Self-adaptive iterative learning compliant control method based on mechanical arm impedance control

Abstract

The invention belongs to the technical field of robots, and particularly relates to a self-adaptive variable parameter iterative learning compliance control method based on mechanical arm impedance control. Comprising the following steps that 1, a robot controller collects information of a six-dimensional force sensor; 2, dynamically adjusting the size of an updating factor according to the change of external contact information by adopting a fuzzy control method; 3, sub-optimal sliding mode control is introduced, and the relation between buffeting and the convergence speed is restrained; and 4, by means of the obtained data, a mechanical arm variable parameter iterative compliance control method based on self-adaptive impedance control is provided, impedance parameters are corrected in real time, and zero-error steady-state tracking is achieved. The force tracking effect of the mechanical arm in a complex unknown environment can be improved, and then the compliance control effect of the robot is improved to a large extent.

Description

Technical Field

[0001] This invention belongs to the field of robotics technology, specifically an adaptive iterative learning compliant control method based on impedance control of a robotic arm. Background Technology

[0002] In recent years, robots have been widely used in the manufacturing industry. A series of complex tasks can be completed by controlling the position of their end effectors. As production requirements become increasingly demanding, there is a growing expectation that robotic arms can perform tasks that interact with the environment. This necessitates the sequential control of the robotic arms.

[0003] Impedance control, by constructing a dynamic model of force and position, enables the robot's end effector to establish a dynamic model of position and force with the workpiece surface, thus achieving synchronous control of robot motion and contact forces. By adjusting the robot's impedance parameters, constant force tracking of the workpiece surface can be achieved. However, under uncertain environmental and stiffness parameters, the steady-state error of the force in contact with the environment is not zero. Therefore, optimizing impedance control to improve the force control accuracy of the robotic arm's end effector in contact with the environment is of great research necessity. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides an adaptive iterative learning compliant control method based on robotic arm impedance control, which can improve the force tracking performance of the robotic arm in complex and unknown environments, thereby significantly enhancing the compliant control performance of the robot.

[0005] The technical solution of this invention is described below in conjunction with the accompanying drawings:

[0006] This invention provides an adaptive variable parameter iterative learning compliant control method based on robotic arm impedance control, comprising the following steps:

[0007] Step 1: The robot controller collects information from the six-dimensional force sensor;

[0008] Step 2: Use fuzzy control to dynamically adjust the size of the update factor based on changes in external contact information;

[0009] Step 3: Suboptimal sliding mode control is introduced to suppress the relationship between chattering and convergence speed;

[0010] Step 4: Using the obtained data, we propose an adaptive iterative compliant control method for the robotic arm based on adaptive impedance control, which corrects the impedance parameters in real time and achieves steady-state tracking with zero error.

[0011] Furthermore, the specific method for step one is as follows:

[0012] 11) Perform tool gravity compensation and sensor zero-point drift compensation on the collected torque, and compensate for the transformation relationship between the robot base coordinates and world coordinates;

[0013] 12) The compensated force signal is processed by low-pass filtering to obtain the torque of the actual contact measured by the six-dimensional force sensor.

[0014] Furthermore, the specific method for step two is as follows:

[0015] 21) The admittance control model consisting of the robot and the environment is represented as:

[0016]

[0017] In the formula, , , These are the inertia coefficient matrix, damping coefficient matrix, and stiffness coefficient matrix of the end effector, respectively, and all are positive definite matrices; among them, and These are the actual environment location matrix and the desired environment location matrix, respectively. and These are the actual contact force matrix and the expected contact force matrix when the end effector comes into contact with the environment, respectively. , , These are the reference trajectory, running speed, and acceleration of the robot's end effector, respectively. , , These represent the desired acceleration, velocity, and position. The difference between the contact force and the desired force. ; For the robot to have the desired contact force with the outside world; The actual contact force between the robot and the outside world;

[0018] 22) The analysis is performed in one dimension, as shown below:

[0019]

[0020] In the formula, , , , , , , , , , These are the components of each variable in the impedance model in a single degree of freedom direction;

[0021] 23) Assume the stiffness of the environment is , The environmental location is A linear environment model is used, as shown below:

[0022]

[0023] in Using position error to determine the reference trajectory Provide compensation;

[0024] 24) Force tracking error is expressed as:

[0025]

[0026] in,

[0027] In the formula, Complex variables introduced for the Laplace transform;

