A fuzzy variable impedance control method for grinding and polishing robots based on fast terminal sliding mode

Abstract

This invention provides a fuzzy variable impedance control method for a grinding and polishing robot based on fast terminal sliding mode, belonging to the field of robot control technology. The method first establishes a robot dynamics model using the Lagrange method. Within the traditional impedance control framework, fast terminal sliding mode replaces the traditional PID control algorithm as the robot's motion controller. A hyperbolic tangent function is used to suppress chattering. Finally, based on the magnitude of force error and force error rate, a fuzzy controller is designed to adjust the impedance parameters in real time to achieve faster response speed and smaller overshoot. Compared with traditional impedance control grinding and polishing methods based on PID and ordinary sliding mode, the designed control algorithm improves robustness and response capability, reduces overshoot and steady-state error, and is of great significance for improving the consistency and accuracy of the polished surface.

Description

Technical Field

[0001] This invention relates to the field of compliant control technology for grinding and polishing robots, and in particular to a fuzzy variable impedance control method for grinding and polishing robots based on fast terminal sliding mode. Background Technology

[0002] Grinding and polishing are common finishing processes used to improve the surface accuracy of parts. With the development of robotics technology, replacing human workers in grinding and polishing is becoming a demand and a trend. Since grinding and polishing is a contact cutting operation, robot-based grinding and polishing requires controlling the grinding and polishing tool to maintain a certain normal pressure during its movement on the part surface. Due to the high rigidity and precision of robots, they maintain high rigidity even when subjected to unknown external impacts (such as collisions or large burrs on the workpiece surface). This can easily lead to damage to precision components at joints and the workpiece. However, robots also need high rigidity to ensure trajectory tracking accuracy. Therefore, a conflict arises between maintaining the compliance of the grinding and polishing contact force and the robot's high mechanical structural rigidity, necessitating robot compliance force control. Furthermore, many unknown disturbances exist during the grinding and polishing process, such as joint friction and mechanical vibration, which poses a significant challenge to the design of compliant control for industrial robots.

[0003] Current robot compliance force control mainly employs passive and active compliance strategies. Passive compliance is highly specialized, has poor applicability, and a small dynamic range of force response; therefore, more research focuses on active control technologies. Active compliance control actively adjusts the interaction between the industrial robot and its environment based on sensor feedback information. It primarily includes impedance control and force / position hybrid control strategies. Compared to force / position hybrid control, impedance control unifies force and position control within a single framework, but it does not directly control the interaction force between the robot's end effector and the environment. Instead, it achieves force control by adjusting the dynamic relationship between the position, velocity, and contact force of the robot's end effector. This requires less task planning, avoids frequent switching of control modes, and has relatively lower requirements for the accuracy of the end effector force sensor measurement. However, the traditional impedance force control framework mainly consists of an inner loop for robot joint position control and an outer loop for compliance force control. The inner loop position control often uses PID control, which suffers from long parameter tuning times and insufficient anti-interference capabilities. This limits the current application of robots in contact processing to scenarios with low precision requirements, which is inextricably linked to the robot's control accuracy and anti-interference capabilities. Summary of the Invention

[0004] The purpose of this invention is to provide a fuzzy variable impedance control method for grinding and polishing robots based on rapid terminal sliding mode, which solves the technical problem that existing grinding and polishing robots cannot achieve the predetermined smooth grinding and polishing operation under unknown interference conditions.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A fuzzy variable impedance control method for a grinding and polishing robot based on fast terminal sliding mode, the method comprising the following steps:

[0007] Step 1: Establish the kinematic model of the n-joint robot and establish the dynamic model of the end effector of the n-joint grinding and polishing robot under external force according to the Lagrange method;

[0008] Step 2: Establish an impedance control model for robot compliant polishing, and plan the robot command position X based on the impedance controller. c After passing through the inverse kinematics module, the robot joint trajectory is output and enters the robot motion controller;

[0009] Step 3: Design the control law for the joint control torque;

[0010] Step 4: Apply the actual force F e With target force F d By comparing the force error e and the force error rate ec, a new instantaneous actual grinding and polishing force is output.

