A robot controller design method based on model reference adaptive impedance

Abstract

The application relates to the technical field of manipulator control, and discloses a manipulator controller design method based on model reference adaptive impedance, which comprises the design of a reference impedance model, the design of an adaptive estimation law and the design of a manipulator control law; the design of the reference impedance model is established by acquiring the tactile force information of the manipulator end, and reference position output is realized; the design of the adaptive estimation law is realized by acquiring the joint position information of the manipulator, acquiring the operating space position of the manipulator and designing an adaptive estimation law based on a sliding mode variable; and the design of the manipulator control law is based on the adaptive estimation law, the joint position information of the manipulator is acquired, and the control law based on the reference impedance model is calculated. The application has high stability and effectiveness, overcomes the problem of model uncertainty caused by the joint friction of the manipulator, the time-varying characteristics of physical parameters and inaccurate measurement, realizes effective and stable flexible grabbing of the manipulator, and meets the requirement of the diversity of the grabbed targets of the manipulator.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of manipulator control, and particularly relates to a manipulator controller design method based on model reference adaptive impedance. BACKGROUND

[0002] A manipulator is an important tool for realizing intelligent operation and human-computer interaction. With the increasing requirement for operation precision, the manipulator is no longer simply controlled to open and close, and the vulnerability of an operation object and the firmness of a grabbing process need to be considered. Special manipulators such as fruit picking and underwater sample collection have the characteristic of operation object diversity, and have the problem of weak operability. If the force is too large during the operation process, the grabbing object is easily damaged, and if the force is too small, the grabbing object is easily dropped. In addition, the manipulator has the characteristic of nonlinearity, and the model of the manipulator cannot be determined due to the uncertainty of physical parameters and joint friction, which brings about the problem of reliability uncertainty of the manipulator control.

[0003] Therefore, under the premise of ensuring that the manipulator stably grabs the object, the manipulator needs to avoid damaging the grabbing object to realize compliant grabbing. The core is position control in free space and force control in the grabbing process, and belongs to the category of force control and position control. The force control and position control of the manipulator include impedance control, admittance control and force / position hybrid control. The force / position hybrid control establishes the relationship between the force and the position deviation between the manipulator and the outside world, and a control law is designed through a force error to realize force tracking. However, great shock will be generated in the case of a large stiffness of the operation object. Unlike the force / position hybrid control method which directly and explicitly controls the force and displacement, the impedance control adjusts the relationship between the force and the motion by changing the stiffness, damping and inertia of the manipulator, and realizes compliant control of the manipulator. However, if the model of the manipulator cannot be accurately determined, the pure impedance control will cause the system to have the potential risk of instability.

[0004] Therefore, the present application provides a manipulator controller design method based on model reference adaptive impedance. The model reference adaptive impedance is designed to realize compliant operation of the manipulator, aiming at the problem of model uncertainty caused by joint friction and errors in the measurement of physical parameters in the operation process of the manipulator. SUMMARY

[0005] In view of the above, the present application aims to provide a manipulator controller design method based on model reference adaptive impedance. The manipulator of the method is an n-degree-of-freedom manipulator, and the joint space model of the manipulator is as follows:

[0006]

[0007] wherein M q , C q , g q , Fq These represent the manipulator's inertia, the sum of centrifugal and Coriolis forces, the gravity term, and the Jacobian matrix, τ. q To control the input torque, that is, the driving force given to the joints of the robotic arm for rotation. F e It is the contact force between the robotic arm and the object being manipulated. q represents the frictional torque of the joints inside the robotic arm. These are the joint position, velocity, and acceleration of the robotic arm.

