Adaptive fuzzy impedance control method for robot arm

Abstract

The purpose of this invention is to address the problems of poor adaptability of traditional fixed impedance control to unknown and dynamically changing environments, low contact force control accuracy, severe overshoot, insufficient compliance, high computational complexity, poor real-time performance, and difficulty in engineering implementation of existing impedance control methods. This invention provides an adaptive fuzzy impedance control method for robotic arms, constructing a fully closed-loop control architecture. Using force deviation and its rate of change as core inputs, a fuzzy controller is used to solve for the real-time compensation of three types of impedance parameters online, achieving adaptive dynamic adjustment of impedance parameters as the environment changes. Simultaneously, optimization techniques such as environmental parameter identification, fixed-time interference observation, anti-saturation compensation, and command filtering are integrated to comprehensively improve the system's control performance and engineering practicality.

Description

Technical Field

[0001] This invention belongs to the field of industrial robot control technology and relates to an adaptive fuzzy impedance control method for a robotic arm. Background Technology

[0002] With the rapid development of intelligent manufacturing in industry, the application scenarios of industrial robotic arms have gradually expanded from traditional free-space position control tasks such as spraying and welding to constrained-space operations that require continuous contact with the environment, such as grinding, assembly, and polishing. In these contact operations, the robotic arm not only needs to ensure the tracking accuracy of its end effector position, but also needs to precisely control the contact force between the end effector and the environment to avoid damage to the work object and the robotic arm itself caused by rigid impacts. This requires the robotic arm to have excellent compliant control capabilities.

[0003] Impedance control is a core technology for achieving active compliant control of robotic arms. It establishes a second-order dynamic relationship between the end-effector position deviation and the contact force, and achieves coordinated control of position and force by adjusting three types of impedance parameters: inertia, damping, and stiffness. However, traditional impedance control schemes generally use fixed impedance parameters, which can only achieve good control results in scenarios where environmental parameters are known and operating conditions are fixed. When facing unknown environments, sudden changes in environmental stiffness, or dynamic contact conditions, fixed impedance parameters cannot adapt to environmental changes, easily leading to problems such as severe contact force overshoot, large steady-state error, and violent oscillation, and even causing rigid impacts, failing to meet the compliance requirements of precision operations.

[0004] To address the shortcomings of fixed impedance control, scholars both domestically and internationally have conducted extensive research on adaptive impedance control.

[0005] Some scholars have proposed adaptive impedance control schemes based on model references. By establishing an accurate dynamic model of the robotic arm and the environment, an adaptive law is designed to adjust the impedance parameters online. However, such schemes are highly dependent on accurate mathematical models. In actual working conditions, the robotic arm has nonlinear factors such as unmodeled dynamics, joint friction, and clearance. Environmental parameters are also difficult to obtain accurately in advance. As a result, such schemes have poor robustness in practical applications and are difficult to implement in engineering.

[0006] Some scholars have combined intelligent algorithms with impedance control, such as neural networks and fuzzy control. Fuzzy control, in particular, does not require a precise mathematical model of the controlled object and can handle system nonlinearity and uncertainty based on expert experience, making it an important research direction for adaptive impedance control. However, existing fuzzy impedance control schemes still have many shortcomings: First, most schemes only adaptively adjust a single impedance parameter (such as damping or stiffness), failing to achieve synchronous compensation for three types of impedance parameters, resulting in limited adaptive capability; second, they do not consider issues such as actuator input saturation, external unknown disturbances, and sensor noise in actual working conditions, which can easily lead to system instability and a significant decrease in control performance in practical applications; third, the system convergence speed is slow, and the convergence time is affected by the initial state of the system, resulting in lag in response to sudden environmental changes and insufficient contact force control accuracy; fourth, they do not incorporate online identification of environmental parameters, resulting in insufficient adaptability of fuzzy rules to various working conditions and difficulty in coping with large-scale changes in environmental parameters.