[0011] Furthermore, in step 1, the dynamic model is as follows:

[0012]

[0013] In the formula, q is the joint angle vector of n×1 at time t. Let q be the first derivative of the joint angle q with respect to time t, which is the joint angular velocity vector. Let q be the second derivative of the joint angle q with respect to time t, which is the joint angular acceleration vector. M(q) is the n×n robot inertia matrix. Let G(q) be an n×n matrix combining centrifugal and Coriolis forces, G(q) be an n×1 gravity matrix, and τ be the torque output by each joint motor. f The external force applied to the robot's end effector. To model the uncertainty terms.

[0014] Furthermore, in step 2: the impedance control model includes an inner loop of motion control and an outer loop of force control, first based on the environmental position X. e With stiffness K e Determine the reference trajectory X r To achieve compliant polishing, an impedance controller was designed. This controller treats the dynamic characteristics of the robot's interaction with the environment as those of a second-order mass-spring-damped system. Based on the real-time force error ΔF, the impedance control module derives a compensation value E for the reference trajectory X. r Compensation will be provided.

[0015] Furthermore, in step 2: the expression for the impedance control model is:

[0016]

[0017] Where ΔF is the error between the expected polishing force and the actual force, and M d B d K d Mass, damping, and stiffness matrices, respectively, X e X represents the environmental location, i.e., the location of the polished surface. r For reference trajectory, X c For the robot trajectory command, E is the value compensated by impedance control, i.e., the difference between the reference trajectory and the trajectory command, and K... e For environmental stiffness, Let be the first derivative of the robot trajectory command with respect to time t. Let be the second derivative of the robot trajectory command with respect to time t. The first derivative of the reference trajectory with respect to time t, The second derivative of the reference trajectory with respect to time t;

[0018] Treating the dynamic characteristics of the robot's interaction with the environment as those of a second-order system, its transfer function G(s) is:

[0019]

[0020] Where s is a complex parameter.

[0021] To achieve uniform polishing, the robot's end-effector polishing reference trajectory is set to...

[0022]

[0023] Where F d For the desired polishing power, K e For environmental stiffness.

[0024] The fuzzy variable impedance control module outputs a compensated trajectory E based on the force error ΔF, thus deriving the robot's trajectory command X. c for:

[0025] X c =X r +E=X r +ΔF·G(s)

[0026] Robot trajectory command X c The robot joint trajectory q is output after passing through the inverse kinematics module. d The data is fed into the robot motion controller and compared with the actual joint angles to obtain the robot motion error. Based on this, the motion controller controls the output torque of each joint through a fast end-of-line sliding mode control strategy.

[0027] Furthermore, in step 3, a fast terminal sliding mode motion controller based on an exponential reaching law is designed for the inner loop, the chattering is suppressed by using the hyperbolic tangent function, and its stability is proved by using the second method of Lyapunov. Then, according to the designed controller, the control torque is output to the established robot dynamic model, and at the same time, an external disturbance τ d is applied to obtain the actual joint angle q and angular velocity of the robot and fed back to the motion controller. The actual joint angle of the robot is kinematically transformed to obtain the end spatial position X of the robot. According to the environmental position X e and environmental stiffness K e the actual grinding and polishing force magnitude F can be obtained e and input into the robot dynamic model at the same time.

[0028] Furthermore, in step 3, first, the fast terminal sliding mode function is designed as follows:

[0029]

[0030] where Λ>0, a and b are both positive odd numbers to be designed, and a < b. The angle error satisfies the Hurwitz condition.

[0031] Define

[0032] where and are the corresponding estimated values.

