast subsystem controller can be designed as: in and All are controller parameters; Using the singular perturbation method, the final overall controller design is: in=in a +in bs +in bf (38) in

Images