[0008] The n-DOF manipulator proposed in this invention has the following model in its operational space:

[0009]

[0010] x、 These represent the position, velocity, and acceleration of the robotic arm within its operating space. The conversion relationship between the parameters in the operating space and joint space is as follows:

[0011]

[0012] This invention designs a method for a robot controller based on model-referenced adaptive impedance. By acquiring tactile force information at the robot's end effector, a reference impedance model of the robot is established based on the tracked force signal and the measured tactile force signal, achieving a reference position output. The robot's operational space position is obtained by acquiring joint position information; an adaptive estimation law based on sliding mode variables is designed according to the reference position of the reference impedance model. A robot control law is designed based on the joint position information and the reference position output by the reference impedance model, and the stability of the robot control law is verified by designing a Lyapunov function. The designed robot control law and adaptive estimation law achieve tracking of the robot's end effector tactile force to a set tactile force signal and asymptotically consistent convergence of the robot's end effector position to the reference position output by the reference impedance model.

[0013] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0014] A design method for a robot controller based on model reference adaptive impedance includes the design of the reference impedance model, the design of the adaptive estimation law, and the design of the robot control law.

[0015] The design of the reference impedance model involves acquiring tactile force information at the end of the robotic arm, establishing a reference impedance model of the robotic arm based on the tracking force signal and the measured tactile force signal, and achieving reference position output.

[0016] The design of the adaptive estimation law involves obtaining the joint position information of the manipulator, obtaining the manipulator's operating space position, and designing an adaptive estimation law based on sliding mode variables according to the reference position of the reference impedance model.

[0017] The design of the robot control law is based on an adaptive estimation law to obtain the joint position information of the robot. The robot control law is designed according to the reference position output by the reference impedance model, and the stability and effectiveness of the robot control law are verified by designing a Lyapunov function.

[0018] Preferably, the mathematical model expression of the reference impedance model is:

[0019]

[0020] Where, matrix M d B d The target impedance parameters are the inertia and damping matrices of the reference impedance model designed for the robot arm, respectively; F e F is the contact force between the robotic arm and the object being manipulated. d It is the standard force signal value, x mr This is the output reference position of the target impedance model in Cartesian coordinates.

[0021] Preferably, the reference impedance model is a second-order impedance model, M d ∈R 3×3 A positive definite diagonal matrix, B d ∈R 3×3 A positive definite diagonal matrix, F d ∈R 3×1 F e ∈R 3×1 By acquiring tactile force information at the end effector of the robotic arm, a reference impedance model of the robotic arm is established based on the tracking force signal and the measured tactile force signal. The reference position x is then obtained based on this model. mr As the target for robot arm position tracking, the target force and the operating force are matched by adjusting the position of the robot arm. When the system is in a steady state, F d =F e ,at this time The value is zero, satisfying the steady-state equilibrium of the impedance model of the reference manipulator.

[0022] Preferably, the design of the adaptive estimation law includes an adaptive estimation law based on the position tracking error. The design and adaptive estimator based on model error The design.

[0023] Preferably, the adaptive estimation law based on position tracking error The mathematical expression is:

[0024] Where P is a positive definite diagonal matrix. Based on the transpose of the linearized regression matrix of the robotic arm model is the inverse of the Jacobian matrix of the manipulator, s is the sliding variable.

[0025] The adaptive estimation law based on the model error is The mathematical expression of the adaptive estimation law based on the model error is

[0026]

[0027] where e(t) is the error between the filtered form of the manipulator model and the estimated model; P(t) is a bounded positive definite adaptive gain matrix; W w (t) is the integral form of the manipulator model; R(t) = a0I is a uniformly positive definite weighting matrix, which represents the importance of the parameter information e(t) to the adaptive estimation law, a0 is a positive real number in R(t), and I is the corresponding matrix. The manipulator model is The estimated model of the manipulator is M q (q), g q (q), is the sum of the inertia, centrifugal and Coriolis forces, the gravity term, and the joint friction torque of the manipulator. is the estimated value of the corresponding parameter.

[0028] The mathematical expression of the bounded positive definite adaptive gain matrix P(t) is

[0029]

[0030] where β(t) is a variable forgetting factor, which is designed as β(t) = β0(1 - ||P(t)|| / k0), β0 and k0 are normal numbers, respectively representing the maximum forgetting rate and the pre-specified upper bound of the norm ||P(t)|| of the gain matrix.