[0033] To suppress the chattering phenomenon in the sliding mode control process, the hyperbolic tangent function tanh(x / ε) is used as the switching function. The expression of the hyperbolic tangent function is:

[0034] [[ID=CO]]

[0035] where x is the independent variable and ε is the parameter value of the function. The larger ε is, the flatter the hyperbolic tangent function graph is.

[0036] The exponential reaching law designed by using the hyperbolic tangent function tanh(x / ε) is:

[0037]

[0038] where η>0, k>0. η and K are the rates of the system approaching the switching surface

[0039] The controller designed based on the exponential reaching law and the hyperbolic tangent function is:

[0040]

[0041] where q dLet q be the expected joint angle of n×1. r Let J be the estimated joint angle of an n×1 matrix, Λ be a positive constant matrix, and J be the estimated joint angle of an n×1 matrix. T F is the transpose of the Jacobian matrix. e The force on the end joint is τ, where τ is the torque output by the motors of each joint. Estimate the output torque τ for each joint. f The torque is the force exerted at the joint by the polishing force at the end of the robot.

[0042] Furthermore, in step 4, fuzzy control is used to adjust the impedance parameters in real time to enhance the performance of the control system. Force error and force error rate are set as inputs to the fuzzy controller, and the damping adjustment is used as the output. Both inputs and outputs are fuzzified using triangular membership functions. Fuzzy adjustment rules are designed, employing a parallel method during fuzzy inference and a centroid method during defuzzification. After fuzzy inference and defuzzification, the damping adjustment value is output, resulting in an updated impedance control model. Then, the new instantaneous actual grinding force is output, with the damping parameter adjustment ΔB as the output. The damping adjustment range is selected, ensuring it remains always greater than 0.

[0043] Furthermore, in step 4, both the input and output adopt the triangular membership function, and the magnitude of the grinding and polishing force error and the force error rate are divided into 7 levels {NB, NM, NS, ZE, PS, PM, PB}, which are fuzzed in the universe of discourse as {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}.

[0044] Furthermore, the updated model yields a new impedance control model:

[0045]

[0046] Then, a new instantaneous actual polishing force is output to reduce overshoot and achieve a fast response.

[0047] The present invention, by adopting the above-described technical solution, has the following beneficial effects:

[0048] The sliding mode control of this invention further improves the response capability, uses a hyperbolic tangent function to suppress chattering, improves the response speed and anti-interference capability of the robot force tracking, and reduces force overshoot, enabling the robot to perform grinding and polishing operations more uniformly and stably. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the impedance-controlled polishing process of the present invention;

[0050] Figure 2 This is the overall block diagram of the fuzzy variable impedance control of the grinding and polishing robot based on the rapid terminal sliding mode of the present invention;

[0051] Figure 3 This is a simplified diagram of the three-axis robot of the present invention;

[0052] Figure 4 This is the fuzzy impedance adjustment rule diagram of the present invention;

[0053] Figure 5 This is the input-output membership function graph of the present invention;

[0054] Figure 6 These are step input position tracking diagrams for two grinding and polishing conditions according to the present invention;

[0055] Figure 7 This is a comparison diagram of step input force tracking under two grinding and polishing conditions according to the present invention;

[0056] Figure 8 These are sinusoidal input position tracking diagrams for two grinding and polishing conditions according to the present invention;

[0057] Figure 9 This is a comparison chart of sinusoidal input force tracking under two grinding and polishing conditions according to the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. However, it should be noted that many details listed in the specification are merely to provide the reader with a thorough understanding of one or more aspects of the present invention, and these aspects of the invention can be implemented even without these specific details.

[0059] A fuzzy variable impedance control method for a grinding and polishing robot based on fast terminal sliding mode, the method comprising the following steps:

[0060] Step 1: Establish the kinematics and dynamics model of the grinding and polishing robot, taking a planar three-axis robot as an example, such as... Figure 3 According to the geometric method, the following forward kinematic model can be established:

[0061]

[0062] Where x and y are the coordinates of the robot's end effector, l1, l2, and l3 are the lengths of each link of the robot, and q1, q2, and q3 are the joint angles.