[0007] In summary, there is currently no adaptive fuzzy impedance control scheme for robotic arms that can adapt to unknown dynamic environments without models, synchronously and adaptively adjust the total impedance parameters, and simultaneously take into account strong robustness, fast response speed and high engineering practicality. This has become a key technical bottleneck restricting the large-scale application of robotic arms in precision contact operations. Summary of the Invention

[0008] The purpose of this invention is to address the problems of poor adaptability of traditional fixed impedance control to unknown and dynamically changing environments, low contact force control accuracy, severe overshoot, insufficient compliance, high computational complexity, poor real-time performance, and difficulty in engineering implementation of existing impedance control methods. This invention provides an adaptive fuzzy impedance control method for robotic arms, constructing a fully closed-loop control architecture. Using force deviation and its rate of change as core inputs, a fuzzy controller is used to solve for the real-time compensation of three types of impedance parameters online, achieving adaptive dynamic adjustment of impedance parameters as the environment changes. Simultaneously, optimization techniques such as environmental parameter identification, fixed-time interference observation, anti-saturation compensation, and command filtering are integrated to comprehensively improve the system's control performance and engineering practicality.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] An adaptive fuzzy impedance control method for a robotic arm includes the following steps:

[0011] Step 1: Establish the dynamic model and reference impedance control model of the target robotic arm, and determine the reference impedance parameters, desired contact force, and nominal reference trajectory of the robotic arm's end effector; the reference impedance parameters include the reference inertia matrix. Reference damping matrix Reference stiffness matrix ;

[0012] Step 2: Real-time acquisition of the actual contact force between the robotic arm's end effector and the environment, and calculation of the force deviation between the actual contact force and the expected contact force. and the rate of change of force deviation Both are used as the core input variables of the fuzzy controller;

[0013] Step 3: Design the membership functions for the input and output variables to complete the conversion from precise to fuzzy quantities; where the output variable is the real-time compensation quantity for impedance parameters, including inertial parameter compensation quantities. Damping parameter compensation amount Stiffness parameter compensation amount ;

[0014] Step 4: Based on the working characteristics of the robotic arm's contact operation, the dynamic response law of the system, and the identification results of environmental parameters, establish a fuzzy control rule base for solving the impedance parameter compensation quantity, perform fuzzy inference on the input fuzzy quantity, and obtain the fuzzy set of output variables.

[0015] Step 5: Defuzzify the fuzzy set of the output variables to obtain the precise values ​​of the compensation amounts for inertia, damping, and stiffness parameters. Then, superimpose the compensation amounts onto the reference impedance parameters to complete the real-time update of the target impedance parameters.

[0016] Step 6: Substitute the real-time updated target impedance parameters into the reference impedance control model to solve for the position correction of the robotic arm end effector. Generate the corrected actual control trajectory based on the nominal reference trajectory and the position correction.

[0017] Step 7: The corrected actual control trajectory is transformed into the target trajectory in joint space through inverse kinematics solution, and input into the inner ring joint position controller of the robotic arm. The joint driving torque is output to drive the robotic arm to perform the corresponding motion. The end contact force and motion state are collected in real time. Steps 2 to 6 are repeated to form a continuous closed-loop adaptive control.

[0018] Furthermore, in step 1, for the rigid serial manipulator, a rigid body dynamics model is established using the Lagrange method, with the following expression:

[0019] ;

[0020] In the formula, The inertial matrix of the robotic arm joint space. For the Coriolis and centrifugal force matrix, For the gravity matrix, , , These are the angles, angular velocities, and angular accelerations of the robotic arm joints. For joint driving torque, The Jacobian matrix at the end effector of the robotic arm. This represents the actual contact force at the end.

[0021] For a flexible joint robotic arm, a dynamic model incorporating joint flexibility is established, expressed as follows: ;

[0022] In the formula, , These are the motor's rotational angle and acceleration, respectively. For the moment of inertia of the motor, Here is the joint stiffness matrix. This provides the input torque to the motor.

[0023] Furthermore, in step 1, the expression for the reference impedance control model is:

[0024] ;

[0025] In the formula, , , These are the target inertia, damping, stiffness, and impedance parameters, which are updated in real time, and the reference impedance parameters are used in the initial state. , , ; , , These are the position, velocity, and acceleration of the nominal reference trajectory at the end point, respectively. , , These are the position, velocity, and acceleration of the corrected actual control trajectory, respectively. The preset desired contact force, This represents the actual contact force at the end.

[0026] In step 5, the update formula for the target impedance parameter is:

[0027] ; .

[0028] Furthermore, step 2 also includes an online environmental parameter identification step: using the fuzzy forgetting factor recursive least squares method, based on real-time collected contact force and end-effector position data, the environmental stiffness is identified online. Location in contact with the environment Furthermore, the rate of change of environmental stiffness and the rate of change of environmental position are used as auxiliary input variables for the fuzzy controller.