[0031] The mathematical expression of the manipulator control law is

[0032]

[0033] where are the corresponding estimated values of the manipulator parameters M q (q), g q (q), ; is the tracking sliding mode function of the manipulator, is the error of the tracking reference position of the end position of the manipulator; is the reference variable of the manipulator; it can be obtained from the above as

[0034] The mathematical expression of the manipulator control law can also be represented as

[0035]

[0036] wherein, is the unknown parameter information estimation value of the manipulator, and η 1, η 2 are known vectors,

[0037] is a system regression matrix composed of known coordinate variables and their derivative groups of the system, and according to different unknown parameters, the manipulator model is linearly represented as:

[0038]

[0039] wherein, is an arbitrary known vector of corresponding dimension, and θ is a vector containing unknown parameter information of the manipulator model.

[0040] The manipulator control law is designed according to the joint position information of the manipulator and the reference position output by the reference impedance model, and the stability of the manipulator control law is verified by designing a Lyapunov function. The designed manipulator control law and adaptive estimation law realize the tracking of the set tactile force signal by the tactile force at the end of the manipulator and the gradual consistent convergence of the reference position output by the reference impedance model to the reference position of the end position of the manipulator. In order to eliminate the time-varying characteristics of the physical parameters, an adaptive estimation law based on model error is designed to compensate for the uncertainty error of the manipulator model. It is ensured that the manipulator model under the manipulator control law is consistent with the reference impedance model, the standard force signal is tracked by the operating force at the end of the manipulator, and the reference position error of the reference impedance model output by the end position of the manipulator gradually converges to zero.

[0041] In addition, the manipulator controller design method based on model reference adaptive impedance of the present application also contains other components that can make the present application operate normally, which are all set in the conventional manner in the art and are common technical means in the art, and will not be described here.

[0042] Compared with the prior art, the present application has the following beneficial effects:

[0043] Through the design of the manipulator controller based on model reference adaptive impedance, the designed manipulator controller realizes the tracking of the set tactile force signal by the tactile force at the end of the manipulator and the gradual consistent convergence of the reference position output by the reference impedance model to the reference position of the end position of the manipulator. It has high stability and effectiveness, overcomes the problems of model uncertainty caused by joint friction of the manipulator, time-varying characteristics of physical parameters and inaccurate measurement, realizes effective and stable compliance grasping of the manipulator, and meets the requirement of diversity of the grasped target of the manipulator. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1A flowchart of a mechanical arm controller design method based on model reference adaptive impedance in an embodiment of the present application is shown in the figure.

[0045] Figure 2 A control system structure diagram of a mechanical arm controller based on model reference adaptive impedance in an embodiment of the present application is shown in the figure.

[0046] Figure 3 A mechanical arm system simulation model in an embodiment of the present application is shown in the figure.

[0047] Figure 4 A mechanical arm operation force tracking standard force signal simulation curve in an embodiment of the present application is shown in the figure.

[0048] Figure 5 A mechanical arm operation space position, reference position tracking simulation curve in an embodiment of the present application is shown in the figure.

[0049] Figure 6 A mechanical arm joint angle simulation curve in an embodiment of the present application is shown in the figure.

[0050] Figure 7 A mechanical arm controller input simulation curve in an embodiment of the present application is shown in the figure.

[0051] Figure 8 A mechanical arm uncertain parameter estimation curve in an embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0052] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the protection scope of the present application.