[0063] Then perform inverse kinematics solution, let the coordinates of the third joint be P(x) p ,y p According to the Law of Cosines, we can obtain:

[0064]

[0065]

[0066] Where L is the length of the line connecting joint 1 and joint 3. The angle between the joint end effector and the X-axis.

[0067] According to the above formula, we can obtain:

[0068]

[0069] Let α be the angle between OP and the horizontal direction, and β be the angle between OP and the robotic arm lever 1, then we can obtain:

[0070] α=arctan2(y p ,x p )

[0071]

[0072] Further, joint angle 1 is introduced:

[0073]

[0074] From the fact that the opposite angles are equal, we can conclude that:

[0075]

[0076] Thus, the inverse kinematics solutions for each joint angle of the three-axis robot are obtained.

[0077] Differentiating the kinematic equations of the robotic arm yields the Jacobian matrix of the robot:

[0078]

[0079] Where s1 represents sinq1, s 12 c1 represents sin(q1+q2), c1 represents cosq1, and so on.

[0080] The velocity of joint 1 is obtained by differentiating its center of mass position:

[0081]

[0082] The velocity of joint 2 is obtained by differentiating its center of mass position:

[0083]

[0084] The velocity of joint 3 is obtained by differentiating its center of mass position:

[0085]

[0086] A dynamic model was established using the Lagrange method, and the translational kinetic energy E of the three-axis robot was calculated. k1 and rotational kinetic energy E k2 They are respectively:

[0087]

[0088]

[0089] Where x ci y ci The position coordinates of the centroids of each joint, m i m ci The masses at the beginning and center of mass of the connecting rod are respectively l ci Let I be the distance from the beginning of link i to the center of mass. i Let be the rotational inertia of the i-th joint.

[0090] Therefore, the total kinetic energy of the three-axis robot is:

[0091] E k =E k1 +E k2

[0092] The total potential energy of the three-axis robot is:

[0093] E p =m c1 gl c1 sinq1+m c2 g[l c1 sinq1+l c2 sin(q1+q2)]

[0094] +m c3 g[l c1 sinq1+l c2 sin(q1+q2)+l c3 sin(q1+q2+q2)]

[0095] The Lagrange operator can be obtained as follows:

[0096]

[0097] The torque at the i-th joint can be obtained as follows:

[0098]

[0099] Write it in the form of a dynamic equation:

[0100]

[0101] Where τ = [τ1τ2τ3] is the control torque vector. M(q) is the system's angular acceleration vector, and M(q) is a 3×3 positive definite inertia matrix. Let G(q) = [G1G2G3] be a 3×1 matrix of centrifugal and Coriolis forces, and let [G1G2G3] be a 3×1 matrix of gravity. For brevity, let c1 denote cosq1. 12 Let cos(q1+q2) represent the first cosine of q1, and s1 represent sinq1. 12 Let sin(q1+q2) be the inertia matrix, and so on. The specific form of the inertia matrix is ​​as follows:

[0102]

[0103] in:

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] Moments of inertia of each rod:

[0111]

[0112] The centrifugal force and Coriolis force matrices are as follows:

[0113]

[0114] in:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] C 33 =0

[0124] The gravity matrix is ​​as follows:

[0125]

[0126] in:

[0127] G1=m3g(l1c1+l2c 12 +l c3 cos 123 )+m2g(l1c1+l c2 c 12 )+m1gl c1 c1

[0128] G2=m3g(l2c 12 +l c3 c 123 )+m2gl c2 c 12

[0129] G3=m3gl c3 c 123

[0130] g is the acceleration due to gravity.

[0131] Step 2: Design the overall system framework for fuzzy variable impedance control of the grinding and polishing robot based on fast terminal sliding mode. When the robot system interacts with the external environment, it is considered as a second-order mass-damped-spring system, such as... Figure 1 As shown, its dynamic characteristics are obtained. A unified framework is provided for the contact transition state and steady state, and the relationship between the elastic deformation and contact force during contact operation is adjusted to further indirectly control the contact force.

