Modeling method for robot surface treatment contact force control model based on variable impedance

Abstract

The application provides a modeling method of a robot surface treatment contact force control model based on variable impedance, which comprises the following steps: step 1, a dynamic model of a robot in an ideal state is established according to Newton Euler method, and a control rate model for calculating torque is designed; step 2B, robot end position variables in a Cartesian space are mapped into a joint space; step 3, the influence of impedance parameters on control performance is analyzed to determine output parameters in a variable impedance control algorithm based on TD3; step 4, according to simulation results, the output parameters in the variable impedance control algorithm of TD3 are determined as impedance parameters; and step 5, the TD3 algorithm is improved. The application combines the traditional TD3 algorithm with a position-based impedance control algorithm, and no longer directly carries out strategy learning on robot end position or joint displacement, but instead utilizes the exploration characteristics of a reinforcement learning algorithm to dynamically adjust impedance parameters, so that the purpose of indirectly realizing force control is achieved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of robot surface treatment contact force, and particularly relates to a modeling method of a robot surface treatment contact force control model based on variable impedance. BACKGROUND

[0002] In a robot surface treatment process, force control has an important influence on the machining quality of a workpiece. Unstable machining contact force can cause overcutting and undercutting of an end tool, thereby directly affecting the profile quality and machining precision of a product. Contact force control is an effective means to realize allowance control and surface consistency. Effective control of contact force in a machining process can not only obtain ideal profile quality and precision, but also reduce the wear of a tool to a certain extent. Effective contact force control is to keep the contact force between the end tool and the workpiece within a permissible range. If the contact force is lower than the range, the tool and the workpiece are difficult to be in contact and machining operation is difficult to be performed. If the contact force exceeds the range, the machining force is too large to cause damage to the tool or the workpiece. Therefore, effective control of machining contact is a key factor to exert the high-performance machining capability of a robot. SUMMARY

[0003] The application aims to provide a modeling method of a robot surface treatment contact force control model based on variable impedance. The modeling method combines a traditional TD3 algorithm with a position-based impedance control algorithm, designs a composite force control algorithm, and no longer directly performs strategy learning on the position of a robot end or the joint displacement amount. Instead, the modeling method utilizes the exploration characteristics of a reinforcement learning algorithm to dynamically adjust impedance parameters, so as to indirectly achieve the purpose of force control. The technical scheme adopted is as follows.

[0004] A modeling method of a robot surface treatment contact force control model based on variable impedance comprises the following steps.

[0005] Step 1: a dynamic model of a robot in an ideal state is established according to the Newton-Euler method, and a control rate model for calculating torque is designed:

[0006]

[0007] wherein q is a joint variable; , and are the first and second derivatives of q, respectively;

[0008] τ-Z is a component of joint torque matrix;

[0009] and are 5x1 matrices;

[0010] M(q) is an inertia matrix, which is a symmetric matrix; is a coupling matrix of centrifugal force and Coriolis force; and G(q) is a gravity matrix.

[0011] K d ,K p - positive definite matrix;

[0012] - desired acceleration;

[0013] Step 2, establishing a robot position-based impedance control strategy model, specifically comprising the following steps:

[0014] Step 2A, simplifying the position-based impedance model:

[0015]

[0016] ΔX=X c -X r ,ΔF=F n -F d ;

[0017]

[0018] wherein M d ,B d ,K d respectively represent the corresponding inertia matrix, damping matrix and stiffness matrix in the impedance model;

[0019] X c - robot end position;

[0020] X r - desired position;

[0021] respectively correspond to the velocity and acceleration of X c , X r ;

[0022] F d - desired force of the end contacting the external environment;

[0023] F n - actual contact force, which can be measured by a force sensor.

[0024] Step 2B, mapping the robot end position X c in the Cartesian space to the joint space:

[0025]

[0026] wherein L -1 (X) - inverse kinematics; J -1 - inverse Jacobian matrix;

[0027] Step 2C, the impedance model in step 2A, the mapping model in step 2B, and the control rate model in step 1 are brought in to obtain a robot position-based impedance control control rate model:

[0028]

[0029] Step 3, let m d ,b d ,k d represent M d ,B d ,K d , the influence of impedance parameters m d ,b d ,k d on control performance is analyzed to determine the output parameters in the TD3-based variable impedance control algorithm;

[0030] Step 4, according to the simulation results, let the impedance parameters m d = 20, and the output parameters in the TD3-based variable impedance control algorithm are determined as the impedance parameters b d ,k d ;

[0031] Step 5, improve the TD3 algorithm, and the improvement includes: replacing the OU noise with the Gaussian noise, and establishing a phased reward function.

[0032] Preferably, in step 2B, the solving process is specifically:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] Where X1, X2, X3 are the coordinates of the robot end position in x, y, z three directions in turn;

[0039] q1, q2, q3, q4, q5 are the joint positions corresponding to the five degrees of freedom of the robot in turn.

[0040] Preferably, the control rate model modeling step in step 1 includes:

[0041] Step 1A, introduce the robot dynamics model under ideal state:

[0042]

[0043] Step 1B, ignore joint friction and external force disturbance, rewrite the robot dynamics model:

[0044]

[0045] Step 1C, simplify the robot to a linear time-invariant system that is easy to control:

[0046]

[0047]

[0048] Step 1D, the system in Step 1C is equivalent to a decoupled linear time-invariant system:

[0049]

[0050] Step 1E, introduce PD control with bias, which forms the modified acceleration with the desired joint angle acceleration:

[0051]

[0052] Step 1F, bring the model in Step 1E into Step 1D:

[0053]

[0054] Step 1G, bring the model in Step 1F into the model in Step 1C.