[0053] EMBODIMENT

[0054] A mechanical arm controller design method based on model reference adaptive impedance includes: reference impedance model design, mechanical arm control law design and adaptive estimation law design. The reference impedance model design part obtains the tactile force information at the end of the mechanical arm, establishes the reference impedance model of the mechanical arm according to the tracking force signal and the measured tactile force signal, and realizes the reference position output. The adaptive estimation law design part obtains the joint position information of the mechanical arm and the operation space position of the mechanical arm; the adaptive estimation law based on the sliding variable is designed according to the reference position of the reference impedance model; the mechanical arm control law design part obtains the joint position information of the mechanical arm based on the adaptive estimation law, calculates the mechanical arm control law based on the reference impedance model, and designs the Lyapunov function to verify the stability and effectiveness of the mechanical arm control law.

[0055] The design scheme in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.

[0056] As shown in FIG. 1, in step S1, the basic details are to acquire the tactile force information at the end of the manipulator, to establish a reference impedance model of the manipulator according to the tracking force signal and the measured tactile force signal, and to realize the reference position output. The mathematical model expression of the reference impedance model of the manipulator is as follows: Figures 1-2

[0057]

[0058] wherein, matrix M d , B d are target impedance parameters, respectively, the inertia and damping matrix of the designed reference impedance model of the manipulator; F e is the contact force between the manipulator and the operating object, F d is the standard force signal value, and x mr is the output reference position of the target impedance model in the Cartesian coordinate system. The reference impedance model is a second-order impedance model, wherein M d ∈R 3×3 is a positive definite diagonal matrix, B d ∈R 3 ×3 is a positive definite diagonal matrix, F d ∈R 3×1 , F e ∈R 3×1 . By acquiring the tactile force information at the end of the manipulator, the reference impedance model of the manipulator is established according to the tracking force signal and the measured tactile force signal. The reference position x mr is obtained as the target of the position tracking of the manipulator, and the matching between the target force and the operating force is realized by adjusting the position of the manipulator. When the system is in a steady state, F d =F e , at this time is zero, and the steady-state balance of the reference impedance model is satisfied.

[0059] The design of the adaptive estimation law is to acquire the joint position information of the manipulator, to acquire the operating space position of the manipulator, and to design the adaptive estimation law based on the sliding mode variable according to the reference position of the reference impedance model.

[0060] The design of the adaptive estimation law includes the design of the adaptive estimation law based on the position tracking error and the design of the adaptive estimation law based on the model error.

[0061] The mathematical expression of the adaptive estimation law based on the position tracking error is as follows: ​

[0062]

[0063] where P is a positive definite diagonal matrix, According to the linearization of the robot model, is the inverse of the robot Jacobian matrix, and s is the sliding variable.

[0064] The adaptive estimation law based on the model error The mathematical expression of the adaptive estimation law is:

[0065]

[0066] where e(t) is the error between the filtered robot model and the estimated model; P(t) is a bounded positive definite adaptive gain matrix; W w (t) is the integral form of the robot model; R(t) = a0I is a uniformly positive definite weighting matrix, which represents the importance of the parameter information e(t) to the adaptive estimation law, and a0 is a positive real number in R(t), and I is the corresponding matrix. The robot model is The estimated model of the robot is M q (q), g q (q), is the sum of the robot inertia, centrifugal force and Coriolis force, gravity term, and joint friction torque. is the estimated value of the corresponding parameter.

[0067] The mathematical expression of the bounded positive definite adaptive gain matrix P(t) is:

[0068]

[0069] where β(t) is a variable forgetting factor, designed as: β(t) = β0(1-||P(t)|| / k0), β0 and k0 are normal numbers, respectively representing the maximum forgetting rate and the upper bound of the gain matrix norm ||P(t)||.

[0070] The mathematical expression of the robot control law is:

[0071]

[0072] where, are the corresponding estimated values of the robot parameters M q (q), g q (q), is the robot tracking sliding mode function, ​Error of the manipulator end position tracking the reference position Reference variable of the manipulator

[0073] The mathematical expression of the manipulator control law can also be expressed as:

[0074]

[0075] Wherein, Unknown parameter information uncertainty estimation value of the manipulator; η1, η2 are known vectors,

[0076] The system regression matrix composed of the known coordinate variables and the derivative thereof of the manipulator model, according to different unknown parameters, the linearization expression of the manipulator model is:

[0077]

[0078] Wherein, θ is a vector of unknown parameter information of the manipulator model.