[0029] Furthermore, in step 3, the input variables will be... , With output variables , , The universe of discourse is divided into 7 fuzzy subsets: negative large NB, negative medium NM, negative small NS, zero ZO, positive small PS, positive medium PM, and positive large PB. The membership functions of the input and output variables adopt triangular membership functions or Gaussian membership functions to complete the normalization mapping and fuzzification processing of the universe of discourse.

[0030] Furthermore, in step 4, the core principle for formulating the fuzzy control rule base is as follows: when the actual contact force is greater than the expected contact force and shows an increasing trend, output a negative stiffness compensation, a positive damping compensation, and a negative inertia compensation to suppress contact force overshoot and rigid impact; when the actual contact force is less than the expected contact force and shows a decreasing trend, output a positive stiffness compensation, an appropriate damping compensation, and a positive inertia compensation to accelerate the contact force response speed and reduce steady-state error; when the contact force deviation approaches zero and the rate of change is gradual, output a parameter compensation that approaches zero to maintain stable system operation.

[0031] Furthermore, in step 5, the defuzzification process uses the centroid method, and the calculation formula is as follows:

[0032]

[0033] In the formula, To obtain the precise value of the parameter compensation amount output after deblurring, To output discrete points within the universe of discourse of the variable, This represents the membership degree value corresponding to the discrete point. The total number of discrete points within the domain of discussion.

[0034] Furthermore, it also includes fixed-time disturbance observation and compensation: designing a fixed-time nonlinear disturbance observer to perform real-time estimation and feedforward compensation for unmodeled dynamics, joint friction, and unknown external nonlinear disturbances of the robotic arm system;

[0035] The expression for the fixed-time nonlinear disturbance observer is: ;

[0036] In the formula, This is an estimate of the unknown interference. For observer intermediate variables, , >0 represents the observer gain. The inertial matrix in Cartesian space. The Coriolis force matrix in Cartesian space. For the gravity term in Cartesian space, For control input subject to saturation constraints, , ;

[0037] Interference estimate Feedforward compensation to joint drive torque In the middle, the compensated control torque is .

[0038] Furthermore, it also includes actuator input saturation suppression: a fixed-time anti-saturation device is designed to compensate for the actuator input saturation nonlinearity. The expression for the anti-saturation auxiliary system is as follows:

[0039] ;

[0040] In the formula, For the anti-saturator state variables, For the gain of the anti-saturator, It is a smooth, approximately saturated, nonlinear, continuous hyperbolic tangent function. For nominal control input;

[0041] Anti-saturator state variables The trajectory correction stage introduced into the inner loop position controller eliminates the impact of input saturation on the system's tracking performance.

[0042] Furthermore, in step 6, a fixed-time command filter is used to filter the virtual control law and the reference trajectory, and an error compensation mechanism is designed to eliminate the filtering error.

[0043] The expression for the fixed-time command filter is:

[0044] ;

[0045] In the formula, This is the filtered signal output by the filter. The virtual control law is the input to the filter. , These are filter parameters;

[0046] The design of the error compensation signal satisfies the following: the filtering error and the trajectory tracking error converge to a bounded neighborhood near the origin within a fixed time, and the upper bound of the convergence time is independent of the initial state of the system.

[0047] In summary, the advantages of this invention are:

[0048] 1) This invention achieves synchronous online adaptive adjustment of three types of impedance parameters—inertia, damping, and stiffness—through a fuzzy controller. It eliminates the need to establish a precise mathematical model of the robotic arm and the environment, and can perfectly adapt to unknown and dynamically changing contact environments. This completely solves the limitations of traditional fixed impedance control and can be widely applied to contact operation scenarios with different stiffness environments.

[0049] 2) Based on the influence of impedance parameters on the dynamic performance of the system, this invention has customized a fuzzy control rule covering all working conditions. It can accurately match the contact conditions, effectively suppress the overshoot and steady-state fluctuation of the contact force, significantly reduce the overshoot of the contact force, and control the steady-state error within 1%. At the same time, it can dynamically adjust the impedance characteristics according to the contact state, effectively avoid the rigid impact between the robotic arm and the environment, protect the work object and the robotic arm body, and greatly improve the safety of human-machine collaboration scenarios.