[0028] 25) After the admittance control model undergoes a Laplace transform, the final steady-state error is expressed as follows:

[0029]

[0030] 26) Using the environmental location instead of the reference trajectory, the formula is written as:

[0031]

[0032] 27) Setting the stiffness gain to 0 will satisfy the stiffness requirement under all conditions. And the situation of unknown environmental information;

[0033] The model was changed to: ;

[0034] 28) Based on the admittance control model, the damping coefficient... Real-time compensation is performed as follows:

[0035]

[0036] In the formula, To adjust in real time according to the error of contact force, for compensation The uncertainty is expressed as follows:

[0037]

[0038] In the formula, The sampling period; For the update factor, a constant To prevent oscillations caused by excessively small denominator values;

[0039] 29) A fuzzy controller is designed to update the weights of the adaptive law in real time according to the changes in external force. The inputs to the fuzzy controller are the contact force error and the rate of change of the error, both using triangular membership functions. The fuzzy subset universe is [-3,3], and the designed fuzzy set is [Nf, Nt, No, Z, Po, Pt, Pf], with subsets representing negative large, negative medium, negative small, zero, positive small, positive medium, and positive large, respectively. The output uses a Gaussian membership function, with the fuzzy subset universe set to [0,1], and the designed fuzzy set is [Lo, Lt, Lh, Lf, Lv, Ls, Le], with subsets representing very small, very small, relatively small, medium, relatively large, large, and very large, respectively. The fuzzy inference process is implemented using the Mamdani method, and the centroid method is used to defuzzify the output.

[0040] When the force error and the rate of change are abruptly caused by the time-varying external environmental information, the update factor is dynamically adjusted according to the designed fuzzy controller to adapt to the changes in environmental information and increase the tracking accuracy.

[0041] Furthermore, the specific method for step three is as follows:

[0042] 31) Design the membership functions and fuzzy rule tables for the input and output, as shown below:

[0043]

[0044] 32) The sliding surface is designed as follows: ,

[0045] In the formula, It is a sliding surface; The derivative of the force error; It is a constant; For force error; for Time corresponding value; The second derivative of the force error;

[0046] 33) The form of the sliding mode controller is as follows:

[0047]

[0048] In the formula, control gain , satisfy , The value is the sliding surface rate of change, which is equal to 0, and the initial value is 0;

[0049] 34) Consider the following nonlinear system, as shown below:

[0050]

[0051] In the formula, This refers to the system status; For control input; and It is an unknown smooth nonlinear function;

[0052] Assume sliding mode variables s and Given that the second derivative of a nonlinear system with respect to s is obtained,

[0053]

[0054] Here, , It is a smooth unknown function;

[0055] 35) Assume: There exist positive constants. , and , making and Established;

[0056] The sliding mode dynamics equation satisfies equation Under the given assumptions, if the parameters , satisfy, Then the sliding mode controller enables the system to achieve second-order sliding mode motion within a finite time.

[0057] 36) The suboptimal sliding mode control method originates from the time-optimal control strategy of the dual integrator. According to the phase plane trajectory diagram, the prerequisite for the implementation of the suboptimal sliding mode control method is... Its derivative is known. Furthermore, since the calculation is performed using discrete sampling, implementing the suboptimal sliding mode control method only requires knowing the values ​​at each sampling point. and Specific information, when the error of the sliding mode variable between two consecutive sampling points When changing the sign, it is considered At this point, through calculation, the suboptimal controller required is obtained. and information;

[0058] 37) The suboptimal sliding mode design is derived from the time-optimal control strategy of the dual integrator, which dynamically adjusts the magnitude and direction of the control signal on the sliding surface;

[0059] 38) The control law is processed in segments;

[0060] 39) Introducing the derivative of the error allows the gain to respond more flexibly to the dynamic changes of the system, thereby achieving faster convergence and lower chattering, as shown below:

[0061]

[0062] In the formula, and This is the initial gain; and To control the magnitude of the gain; and To control the rate of gain decay; and It is an adjustment factor used to control the sensitivity of the gain to the rate of change of error.