[0079] In the application, the object designed according to the reference impedance model is an n-degree-of-freedom manipulator, in order to realize the force tracking of the target force signal, the control law and the adaptive estimation law are designed, wherein the joint space model of the n-degree-of-freedom manipulator is:

[0080]

[0081] Wherein, M q , C q , g q , F q are the inertia, the sum of centrifugal force and Coriolis force, the gravity term and the Jacobian matrix of the manipulator respectively, τ q is the control input torque, i.e. the driving force for rotating the joints of the manipulator, F e is the contact force between the manipulator and the operating object, is the internal joint friction torque of the manipulator, q、 are the joint position, velocity and acceleration of the manipulator respectively.

[0082] The joint space model of the n-degree-of-freedom manipulator is converted into the operating space model:

[0083]

[0084] x、 are the position, velocity and acceleration in the operating space of the manipulator respectively, and the conversion relationship between the corresponding parameters in the operating space and the joint space is:

[0085]

[0086] The basic objective in step S3 is to design a manipulator control law to realize the tracking control of the manipulator operating force to the target force signal, and the design process is as follows:

[0087] In order to realize the tracking of the manipulator end operating space position x to the reference impedance reference position x mr , a sliding mode function is designed as follows: λ1 is a positive definite matrix, A reference velocity vector is designed as follows: From the sliding mode function and the reference velocity vector, we have: Taking the first derivative of both sides and multiplying M x (q) on the left, we can obtain:

[0088]

[0089] Substituting the operating space model, we can obtain:

[0090]

[0091] If the parameters M x (q) of the manipulator model nonlinear equation, g x (q) are all known, and the interaction force F e between the manipulator end and the operating object is measurable, then the manipulator control law can be designed as follows:

[0092]

[0093] Substituting the control law formula τ x0 in the operating space into the operating space model, we can obtain:

[0094]

[0095] A Lyapunov function is designed as follows: It is obvious that V0≥0 because M x (q) is a positive definite matrix.

[0096] Taking the first derivative of V0 with respect to time, and using the property of the anti-symmetric matrix of the manipulator , we have:

[0097]

[0098] Therefore According to the Lyapunov stability theorem, if the parameters M x (q) of the manipulator nonlinear dynamics equation, g x (q) are all known, and the interaction force F x0 between the manipulator end and the operating object is measurable, then the manipulator control law can be designed as follows: The whole known, design control law τ x0 To ensure system stability.

[0099] Due to the measurement problem and the robot joint friction brings robot model uncertainty, unable to obtain the real model parameters of the robot, Respectively, the corresponding estimates of the robot parameters (inertia, centrifugal force and Coriolis force, gravity term and Jacobian matrix). τ x0 The essence of the design of the nominal model control law or known as the ideal control law, reference τ x0 Then the model uncertainty control law design:

[0100]

[0101] According to the conversion relationship between the robot operating space and the joint space, the control law τ q Design as

[0102]

[0103] Where η1, η2 are known vectors, which are expressed as follows:

[0104]

[0105] Because the robot model can be linearized as:

[0106]

[0107] Where, Is an arbitrary corresponding dimension known vector, θ contains the vector of unknown parameters of the robot model information. Is the system regression matrix composed of the system known coordinate variables and their derivatives. The control law τ q In the joint space can be rewritten as:

[0108]

[0109] τ q Is the basic goal of step S3 design robot control law. Where, Is the estimated value of the robot uncertain parameters, Is the robot Jacobian matrix, F e Is the interaction force between the robot end and the operating object.

[0110] Is the adaptive estimation law designed in step S2, including the adaptive estimation law based on position tracking error Design and adaptive estimation law based on model error Design. Where the adaptive estimation law based on position tracking error Designed as follows:

[0111]

[0112] Where P is a positive definite diagonal matrix. The transpose of the linearized regression matrix based on the robotic arm model. Let be the inverse of the Jacobian matrix of the robot arm, and s be the sliding mode variable.