[0050] 3) This invention integrates a fixed-time nonlinear disturbance observer, which can estimate and compensate for nonlinear factors such as unmodeled dynamics of the robotic arm, joint friction, and unknown external disturbances in real time. At the same time, a fixed-time anti-saturation device is designed to effectively suppress the impact of actuator input saturation on system performance, so that the system can still maintain excellent control performance under non-ideal working conditions. Its anti-interference ability and robustness are significantly better than existing solutions.

[0051] 4) This invention combines fixed-time control theory to design a fixed-time command filter and an interference observer, so that the upper bound of the convergence time of the system tracking error is independent of the initial state. It can respond quickly when faced with sudden changes in environmental parameters, and the adjustment time is greatly shortened. This solves the problems of slow convergence speed and great influence of the initial state in existing algorithms, and greatly improves the system stability. Attached Figure Description

[0052] Figure 1 This is a complete flowchart of the control method of the present invention. Detailed Implementation

[0053] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0054] This invention provides an adaptive fuzzy impedance control method for a robotic arm, comprising the following steps:

[0055] Step 1: Establishment of robotic arm dynamics model and reference impedance control model.

[0056] Step 1.1: For the target control object (rigid serial manipulator / flexible joint manipulator), establish the corresponding dynamic model, clarify the mapping relationship between joint space and Cartesian space, and provide a dynamic basis for subsequent control;

[0057] For an n-DOF rigid serial manipulator, a rigid body dynamics model is established using the Lagrangian method, with the following expression:

[0058]

[0059] In the formula, The inertial matrix of the robotic arm joint space. For the Coriolis and centrifugal force matrix, For the gravity matrix, , , These are the angles, angular velocities, and angular accelerations of the robotic arm joints. For joint driving torque, The Jacobian matrix at the end effector of the robotic arm. This represents the actual contact force at the end.

[0060] Assuming the mass of each link in the robotic arm is concentrated at its end, the link parameters are: mass of the first link... =1kg, length =0.5m; Mass of the second connecting rod =1kg, length =1m; Mass of the third link =1kg, length =1m; gravitational acceleration g=9.8 ;

[0061] Based on the rigid body dynamics model, the inertia matrix Coriolis and centrifugal force matrix Gravity matrix The specific expression is as follows:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] In the formula, ; , , These are the rotation angles of the lumbar joint, shoulder joint, and elbow joint, respectively.

[0068] For a flexible joint robotic arm, a dynamic model incorporating joint flexibility is established, expressed as follows:

[0069]

[0070] In the formula, , These are the motor's rotational angle and acceleration, respectively. For the moment of inertia of the motor, Here is the joint stiffness matrix. This provides the input torque to the motor.

[0071] Step 1.2: Establish a second-order linear reference impedance control model in Cartesian space, and define the dynamic relationship between the end-effector position correction and the contact force, expressed as:

[0072]

[0073] In the formula, , , These are the target inertia, damping, stiffness, and impedance parameters, which are updated in real time, and the reference impedance parameters are used in the initial state. , , ; , , These are the position, velocity, and acceleration of the nominal reference trajectory at the end point, respectively. , , These are the position, velocity, and acceleration of the corrected actual control trajectory, respectively. The preset desired contact force, This represents the actual contact force at the end.

[0074] Step 1.3: Based on the robot arm's body parameters and operational requirements, complete the reference impedance parameters. , , Expected contact force With end nominal reference trajectory Initialization settings.

[0075] Based on the operational requirements, the initial reference impedance parameters are: reference inertia matrix. Reference damping matrix Reference stiffness matrix ;

[0076] Set the x-direction as the contact force control direction, and set the desired contact force. =32N, the y and z directions are the position control directions, and the desired contact force is 0;

[0077] Nominal reference trajectory of robotic arm end effector: x direction =0.866m, y direction =1.5m, z-direction =0.25m, the initial joint angle of the robotic arm is , , The initial end position is (0.876, 1.5, 0.25), which matches the initial contact position with the environment.

[0078] Step 2: Feedback signal acquisition and input variable calculation.

[0079] Step 2.1: Using a six-dimensional force / torque sensor installed at the end of the robotic arm, the actual contact force between the end of the robotic arm and the environment is collected in real time. The acquired force signal was filtered and denoised using a first-order low-pass filter with a cutoff frequency of 100Hz.

[0080] Step 2.2: Calculate the contact force control deviation. and the rate of change of force deviation These two variables are determined as the core input variables of the fuzzy controller.