[0063] Furthermore, the specific method for step four is as follows:

[0064] 41) The PD suboptimal sliding mode control method is adopted, and the control input is:

[0065]

[0066] In the formula, , For the proportional and derivative control gains of the PD control;

[0067] 42) By replacing the sign function with a continuous hyperbolic tangent function, the final control input expression is obtained:

[0068]

[0069] In the formula, , =33, , The value of determines the steepness of the hyperbolic tangent function;

[0070] 43) The impedance equation is designed as follows:

[0071] formula

[0072] Therefore, it is rewritten as: ,

[0073]

[0074] 44) The discrete form of the controller is represented as:

[0075]

[0076] 45) The robot inversely solves the joint angles and outputs them to the robot to perform positional actions.

[0077] The beneficial effects of this invention are as follows:

[0078] 1) In terms of robot force / position control, this invention addresses the drawback of low workpiece force tracking accuracy under different surfaces, and solves the problem of large force / position tracking error of robot on workpiece surface. It obtains an adaptive law by dynamically adjusting the self-learning factor to dynamically compensate the damping coefficient of the admittance control model, and introduces PD-suboptimal sliding mode control to effectively constrain the force when the end of the robot arm contacts the environment, reduce contact chatter, and enhance the robustness of the control system.

[0079] 2) This invention enables robotic arms to better perform compliant control in unknown environments, providing more reliable system stability; it also improves the adaptability of robotic arms in complex environments and enhances the compliance of robot tool ends, fully demonstrating its practicality and universality. Attached Figure Description

[0080] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0081] Figure 1 This is a schematic diagram of the input for fuzzy control.

[0082] Figure 2 Output a diagram illustrating the membership function;

[0083] Figure 3 This is a schematic diagram of the phase plane.

[0084] Figure 4 This is a schematic diagram illustrating the force tracking effect of a robot in a plane.

[0085] Figure 5 This is a schematic diagram illustrating the force tracking effect of a robot on an inclined plane.

[0086] Figure 6 This is a schematic diagram of the robot force tracking effect on a curved surface. Detailed Implementation

[0087] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0088] Example 1

[0089] This invention provides an adaptive iterative learning compliant control method based on robotic arm impedance control, comprising the following steps:

[0090] Step 1: The robot controller acquires information from the six-dimensional force sensor. The specific method is as follows:

[0091] 11) Perform tool gravity compensation and sensor zero-point drift compensation on the collected torque, and compensate for the transformation relationship between the robot base coordinates and world coordinates;

[0092] 12) The compensated force signal is processed by low-pass filtering to obtain the torque of the actual contact measured by the six-dimensional force sensor.

[0093] Step 2: Employ fuzzy control to dynamically adjust the update factor based on changes in external contact information. The specific method is as follows:

[0094] 21) The admittance control model consisting of the robot and the environment is represented as:

[0095]

[0096] In the formula, , , These are the inertia coefficient matrix, damping coefficient matrix, and stiffness coefficient matrix of the end effector, respectively, and all are positive definite matrices; among them, and These are the actual environment location matrix and the desired environment location matrix, respectively. and These are the actual contact force matrix and the expected contact force matrix when the end effector comes into contact with the environment, respectively. , , These are the reference trajectory, running speed, and acceleration of the robot's end effector, respectively. , , These represent the desired acceleration, velocity, and position. The difference between the contact force and the desired force. ; For the robot to have the desired contact force with the outside world; The actual contact force between the robot and the outside world;

[0097] 22) The analysis is performed in one dimension, as shown below:

[0098]

[0099] In the formula, , , , , , , , , , These are the components of each variable in the impedance model in a single degree of freedom direction;

[0100] 23) Assume the stiffness of the environment is , The environmental location is A linear environment model is used, as shown below:

[0101]

[0102] in Using position error to determine the reference trajectory Provide compensation;

[0103] 24) Force tracking error is expressed as:

[0104]

[0105] in,

[0106] In the formula, Complex variables introduced for the Laplace transform;

[0107] 25) After the admittance control model undergoes a Laplace transform, the final steady-state error is expressed as follows:

[0108]

[0109] 26) Due to the uncertainty of actual environmental information, it is difficult to obtain accurate... The environmental location is used instead of the reference trajectory, as shown below:

[0110]

[0111] 27) This invention sets the stiffness gain to 0, which will satisfy the stiffness requirement under any circumstances. And the situation of unknown environmental information;

[0112] The model was changed to: ;

[0113] 28) Based on the admittance control model, the damping coefficient... Real-time compensation is performed as follows:

[0114]

[0115] In the formula, To adjust in real time according to the error of contact force, for compensation The uncertainty is expressed as follows:

[0116]