[0113] To prove the effectiveness of the robot control law designed in step S3 and the adaptive estimation law designed in step S2, the stability of the control system is proven. First, the control law τ... q Substituting the robotic arm's operational space model, we obtain:

[0114]

[0115] in, This represents the error between the estimated and true values ​​of the uncertain term. The Lyapunov function is designed as follows:

[0116]

[0117] Where V1≥0, taking the derivative with respect to V1, we get:

[0118]

[0119] so According to Lyapunov's stability theorem, if the parameter M in the nonlinear dynamic equation of the manipulator... x (q) g x (q) Parameters unknown, design control law τ q Ensure system stability.

[0120] The adaptive estimation law designed for step S2, wherein the adaptive estimation law is based on the position tracking error. The design steps are as follows.

[0121] Define ω(s) as To stabilize an appropriate filter ω(t) = ae -at The impulse response of ω(s). where 'a' is the bandwidth of the filter. Applying the filter ω(s) to the dynamic equations of the robot arm, and convolving it with respect to both ends of the joint space model of the robot arm, we have:

[0122]

[0123] Using the integral-by-parts method, the joint space filtering form model of the robot arm is as follows:

[0124]

[0125] The manipulator joint space filtered form model can be rewritten in a new regression matrix form as: y(t) = W w (t)θ, y(t) is the first order filtered form of the linearized parameters of the manipulator dynamic model. W w can be directly obtained by filtering the regression matrix Y q (t) = W Thus, W can be directly obtained by measuring q w , without the need of This is the main reason for using a first order filter to implement the filtering calculation. Let be the estimate of the uncertain parameter θ, then the estimate of y(t) can be rewritten as:

[0126]

[0127] The prediction error e(t) of the filtered form can be rewritten as:

[0128]

[0129] where, Adaptive estimation law based on position tracking error is designed as follows:

[0130]

[0131] R(t) is called a uniformly positive definite weighting matrix, which represents the importance of the parameter information e(t) to the adaptive estimation law. R(t) is defined as: R(t) = a0I, a0is a normal number, and I is the corresponding unit matrix. P(t) is called a bounded positive definite adaptive gain matrix, and P(t) is defined as:

[0132]

[0133] where β(t) is called a variable forgetting factor, and its definition is: β(t) = β0(1-||P(t)|| / k0), β0and k0are normal numbers, respectively representing the maximum forgetting rate and the pre-specified upper bound of the gain matrix norm ||P(t)||.

[0134] ​The variable forgetting factor β(t) means that when ||P(t)|| is small, only β0 needs to be considered, ignoring other factors of the forgetting factor. As ||P(t)|| increases, the forgetting rate decreases. Forgetting stops when ||P(t)|| reaches a certain norm. Since a large β0 means an excessively fast forgetting rate, choosing β0 also represents a trade-off between the parameter tracking speed and the oscillation of the estimated parameters. Choosing ||P(t)|| is called the least squares estimator with a forgetting factor, also known as the bounded-gain-forgetting (BGF) estimator. Choosing P(0)≤β0I ensures... Positive definiteness.

[0135] To further prove the effectiveness of the robot control law designed in step S3 and the adaptive estimation law designed in step S2, the stability of the control system is proven. The Lyapunov function is designed as follows:

[0136]

[0137] in, This represents the error between the estimated and true values ​​of the uncertain term. Clearly, V² ≥ 0. Taking the derivative of V² and using a robotic arm... As properties of antisymmetric matrices, we have:

[0138]

[0139] The adaptive estimation law formula and the formula for positive definite adaptive update rate Substituting the variable forgetting factor β(t) = β0(1 - ||P(t)|| / k0) into... We can obtain:

[0140]

[0141] When choosing When P(t) is positive definite and because β(t)≥0, therefore we know According to Lyapunov's stability theorem, the designed control law guarantees that the system is stable.