[0081] Step 2.3: Using the fuzzy forgetting factor recursive least squares method, based on real-time collected contact force and end-effector position data, the environmental stiffness is identified online. Location in contact with the environment The environmental stiffness change rate and environmental position change rate are calculated and used as auxiliary input variables for the fuzzy controller to improve the working condition adaptability of the fuzzy rules.

[0082] The recursive formula for environmental parameter identification is:

[0083]

[0084] In the formula, Let be the vector of environmental parameters to be estimated. For data vectors, Here is the gain matrix. Let covariance matrix be the variance matrix. For the variable forgetting factor;

[0085] The environmental stiffness in the x-direction is identified online using the fuzzy forgetting factor recursive least squares method. Location in contact with the environment Initial values ​​of the covariance matrix Initial estimates of environmental parameters , =0.866m; Variable forgetting factor The universe of discourse is [0.95, 1], based on the absolute value of the force deviation. Dynamic adjustment

[0086] amnesia factor The adjustment is achieved through dynamic adjustment using an auxiliary fuzzy controller. The adjustment logic is: absolute value of force deviation. When the value increases, it indicates a sudden change in the environment. The forgetting factor is reduced to decrease the weight of historical data, thereby improving the parameter identification response speed; the absolute value of the force deviation... When the value is decreased, the judgment system tends to stabilize. Increasing the forgetting factor enhances the stability of the recognition results. The value range is [0.95, 1].

[0087] Step 3: Fuzzification of input and output variables of the fuzzy controller.

[0088] Step 3.1, Determine the input variables ( , ) and output variables ( , , The basic domain of discourse, preferably, determines the input variables. The fundamental domain of discourse is [-16, 16] N. The fundamental universe of discourse is [-80, 80] N / s, and the output variable is... The fundamental domain of discourse is [-500, 500]. The fundamental domain of discourse is [-40, 40]. The fundamental domain is [-0.8, 0.8];

[0089] Based on the maximum deviation range of the working conditions, the normalization mapping of the universe of discourse is completed, and the basic universe of discourse is mapped to the standard universe of discourse [-3,3].

[0090] Step 3.2: Divide the standard universe of discourse of both input and output variables into 7 fuzzy subsets, namely negative large NB, negative medium NM, negative small NS, zero ZO, positive small PS, positive medium PM, and positive large PB, covering the entire working condition range;

[0091] Step 3.3: Design the membership functions for the input and output variables. In this embodiment, a triangular membership function is used, employing a high-resolution membership design near the zero value ZO to improve steady-state control accuracy. The input variables... The membership functions correspond to the following relationships: NB corresponds to [-3,-2], NM corresponds to [-3,-1], NS corresponds to [-2,0], ZO corresponds to [-1,1], PS corresponds to [0,2], PM corresponds to [1,3], and PB corresponds to [2,3]. The membership functions of the remaining variables adopt the same design logic. A low-resolution design is used at the edge of the universe of discourse to improve the system's anti-disturbance capability. For high-precision operation scenarios, it can be replaced with a Gaussian membership function to further improve control smoothness.

[0092] Step 4: Design of the fuzzy control rule base and fuzzy inference for adaptive impedance parameter adjustment.

[0093] Step 4.1: Based on the working characteristics of the robotic arm's contact operation, the dynamic response law of the system, and the influence law of impedance parameters on the dynamic performance of the system, and combined with the expert control experience of those skilled in the art, formulate IF-THEN form fuzzy control rules.

[0094] The influence of impedance parameters on system performance follows the law: stiffness parameters The main factors affecting the steady-state error of the contact force and the response speed are... Increasing the damping parameter will speed up the response, but will also increase the contact force overshoot; It mainly affects system oscillation and shock suppression. Increasing this value will effectively suppress overshoot and oscillation, but excessively high values ​​will lead to system response lag; inertia parameter It mainly affects the speed of the system's dynamic response. Increasing the size will reduce contact impact, but will prolong the system stabilization time.

[0095] Step 4.2, the core principle for formulating fuzzy control rules is:

[0096] when For Zhengda PB, When PB is positive, it indicates that the actual contact force is much greater than the expected contact force and continues to increase, posing a serious risk of overshoot and rigid impact. In this case, the output should be negative NB for stiffness compensation. Damping compensation of Zhengda PB The inertial compensation amount of the large negative NB This rapidly reduces system stiffness, increases damping, and suppresses contact force overshoot and impact.