[0132] The stiffness model of environmental forces is as follows:

[0133] F e =K e (XX e )

[0134] If we disregard the tracking error at the end effector of the robotic arm, then X = X c ,have:

[0135] F e =K e (X c -X e )

[0136] Therefore, the contact force error is:

[0137] ΔF=F d -F e

[0138] The impedance control model can be expressed as:

[0139]

[0140] Where M d B d K d The diagonal matrices for mass, damping, and stiffness are respectively represented, where E is the value compensated by impedance control, i.e., the difference between the reference trajectory and the trajectory command.

[0141] Treating it as a second-order system, its transfer function G(s) is:

[0142]

[0143] To achieve uniform polishing, the reference trajectory at the end of the robotic arm can be set to...

[0144]

[0145] Further robot trajectory command x c It can be written as

[0146] X c =X r +E=X r +ΔF·G(s)

[0147] The block diagram of the fuzzy impedance-changing control system for a grinding and polishing robot based on rapid terminal sliding mode is as follows: Figure 2 As shown. The terminal reference trajectory X... r By environmental location X e According to environmental stiffness K e The robot trajectory command X is adaptively generated and compensated by the fuzzy impedance control module. c The inverse kinematics module converts the trajectory commands in Cartesian space into robot joint space commands, while the fast end effector sliding mode motion controller module is responsible for outputting joint control torques to drive the robot to track the joint trajectory command X. c The robot's end effector Cartesian space coordinates are then obtained through the positive kinematics module. The grinding and polishing force is calculated based on the environmental stiffness and compared with the desired force. The difference is input into the fuzzy variable impedance control module to form a closed-loop control.

[0148] Step 3: The dynamic equation of the end effector of an n-joint robot subjected to external forces, considering modeling uncertainties, can be expressed as:

[0149]

[0150] Where q is an n×1 joint position vector, and M(q) is an n×n robot inertia matrix. Let G(q) be an n×n matrix combining centrifugal and Coriolis forces, G(q) be an n×1 gravity matrix, and τ be the torque output by each joint motor.f is the external force applied to the end of the robot, is the modeling uncertainty.

[0151] Define Define Design a fast terminal sliding mode function

[0152]

[0153] where Λ>0, a and b are both positive odd numbers to be designed, and a < b, satisfying the Hurwitz condition.

[0154] Therefore, to avoid the influence of chattering, the hyperbolic tangent function is used to replace the sign function as the switching function to suppress chattering. The expression of the hyperbolic tangent function is:

[0155]

[0156] where ε>0, and the steepness of the hyperbolic tangent function is related to the value of ε.

[0157] Then the controller design based on the exponential reaching law and the hyperbolic tangent function is:

[0158]

[0159] where q is the actual joint angle of n×1, q d is the desired joint angle of n×1, q r is the estimated value of the joint angle of n×1, q~ is the difference between the actual value and the expected value of the joint angle, where η>0, k>0, η and k are the rates at which the system approaches the switching surface, Λ is a positive constant matrix, M is the n×n robot inertia matrix, C is the n×n combined matrix of centrifugal force and Coriolis force, G is the n×1 gravity matrix, τ is the torque output by each joint motor, is the estimated output torque of each joint, τ f is the grinding and polishing force acting on the joint.

[0160] The stability of the controller can be proved by the second Lyapunov method.