[0117] In the formula, The sampling period; For the update factor, a constant To prevent oscillations caused by excessively small denominator values;

[0118] 29) See Figure 1 and Figure 2 A fuzzy controller was designed to update the weights of the adaptive law in real time according to changes in external force. The inputs to the fuzzy controller are the contact force error and its rate of change, both using triangular membership functions. The fuzzy subset universe is [-3,3], and the designed fuzzy set is [Nf, Nt, No, Z, Po, Pt, Pf], with subsets representing negative large, negative medium, negative small, zero, positive small, positive medium, and positive large, respectively. The output uses a Gaussian membership function, with the fuzzy subset universe set to [0,1], and the designed fuzzy set is [Lo, Lt, Lh, Lf, Lv, Ls, Le], with subsets representing very small, very small, relatively small, medium, relatively large, large, and very large, respectively. The fuzzy inference process is implemented using the Mamdani method, and the centroid method is used to defuzzify the output.

[0119] When the force error and the rate of change are abruptly caused by the time-varying external environmental information, the update factor can be dynamically adjusted according to the designed fuzzy controller to adapt to the changes in environmental information and increase tracking accuracy.

[0120] Step 3: Suboptimal sliding mode control is introduced to suppress the relationship between chattering and convergence speed. The specific method is as follows:

[0121] 31) Design the membership functions and fuzzy rule tables for the input and output, as shown below:

[0122]

[0123] 32) The suboptimal sliding mode control method evolved from the time-optimal control method for linear systems. Its biggest feature is that the convergence region can be preset. Previous control methods only considered the case where the system state has a maximum value in a certain region. When the system state passes through multiple regions, and the state in each region has a maximum value, a multi-region suboptimal sliding mode control method can be designed by introducing a switching logic. When there is a time delay in the control input, the analysis shows that the time delay is not directly related to the system stability, but the convergence region of the system is related to the time delay parameter.

[0124] The sliding surface is designed as follows: ,

[0125] In the formula, It is a sliding surface; The derivative of the force error; It is a constant; For force error; for Time corresponding value; The second derivative of the force error;

[0126] 33) The form of the sliding mode controller is as follows:

[0127]

[0128] In the formula, control gain , satisfy , The value is the sliding surface rate of change, which is equal to 0, and the initial value is 0;

[0129] 34) Consider the following nonlinear system, as shown below:

[0130]

[0131] In the formula, This refers to the system status; For control input; and It is an unknown smooth nonlinear function;

[0132] Assume sliding mode variables s and Given that the second derivative of a nonlinear system with respect to s is obtained,

[0133]

[0134] Here, , It is a smooth unknown function;

[0135] 35) Assume: There exist positive constants. , and , making and Established;

[0136] Lemma: In the sliding mode dynamics equations satisfying equation Under the given assumptions, if the parameters , satisfy, Then the sliding mode controller enables the system to achieve second-order sliding mode motion within a finite time.

[0137] 36) See Figure 3 The idea behind the suboptimal sliding mode control method mainly originates from the time-optimal control strategy of the dual integrator. Based on its phase plane trajectory diagram, the prerequisite for the implementation of the suboptimal sliding mode control method is... Its derivative is known. Furthermore, since the calculation is performed using discrete sampling, implementing the suboptimal sliding mode control method only requires knowing the values ​​at each sampling point. and Specific information, typically, refers to the error of the sliding mode variable between two consecutive sampling points. When the sign is changed, it can be considered that At this point, through calculation, the suboptimal controller required can be obtained. and information.

[0138] 37) Dual Integrator Strategy: The suboptimal sliding mode design concept originates from the time-optimal control strategy of the dual integrator, which dynamically adjusts the magnitude and direction of the control signal near the sliding surface. This piecewise design ensures that the control signal is within the sliding surface (i.e., near the sliding surface) The switching becomes smoother, reducing the frequency and magnitude of switching.

[0139] 38) Segmented processing design: The segmented processing of the control law prevents the control signal from switching frequently near the sliding surface, thereby reducing high-frequency chattering.

[0140] when near At this time, the amplitude of the control signal is reduced, thereby avoiding drastic switching.

[0141] when When the distance from the sliding surface is greater, the control signal is increased to ensure the convergence speed.

[0142] 39) To achieve a better balance between suppressing chattering and improving convergence speed, the gain is dynamically adjusted by incorporating the sliding surface variation law. By introducing the derivative of the error, the gain can respond more flexibly to the dynamic changes of the system, thereby achieving faster convergence and lower chattering.