[0097] when For negative big NB, When NB is negative, it indicates that the actual contact force is much smaller than the expected contact force and continues to decrease, resulting in a very large steady-state error. At this time, the output should be a positive stiffness compensation amount of PB. Damping compensation of small PS Inertial compensation amount of Zhengda PB This improves system stiffness, accelerates contact force response, and reduces steady-state error;

[0098] when is zero ZO, When the ZO is zero, it indicates that the actual contact force is consistent with the expected contact force and the system is in a stable state. At this time, the parameter compensation amount with zero ZO is output to maintain the reference impedance parameter unchanged and ensure the stable operation of the system.

[0099] For other operating conditions, based on the above core principles, continuous and smooth parameter compensation rules are formulated according to the matching relationship of fuzzy subsets to avoid system oscillations caused by sudden changes in impedance parameters.

[0100] Step 4.3: Based on the above rule-making principles, construct a complete table of 49 fuzzy control rules, covering all combinations of fuzzy subsets, to form an executable fuzzy control rule base;

[0101] The core rules are shown in the table below:

[0102] Step 4.4: Using the Mamdani maximum-minimum inference method, fuzzy inference is performed on the input fuzzy quantities based on the fuzzy control rule base to obtain the fuzzy set of output variables (impedance parameter compensation quantities).

[0103] Step 5: Defuzzification and real-time updating of target impedance parameters.

[0104] Step 5.1: Use the centroid method to defuzzify the fuzzy set of the output variable, transforming the fuzzy set into the precise value of the impedance parameter compensation. The defuzzification calculation formula is as follows:

[0105]

[0106] In the formula, To obtain the precise value of the parameter compensation amount output after deblurring, To output discrete points within the universe of discourse of the variable, This represents the membership degree value corresponding to the discrete point. The total number of discrete points within the universe of discourse;

[0107] Step 5.2: After defuzzification, the inertial parameter compensation amount is obtained. Damping parameter compensation amount Stiffness parameter compensation amount The precise value;

[0108] Step 5.3: Add the parameter compensation amount to the reference impedance parameter to complete the real-time update of the target impedance parameter. The update formula is:

[0109]

[0110]

[0111]

[0112] Step 6: Fixed-time interference observation and input saturation compensation.

[0113] Step 6.1: Design a fixed-time nonlinear disturbance observer to estimate the unmodeled dynamics, joint friction, and unknown external nonlinear disturbances of the robotic arm system in real time. The observer expression is:

[0114]

[0115] In the formula, This is an estimate of the unknown interference. For observer intermediate variables, , >0 represents the observer gain. The inertial matrix in Cartesian space. The Coriolis force matrix in Cartesian space. For the gravity term in Cartesian space, For control input subject to saturation constraints, , ;

[0116] Step 6.2: Estimate the interference value Feedforward compensation to joint drive torque In the process of eliminating the impact of unknown disturbances on the system control performance, the compensated control torque is: ;

[0117] Step 6.3: Design a fixed-time anti-saturation device to compensate for the saturation nonlinearity of the actuator input. The expression for the anti-saturation auxiliary system is:

[0118]

[0119] In the formula, For the anti-saturator state variables, For the gain of the anti-saturator, It is a smooth, approximately saturated, nonlinear, continuous hyperbolic tangent function. For nominal control input;

[0120] Step 6.4: Set the anti-saturator state variables The trajectory correction stage introduced into the inner loop position controller eliminates the trajectory tracking deviation and system instability risk caused by input saturation.

[0121] Step 7: Control trajectory correction and robotic arm motion control.

[0122] Step 7.1: Substitute the real-time updated target impedance parameters into the reference impedance control model established in Step 1, and solve for the correction amount of the robotic arm end position.

[0123] Step 7.2: A fixed-time command filter is used to filter the virtual control law and the nominal reference trajectory. Simultaneously, an error compensation mechanism is designed to eliminate filtering errors and avoid the "computational explosion" problem of the traditional backstepping method. The filter expression is:

[0124]

[0125] In the formula, This is the filtered signal output by the filter. The virtual control law is the input to the filter. , These are filter parameters;

[0126] Step 7.3: Based on the nominal reference trajectory, position correction, and anti-saturator state variables, generate the corrected actual control trajectory. ;

[0127] Step 7.4: Transfer the corrected actual control trajectory The inverse kinematics solution is transformed into a target trajectory in joint space, which is then input to the inner ring joint position controller of the robotic arm and outputs the joint driving torque to drive the robotic arm to perform the corresponding motion.