[0161] Step 4: When the force error e and the force error rate ec are large, in order to speed up the response speed of the control system, the damping coefficient should be small; when the force error and the force error rate are small, in order to reduce the overshoot of the control system and improve the anti-interference ability, the damping coefficient should be large. Determine the fuzzy rules according to this principle and design a fuzzy controller. Let the inputs of the fuzzy controller be the force error e and the force error rate ec, and the output be the adjustment amount ΔB of the damping parameter. The input and output both adopt triangular membership functions. The universes of discourse of the force error, the change rate of the force error, and the adjustment value of the damping are [0,F E]、[0,F EC ]、[-B m B m Let their fuzzy sets be {NB, NM, NS, ZE, PS, PM, PB}, which correspond to being fuzzy in the universe of discourse as {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}, respectively. Their membership functions are as follows: Figure 5 As shown, the fuzzy force error rates of the input and output linguistic variables are also fuzzified using the same method. A parallel method is employed during fuzzy inference, and a centroid method is used during defuzzification. After fuzzy inference and defuzzification, the damping adjustment value is output, achieving adaptive adjustment of the impedance parameter. An updated impedance control model is then obtained, and finally, a new instantaneous actual polishing force is output.

[0162] A grinding and polishing simulation experiment was conducted on a planar part with a relative height of 1m to robot joint 1. The grinding and polishing environment was simulated using a unit step input at 0s (i.e., environment height of 1m) and a sinusoidal input to simulate planar grinding and polishing and sinusoidal surface grinding and polishing, respectively. A pulse signal with a height of 1mm was added to the part to simulate large, unknown burrs on the part surface, and a high-frequency, low-amplitude sinusoidal function c = 0.1sin30t (unit: mm) was added to simulate a rough surface with a surface roughness Ra = 100μm before grinding and polishing. The obtained grinding and polishing step and sinusoidal position tracking results are as follows: Figure 6 and Figure 8 As shown in the figure. The force tracking results are compared with those of traditional PID control methods and fast terminal sliding mode without fuzzy adaptive methods, as shown in the figure. Figure 7 and Figure 9 As shown in the figure. The simulation results above demonstrate that the proposed method outperforms current mainstream impedance control methods.

[0163] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A fuzzy variable impedance control method for a grinding and polishing robot based on fast terminal sliding mode, characterized in that, The method includes the following steps: Step 1: Establish n The kinematic model of the articulated robot was established based on the Lagrange method. n Dynamic model of the end effector of an articulated grinding and polishing robot under external force; Step 2: Establish an impedance control model for robot compliant polishing, and plan the robot command position based on the impedance controller. After passing through the inverse kinematics module, the robot joint trajectory is output and fed into the robot motion controller; Step 3: Design the control law for the joint control torque; Step 4: Apply actual force With target force By comparison, the force error is obtained. e Force error rate ec, Then output the new instantaneous actual polishing force; In step 2: the impedance control model includes an inner motion control loop and an outer force control loop, first based on the environmental location. With stiffness Determine the reference trajectory To achieve compliant polishing, an impedance controller was designed, which treats the dynamic characteristics of the robot's interaction with the environment as those of a second-order mass-spring-damped system, based on real-time force errors. The compensation value is obtained through the impedance control module. E For reference trajectory Provide compensation; In step 2: the expression for the impedance control model is: in To account for the error between the expected polishing force and the actual force, , , Mass, damping, and stiffness matrices respectively. This refers to the environmental location, specifically the location of the polished surface. For reference trajectory, The value compensated for by impedance control, i.e., the difference between the reference trajectory and the trajectory command. For environmental stiffness, For robot trajectory commands to time t The first derivative, For robot trajectory commands to time t The second derivative, For reference trajectory time t The first derivative, For reference trajectory time t The second derivative; Treating the dynamic characteristics of robot-environment interaction as characteristics of a second-order system, its transfer function... G(s) for: in As a complex parameter, in order to achieve uniform polishing, the robot end-effector polishing reference trajectory is set to... in To achieve the desired polishing power, For environmental stiffness; The fuzzy variable impedance control module is based on force error. Output compensation trajectory E To obtain the robot's trajectory command for: Robot trajectory commands The robot's joint trajectories are output after passing through the inverse kinematics module. The data is fed into the robot motion controller and compared with the actual joint angles to obtain the robot motion error. Based on this, the motion controller controls the output torque of each joint through a fast end-of-line sliding mode control strategy.