[0143]

[0144] In the formula, and This is the initial gain; and To control the magnitude of the gain; and To control the rate of gain decay; and It is an adjustment factor used to control the sensitivity of the gain to the rate of change of error;

[0145] Step 4: Using the obtained data, an iterative compliant control method for variable parameters of the robotic arm based on adaptive impedance control is proposed. The impedance parameters are corrected in real time to achieve zero-error steady-state tracking. The specific method is as follows:

[0146] 41) To minimize vibration and increase system robustness, a PD suboptimal sliding mode control method is adopted, with the control input being:

[0147]

[0148] In the formula, , The proportional and derivative control gains of the PD control are given; the proposed PD-suboptimal sliding mode control is a combination of PD control and suboptimal sliding mode control. Therefore, it has the characteristics of both linear PD control and nonlinear SMC control.

[0149] 42) By replacing the sign function with a continuous hyperbolic tangent function, the final control input expression is obtained:

[0150]

[0151] In the formula, , =33, , The value of determines the steepness of the hyperbolic tangent function;

[0152] 43) The impedance equation is designed as follows:

[0153] formula

[0154] Therefore, it is rewritten as: ,

[0155]

[0156] 44) The discrete form of the controller is represented as:

[0157]

[0158] 45) Finally, the robot inversely solves the problem into joint angles and outputs them to the robot to perform positional actions.

[0159] Example 2

[0160] This embodiment demonstrates the experimental verification of a six-degree-of-freedom robotic arm.

[0161] Force tracking effect when the robot's end effector contacts a plane: Figure 4 As shown.

[0162] The force tracking effect is as follows when the robot's end effector contacts the inclined plane: Figure 5 As shown.

[0163] Force tracking effect when the robot's end effector contacts a curved surface: Figure 6 As shown.

[0164] The experimental results above show that the adaptive variable parameter iterative learning compliant control method based on robotic arm impedance control described in this invention can effectively adapt to the environment of complex curved workpieces and has good tracking effect on position and force.

[0165] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An adaptive iterative learning compliant control method based on robotic arm impedance control, characterized in that, Includes the following steps Step 1: The robot controller collects information from the six-dimensional force sensor; Step 2: Use fuzzy control to dynamically adjust the size of the update factor based on changes in external contact information; Step 3: Suboptimal sliding mode control is introduced to suppress the relationship between chattering and convergence speed; Step 4: Using the obtained data, propose an iterative compliant control method for variable parameters of the robotic arm based on adaptive impedance control, and perform real-time correction of the impedance parameters to achieve zero-error steady-state tracking.

2. The adaptive iterative learning compliant control method based on robotic arm impedance control according to claim 1, characterized in that, The specific method for step one is as follows: 11) Perform tool gravity compensation and sensor zero-point drift compensation on the collected torque, and compensate for the transformation relationship between the robot base coordinates and world coordinates; 12) The compensated force signal is processed by low-pass filtering to obtain the torque of the actual contact measured by the six-dimensional force sensor.