[0142] like Figure 3 As shown, to verify the effective performance of the designed controller without loss of generality, a planar two-bar rotating structure is used as the controlled object of the robot. The designed reference impedance model is as follows: Robot control law: The adaptive estimation law for the robotic arm is: As an overall control strategy.

[0143] like Figure 3As shown, the physical parameters of the robotic arm are set as m1 = 0.1 kg, m2 = 0.1 kg, and l1 = l2 = 0.1 m. In the robotic arm controller, the desired impedance parameter is set to M. d =diag(1,1), B d =diag(10,10), sliding mode function coefficients λ1 = 30, adaptive estimator a0 = 10, β0 = 10, first-order filter bandwidth parameter a = 2. Internal friction of the manipulator introduces disturbance torque: Where D = diag(20,20) and N = diag(10,10). The initial motion parameters are set as q1(0) = π / 3. q2(0)=π / 3, Regression matrix Y q Through Y q =[Y 11 Y 12 Y 13 ;Y 21 Y 22 Y 23 Y was obtained. q Each element value in the array can be represented as:

[0144]

[0145]

[0146]

[0147] Y 21 =0

[0148]

[0149]

[0150] like Figure 3 As shown, the motion of the robotic arm can be divided into free space motion and force-induced motion after contact with the manipulated object. When the robotic arm is performing underwater tasks, the end effector speed is low. We can ignore the damping and inertia terms of the manipulated object on the operating force, and only consider the effect of the position of motion. The manipulated object can be considered as a linear spring. We only consider the tactile force F in the x-axis direction. e In Cartesian coordinates, the manipulator's operating force is expressed as:

[0151]

[0152] Where, x e k represents the critical position where the robotic arm makes contact with the object being manipulated. e This represents the stiffness coefficient of the grasped target. When x <x eWhen x ≥ x, the underwater manipulator moves in free space; when x ≥ x e This can be viewed as the underwater manipulator coming into contact with the object being manipulated. In this case, the force model of the object can be simplified to a spring model. Let x be the critical position of contact between the object and the manipulator. e =0.15m, stiffness coefficient k e =200N / m.

[0153] In the simulation experiment, a standard force signal was set as the target force for the robot's end effector. A tracking force was set in the x-axis direction of the robot's end effector operating space, while no target force value was set in the y-axis direction. The target force value F in the x-axis direction was set. d =10(1+2sin(0.25t)), the simulation time is set to 60s, and the force-displacement tracking effect is observed.

[0154] like Figures 4-6 As shown, the manipulator's end effector can track the target force value, and simultaneously, the manipulator's end effector position tracks the reference position of the reference impedance model. Whether in free space or constrained motion in contact with the target, the manipulator can ensure tracking of the reference position output by the reference impedance model, and the manipulator's end effector force is consistent and equal to the standard force. The manipulator initially operates in a free position without contact with the target. When it moves 0.15m while tracking the reference position, it interacts with the target, still tracking the reference position. At this point, the manipulator begins tracking the target force until the tracking force error asymptotically converges to zero.

[0155] Depend on Figures 7-8 It can be seen that, under conditions of system model uncertainty and external disturbances, the overall manipulator system still maintains target force tracking. The adaptive estimation law of the manipulator's internal uncertainty compensates for its own model uncertainty, satisfying the robust stability characteristics. Simulation results verify the effectiveness of the manipulator's force tracking under conditions where joint friction causes uncertainty in the manipulator model.

[0156] The above describes a robot controller designed based on model reference adaptive impedance. A Lyapunov function is designed to ensure system stability. A two-joint degree-of-freedom robot model is designed, and the force tracking performance of the controller is verified on the MATLAB / SIMULINK platform, ensuring the stability and reliability of the control system. The control law designed with the adaptive impedance model ensures that the robot's end effector tracks the designed force tracking signal. Furthermore, it overcomes the model uncertainties caused by joint friction, time-varying physical parameters, and inaccurate measurements, thus meeting the diverse target grasping requirements of the robot.