2. The fuzzy variable impedance control method for a grinding and polishing robot based on a fast terminal sliding mode, as described in claim 1, is characterized in that: In step 1, the dynamic model is as follows: In the formula q for t time The joint angle vector, For joint angle q Regarding time t The first derivative is the joint angular velocity vector. For joint angle q Regarding time t The second derivative of is the joint angular acceleration vector. for The robot's inertial matrix, for The matrix combining centrifugal force and Coriolis force, for The gravity matrix, This refers to the torque output by the motors at each joint. The external force applied to the robot's end effector. To model the uncertainty terms.

3. The fuzzy variable impedance control method for a grinding and polishing robot based on a fast terminal sliding mode as described in claim 1, characterized in that: In step 3, a fast terminal sliding mode motion controller based on the exponential reaching law is designed for the inner loop, and the hyperbolic tangent function is used to suppress chattering. The stability is proven using Lyapunov's second method. Then, the control torque output by the designed controller is fed into the established robot dynamics model, while external disturbances are applied. To obtain the actual joint angles of the robot q With angular velocity The actual joint angles of the robot are fed back to the motion controller, and the spatial position of the robot's end effector is obtained after positive kinematics. X According to the location of the environment Environmental stiffness The actual grinding and polishing force can be obtained. It is also input into the robot dynamics model.

4. The fuzzy variable impedance control method for a grinding and polishing robot based on a fast terminal sliding mode, as described in claim 3, is characterized in that: In step 3, the fast terminal sliding mode function is designed as follows: in , a , b All are positive odd numbers to be designed, and Satisfying the Hurwitz condition, the angular error is defined. , ; in and The corresponding estimated value; To suppress chattering during sliding mode control, a hyperbolic tangent function is used. As a switching function, the hyperbolic tangent function is expressed as follows: in x As the independent variable, For the parameter values ​​of the function, The larger the value, the smoother the graph of the hyperbolic tangent function; Using hyperbolic tangent function The exponential law of convergence of design is: in , , and For the rate at which the system approaches the switching surface, The controller design based on the exponential reaching law and the hyperbolic tangent function is as follows: in for The desired joint angle, for The estimated value of the joint angle, It is a positive constant matrix. This is the transpose of the Jacobian matrix. For the end joint to bear the force, This refers to the torque output by the motors at each joint. Estimate the output torque for each joint. The torque is the force exerted at the joint by the polishing force at the end of the robot.

5. The fuzzy variable impedance control method for a grinding and polishing robot based on a fast terminal sliding mode according to claim 1, characterized in that: In step 4, fuzzy control is used to adjust the impedance parameters in real time to enhance the performance of the control system. Force error and force error rate are set as inputs to the fuzzy controller, and the damping adjustment is set as the output. Both inputs and outputs are fuzzified using triangular membership functions. Fuzzy adjustment rules are designed, and a parallel method is used during fuzzy inference. The centroid method is used during defuzzification. After fuzzy inference and defuzzification, the damping adjustment value is output, resulting in an updated impedance control model. Then, the new instantaneous actual grinding and polishing force and the adjustment amount of the damping parameter are output. As an output, the selected damping adjustment range should always be greater than 0.

6. The fuzzy variable impedance control method for a grinding and polishing robot based on a fast terminal sliding mode, as described in claim 5, is characterized in that: In step 4, both input and output adopt triangular membership functions. The magnitude of grinding and polishing force error and force error rate are divided into 7 levels {NB, NM, NS, ZE, PS, PM, PB}, which are fuzzed in the universe of discourse as {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}.

7. The fuzzy variable impedance control method for a grinding and polishing robot based on a fast terminal sliding mode, as described in claim 6, is characterized in that: The updated impedance control model is as follows: Then, a new instantaneous actual polishing force is output to reduce overshoot and achieve a fast response.

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