3. The adaptive iterative learning compliant control method based on robotic arm impedance control according to claim 1, characterized in that, The specific method for step two is as follows: 21) The admittance control model consisting of the robot and the environment is represented as: ； In the formula, , , These are the inertia coefficient matrix, damping coefficient matrix, and stiffness coefficient matrix of the end effector, respectively, and all are positive definite matrices; among them, and These are the actual environment location matrix and the desired environment location matrix, respectively. and These are the actual contact force matrix and the expected contact force matrix when the end effector comes into contact with the environment, respectively. , , These are the reference trajectory, running speed, and acceleration of the robot's end effector, respectively. , , These represent the desired acceleration, velocity, and position. The difference between the contact force and the desired force. ; For the robot to have the desired contact force with the outside world; The actual contact force between the robot and the outside world; 22) The analysis is performed in one dimension, as shown below: ； In the formula, , , , , , , , , , These are the components of each variable in the impedance model in a single degree of freedom direction; 23) Assume the stiffness of the environment is , The environmental location is A linear environment model is used, as shown below: ； in Using position error to determine the reference trajectory Provide compensation; 24) Force tracking error is expressed as: ； in, ; In the formula, Complex variables introduced for the Laplace transform; 25) After the admittance control model undergoes a Laplace transform, the final steady-state error is expressed as follows: ； 26) Use the environmental location instead of the reference trajectory, as shown below: ； 27) Setting the stiffness gain to 0 will satisfy the stiffness requirement under all conditions. And the situation of unknown environmental information; The model was changed to: ; 28) Based on the admittance control model, the damping coefficient... Real-time compensation is performed as follows: ； In the formula, To adjust in real time according to the error of contact force, for compensation The uncertainty is expressed as follows: ； In the formula, The sampling period; For the update factor, a constant To prevent oscillations caused by excessively small denominator values; 29) By designing a fuzzy controller, the weights of the adaptive law are updated in real time according to the changes in external force. In the designed fuzzy controller, the inputs are the contact force error and the rate of change of the error, both of which use triangular membership functions. The fuzzy subset universe of discourse is [-3,3], and the designed fuzzy set is [Nf, Nt, No, Z, Po, Pt, Pf], with the subset meanings being negative large, negative medium, negative small, zero, positive small, positive medium, and positive large, respectively. The output uses a Gaussian membership function, with the fuzzy subset universe of discourse set to [0,1], and the designed fuzzy set is [Lo, Lt, Lh, Lf, Lv, Ls, Le], with the subset meanings being very small, very small, relatively small, medium, relatively large, large, and very large, respectively. The fuzzy inference process is implemented using the Mamdani method, and the centroid method is used to defuzzify the output. When the force error and the rate of change are abruptly caused by the time-varying external environmental information, the update factor is dynamically adjusted according to the designed fuzzy controller to adapt to the changes in environmental information and increase the tracking accuracy.

4. The adaptive iterative learning compliant control method based on robotic arm impedance control according to claim 1, characterized in that, The specific method for step three is as follows: 31) Design the membership functions and fuzzy rule tables for the input and output, as shown below: ； 32) The sliding surface is designed as follows: , ; In the formula, It is a sliding surface; The derivative of the force error; It is a constant; For force error; for Time corresponding value; The second derivative of the force error; 33) The form of the sliding mode controller is as follows: ； In the formula, control gain , satisfy , The value is the sliding surface rate of change, which is equal to 0, and the initial value is 0; 34) Consider the following nonlinear system, as shown below: ； In the formula, This refers to the system status; For control input; and It is an unknown smooth nonlinear function; Assume sliding mode variables s and Given that the second derivative of a nonlinear system with respect to s is obtained, ； Here, , It is a smooth unknown function; 35) Assume: There exist positive constants. , and , making and Established; The sliding mode dynamics equation satisfies equation Under the given assumptions, if the parameters , satisfy, Then the sliding mode controller enables the system to achieve second-order sliding mode motion within a finite time. 36) The suboptimal sliding mode control method originates from the time-optimal control strategy of the dual integrator. According to the phase plane trajectory diagram, the prerequisite for the implementation of the suboptimal sliding mode control method is... Its derivative is known. Furthermore, since the calculation is performed using discrete sampling, implementing the suboptimal sliding mode control method only requires knowing the values ​​at each sampling point. and Specific information, when the error of the sliding mode variable between two consecutive sampling points When changing the sign, it is considered At this point, through calculation, the suboptimal controller required is obtained. and information; 37) The suboptimal sliding mode design is derived from the time-optimal control strategy of the dual integrator, which dynamically adjusts the magnitude and direction of the control signal on the sliding surface; 38) The control law is processed in segments; 39) Introducing the derivative of the error allows the gain to respond more flexibly to the dynamic changes of the system, thereby achieving faster convergence and lower chattering, as shown below: ； In the formula, and This is the initial gain; and To control the magnitude of the gain; and To control the rate of gain decay; and It is an adjustment factor used to control the sensitivity of the gain to the rate of change of error.

5. The adaptive iterative learning compliant control method based on robotic arm impedance control according to claim 1, characterized in that, The specific method for step four is as follows: 41) The PD suboptimal sliding mode control method is adopted, and the control input is: ； In the formula, , For the proportional and derivative control gains of the PD control; 42) By replacing the sign function with a continuous hyperbolic tangent function, the final control input expression is obtained: ； In the formula, , =33, , The value of determines the steepness of the hyperbolic tangent function; 43) The impedance equation is designed as follows: ; official ; Therefore, it is rewritten as: , ； 4) The discrete form of the controller is expressed as: ； 45) The robot inversely solves the joint angles and outputs them to the robot to perform positional actions.

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