[0157] Embodiments of the application have been described above, with examples of the description being illustrative, not exhaustive, and not limited to the disclosed embodiments. Many modifications and variations of the described embodiments are possible in light of the above teachings. It is, therefore, to be understood that within the scope of the claims and their equivalents, the application can be practiced otherwise than as specifically described.

Claims

1. A model reference adaptive impedance based robot controller design method, characterized by, The method comprises the following steps: S1, reference impedance model design: the reference impedance model design is realized by acquiring the mechanical hand end tactile force information, establishing the reference impedance model of the mechanical hand according to the tracking force signal and the measured tactile force signal, and realizing the reference position output; S2, adaptive estimation law design: the adaptive estimation law design is realized by acquiring the mechanical hand joint position information, acquiring the mechanical hand operation space position, and designing the adaptive estimation law based on the sliding mode variable according to the reference position of the reference impedance model; S3, mechanical hand control law design: the mechanical hand control law design is realized based on the adaptive estimation law, the reference position output by the reference impedance model, and the stability and effectiveness of the mechanical hand control law verified by designing the Lyapunov function according to the joint position information of the mechanical hand; The design of the adaptive estimation law, including the adaptive estimation law based on position tracking error The design of the adaptive estimation law based on model error The design of the adaptive estimation law Adaptive estimation law based on position tracking error The mathematical expression is: wherein, is a positive definite diagonal matrix, is the transpose of the linearized regression matrix according to the robot model, is the inverse of the robot Jacobian matrix, is the sliding mode variable; The model error-based adaptive estimation law The mathematical expression is: where is the error between the filtered form of the robot model and the robot estimate model; is called a bounded positive definite adaptive gain matrix; is the integral form of the robot model; is called a uniformly positive definite weighting matrix and represents the importance of the parameter information to the adaptive estimation law, where is a positive real number, is the corresponding matrix.

2. The model reference adaptive impedance based robot controller design method of claim 1, wherein, The mathematical model expression of the reference impedance model is: Wherein, the matrix , is the target impedance parameter, respectively, the expected inertia, damping matrix of the manipulator; is the contact force between the manipulator and the operating object, is the standard force signal value, is the output reference position of the target impedance model in the Cartesian coordinate system.

3. The model reference adaptive impedance based robot controller design method of claim 2, wherein, The reference impedance model is a second-order impedance model, , a positive definite diagonal matrix, , , by acquiring the end-of-hand tactile force information, establishing the reference impedance model of the manipulator according to the tracking force signal and the measured tactile force signal, and acquiring the reference position as the position tracking target of the manipulator, the matching between the target force and the operation force is realized by adjusting the position of the manipulator, when the system is in a steady state, at this time is zero, which satisfies the steady-state balance of the reference impedance model of the manipulator.

4. The model reference adaptive impedance based robot controller design method of claim 1, wherein, The bounded positive definite adaptive gain matrix The mathematical expression is: wherein The so-called variable forgetting factor is designed as , , are positive constants, respectively, representing the maximum forgetting rate and the upper bound of the gain matrix norm pre-specified.

5. The model reference adaptive impedance based robot controller design method of claim 1, wherein, The mathematical expression of the mechanical hand control law is: wherein are respective estimates of the manipulator parameters , ; is a manipulator tracking sliding mode function, is an error of the manipulator end position tracking reference position; is a manipulator reference variable; from which it follows that .

6. The model reference adaptive impedance based robot controller design method of claim 5, wherein, The mathematical expression of the mechanical hand control law is: wherein, is an unknown parameter information of the robot, , is a known vector, The system regression matrix consisting of the coordinate variables and their derivatives known from the robot model is linearized according to the unknown parameters as follows: wherein, , is an arbitrary known vector of respective dimension, is a vector of unknown parameters information of the robot model.

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