[0128] Step 7.5: Collect the contact force and motion state of the robotic arm end effector in real time, and repeat steps 2 to 7 to form a continuous closed-loop adaptive control, so as to realize the real-time precise control and compliance adaptive adjustment of the contact force of the robotic arm end effector.

[0129] Step 8: Stability analysis of the closed-loop control system.

[0130] Using Lyapunov stability theory and fixed-time stability theory, a Lyapunov function is constructed to prove the stability of the closed-loop control system of this invention, verifying the global fixed-time asymptotic stability of the system under environmental parameter changes, external disturbances, and input saturation constraints.

[0131] Specifically, constructing Lyapunov functions ,in Let Lyapunov be the trajectory tracking error. Here is the Lyapunov function for the filtering error compensation signal. Let Lyapunov be the parameter estimation error. This is the Lyapunov function that interferes with observation errors.

[0132] It can be proved by taking the derivative of the Lyapunov function. ,in , , C is a bounded positive constant.

[0133] According to the fixed-time stability lemma, it can be proved that all signals in the closed-loop system are bounded by a fixed time, and the tracking error converges to any small neighborhood near the origin within a fixed time, with an upper bound on the convergence time. Regardless of the initial state of the system, the system is globally asymptotically stable over a fixed time.

[0134] Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

Claims

1. An adaptive fuzzy impedance control method for a robotic arm, characterized in that, Includes the following steps: Step 1: Establish the dynamic model and reference impedance control model of the target robotic arm, and determine the reference impedance parameters, desired contact force and nominal reference trajectory of the robotic arm end effector; The reference impedance parameters include the reference inertia matrix. Reference damping matrix Reference stiffness matrix ; Step 2: Real-time acquisition of the actual contact force between the robotic arm's end effector and the environment, and calculation of the force deviation between the actual contact force and the expected contact force. and the rate of change of force deviation Both are used as the core input variables of the fuzzy controller; Step 3: Design the membership functions for the input and output variables to complete the conversion from precise to fuzzy quantities; where the output variable is the real-time compensation quantity for impedance parameters, including inertial parameter compensation quantities. Damping parameter compensation amount Stiffness parameter compensation amount ; Step 4: Based on the working characteristics of the robotic arm's contact operation, the dynamic response law of the system, and the identification results of environmental parameters, establish a fuzzy control rule base for solving the impedance parameter compensation quantity, perform fuzzy inference on the input fuzzy quantity, and obtain the fuzzy set of output variables. Step 5: Defuzzify the fuzzy set of the output variables to obtain the precise values ​​of the compensation amounts for inertia, damping, and stiffness parameters. Then, superimpose the compensation amounts onto the reference impedance parameters to complete the real-time update of the target impedance parameters. Step 6: Substitute the real-time updated target impedance parameters into the reference impedance control model to solve for the position correction of the robotic arm end effector. Generate the corrected actual control trajectory based on the nominal reference trajectory and the position correction. Step 7: The corrected actual control trajectory is transformed into the target trajectory in joint space through inverse kinematics solution, and input into the inner ring joint position controller of the robotic arm. The joint driving torque is output to drive the robotic arm to perform the corresponding motion. The end contact force and motion state are collected in real time. Steps 2 to 6 are repeated to form a continuous closed-loop adaptive control.

2. The adaptive fuzzy impedance control method for a robotic arm according to claim 1, characterized in that, In step 1, for the rigid serial manipulator, a rigid body dynamics model is established using the Lagrangian method, with the following expression: ； In the formula, The inertial matrix of the robotic arm joint space. For the Coriolis and centrifugal force matrix, For the gravity matrix, , , These are the angles, angular velocities, and angular accelerations of the robotic arm joints. For joint driving torque, The Jacobian matrix at the end effector of the robotic arm. This represents the actual contact force at the end. For a flexible joint robotic arm, a dynamic model incorporating joint flexibility is established, expressed as follows: ; In the formula, , These are the motor's rotational angle and acceleration, respectively. For the moment of inertia of the motor, Here is the joint stiffness matrix. This provides the input torque to the motor.

3. The adaptive fuzzy impedance control method for a robotic arm according to claim 2, characterized in that, In step 1, the expression for the reference impedance control model is: ； In the formula, , , These are the target inertia, damping, stiffness, and impedance parameters, which are updated in real time, and the reference impedance parameters are used in the initial state. , , ; , , These are the position, velocity, and acceleration of the nominal reference trajectory at the end point, respectively. , , These are the position, velocity, and acceleration of the corrected actual control trajectory, respectively. The preset desired contact force, This represents the actual contact force at the end. In step 5, the update formula for the target impedance parameter is: ； 。 4. The adaptive fuzzy impedance control method for a robotic arm according to claim 1, characterized in that, Step 2 also includes an online environmental parameter identification step: using the fuzzy forgetting factor recursive least squares method, based on real-time collected contact force and end-effector position data, the environmental stiffness is identified online. Location in contact with the environment Furthermore, the rate of change of environmental stiffness and the rate of change of environmental position are used as auxiliary input variables for the fuzzy controller.

5. The adaptive fuzzy impedance control method for a robotic arm according to claim 1, characterized in that, In step 3, the input variables are... , With output variables , , The universe of discourse is divided into 7 fuzzy subsets: negative large NB, negative medium NM, negative small NS, zero ZO, positive small PS, positive medium PM, and positive large PB. The membership functions of the input and output variables adopt triangular membership functions or Gaussian membership functions to complete the normalization mapping and fuzzification processing of the universe of discourse.

6. The adaptive fuzzy impedance control method for a robotic arm according to claim 1, characterized in that, In step 4, the core principle for formulating the fuzzy control rule base is as follows: when the actual contact force is greater than the expected contact force and shows an increasing trend, output negative stiffness compensation, positive damping compensation, and negative inertia compensation to suppress contact force overshoot and rigid impact; when the actual contact force is less than the expected contact force and shows a decreasing trend, output positive stiffness compensation, appropriate damping compensation, and positive inertia compensation to accelerate the contact force response speed and reduce steady-state error; when the contact force deviation approaches zero and the rate of change is gradual, output parameter compensation that approaches zero to maintain stable system operation.

7. The adaptive fuzzy impedance control method for a robotic arm according to claim 1, characterized in that, In step 5, the centroid method is used for defuzzification, and the calculation formula is as follows: In the formula, To obtain the precise value of the parameter compensation amount output after deblurring, To output discrete points within the universe of discourse of the variable, This represents the membership degree value corresponding to the discrete point. The total number of discrete points within the domain of discussion.

8. The adaptive fuzzy impedance control method for a robotic arm according to claim 1, characterized in that, It also includes fixed-time disturbance observation and compensation: designing a fixed-time nonlinear disturbance observer to perform real-time estimation and feedforward compensation of unmodeled dynamics, joint friction, and unknown external nonlinear disturbances of the robotic arm system; The expression for the fixed-time nonlinear disturbance observer is: ; In the formula, This is an estimate of the unknown interference. For observer intermediate variables, , >0 represents the observer gain. The inertial matrix in Cartesian space. The Coriolis force matrix in Cartesian space. For the gravity term in Cartesian space, For control input subject to saturation constraints, , ; Interference estimate Feedforward compensation to joint drive torque In the middle, the compensated control torque is .

9. The adaptive fuzzy impedance control method for a robotic arm according to claim 8, characterized in that, This also includes actuator input saturation suppression: a fixed-time anti-saturation device is designed to compensate for actuator input saturation nonlinearity. The expression for the anti-saturation auxiliary system is as follows: ； In the formula, For the anti-saturator state variables, For the gain of the anti-saturator, It is a smooth, approximately saturated, nonlinear, continuous hyperbolic tangent function. For nominal control input; Anti-saturator state variables The trajectory correction stage introduced into the inner loop position controller eliminates the impact of input saturation on the system's tracking performance.

10. The adaptive fuzzy impedance control method for a robotic arm according to claim 1, characterized in that, In step 6, a fixed-time command filter is used to filter the virtual control law and the reference trajectory, and an error compensation mechanism is designed to eliminate the filtering error. The expression for the fixed-time command filter is: ； In the formula, This is the filtered signal output by the filter. The virtual control law is the input to the filter. , These are filter parameters; The design of the error compensation signal satisfies the following: the filtering error and the trajectory tracking error converge to a bounded neighborhood near the origin within a fixed time, and the upper bound of the convergence time is independent of the initial state of the system.

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