[0055] Preferably, in Step 3, the impedance parameters are selected from the following ranges:

[0056] m d = [20, 50, 100, 500, 1000];

[0057] b d = [3500, 5000, 10000, 15000, 20000];

[0058] k d = [50, 100, 500, 1000, 1500].

[0059] Preferably, in Step 5, the reward function is designed to have two parts: distance reward and contact force difference reward, and the reward function is:

[0060]

[0061] Preferably, the end effector of the robot comprises:

[0062] a chuck and a grinding disc connected in sequence with the output shaft of the motor;

[0063] The force sensor is a force feedback device for monitoring the actual contact force F n The sensing end penetrates through the motor clamp and contacts the motor shell, which is fixed to the connecting flange and is coaxial with the motor, thereby ensuring the normal contact force F n The one-dimensional force sensor can directly measure the contact force F;

[0064] The connecting flange is fixed to the B shaft and connected to the flange extension.

[0065] Compared with the prior art, the advantages of the present application are:

[0066] 1. First, the robot surface treatment impedance control model is established, and the influence of the impedance parameters on the system performance is analyzed; second, a compound force control algorithm is designed by combining the TD3 algorithm with the impedance control algorithm. The training speed of the model-free algorithm is improved by limiting the action space range, introducing OU exploration noise, and designing a reward function.

[0067] 2. The planar and curved workpieces are used as processing objects to complete the removal operation of the workpiece surface coating. Experimental results show that under the variable impedance control algorithm, the average errors of the planar and curved workpieces are 0.2658 N and 0.4352 N, respectively. After point cloud detection, the area of the planar workpiece tolerance is about 85.6%, and the area of the curved workpiece is about 67.08%, which can ensure the flatness of the workpiece surface to a certain extent. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 It is a Newton-Euler recursive principle diagram;

[0069] Figure 2 It is a position-based impedance control control rate model structure diagram in step 2C;

[0070] Figure 3 It is a contact state diagram of the end and the external environment;

[0071] Figure 4 It is an anti-parameter setting simulation model;

[0072] Figure 5 It is a structure framework diagram of the robot surface treatment contact force control model based on variable impedance;

[0073] Figure 6 It is a TD3-based variable impedance control simulation flowchart;

[0074] Figure 7 It is a planar workpiece surface treatment contact force curve diagram;

[0075] Figure 8 It is a planar workpiece experimental result diagram;

[0076] Figure 9 for planar workpiece detection cloud map;

[0077] Figure 10 for curved workpiece surface treatment contact force curve map;

[0078] Figure 11 for curved workpiece experimental results;

[0079] Figure 12 for planar workpiece detection cloud map;

[0080] Figure 13 for end effector structure diagram;

[0081] Figure 14 for the influence of inertia coefficient on system performance;

[0082] Figure 15 for the influence of damping coefficient on system performance;

[0083] Figure 16 for the influence of stiffness coefficient on system performance;

[0084] Figure 17 for robot end mechanism explosion diagram. DETAILED DESCRIPTION

[0085] The modeling method of the robot surface treatment contact force control model based on variable impedance will be described in more detail below in conjunction with the schematic drawings, which represent the preferred embodiments of the present application, it should be understood that those skilled in the art can modify the present application described herein while still achieving the advantageous effects of the present application. Therefore, the following description should be understood as extensive knowledge to those skilled in the art, and not as a limitation on the present application.

[0086] As Figures 1 to 13 , a modeling method of a robot surface treatment contact force control model based on variable impedance, comprising the following steps:

[0087] Step 1, according to Newton Euler method to establish the dynamics model of robot ideal state, design its control rate model of calculating torque:

[0088]

[0089] Where, q- joint variable; In turn, the first and second derivatives of q;

[0090] The joint is the five degrees of freedom joint of the robot (XYZAB axis), q = [d1 d2 d3 q4 q5], the first three joints are translational, and the last two are rotational, and the joint variable q is how much these joints move (translational travel, rotational angle).

[0091] τ - Z component of joint torque matrix;

[0092] are [5 x 1] matrices;

[0093] e = q d - joint variable error.

[0094] M(q) - inertia matrix, symmetric matrix; - centrifugal and Coriolis force coupling matrix; G(q) - gravity matrix;

[0095] K d ,K p - positive definite matrix;

[0096] - desired acceleration.

[0097] The control rate model modeling step includes:

[0098] Step 1A, introduce the robot dynamics model under ideal state (existing model):

[0099]

[0100] where the variable are [5 x 1] matrices, where q = [d1 d2 d3 q4 q5] is the joint variable, is its first and second derivative form; J(q) represents the end effector Jacobian matrix; F ext represents the external force applied by the end effector, which can be measured by the force sensor mounted at the end; M(q) represents the inertia matrix, which is a symmetric matrix; represents the centrifugal and Coriolis force coupling matrix; G(q) represents the gravity matrix; represents the friction force term.

[0101] Step 1B, considering that the above dynamics model is established under ideal conditions, there is still a big difference with the actual application. Therefore, in the selection of subsequent control algorithm, the position-based impedance control which has relatively loose requirements for the dynamics model is selected as the main control algorithm, and the position compensation is obtained according to the force difference. Among them, the position controller in Cartesian space is used to guide the robot motion. Therefore, on the basis of step 1A, the torque control scheme is derived and calculated as the position inner loop in the subsequent impedance control.

[0102] Ignoring joint friction force and external force disturbance, rewrite the robot dynamics model:

[0103]

[0104] Step 1C, During the position tracking process, the desired trajectory q d (t) is a continuous curve varying with time, which means q d (t) is twice differentiable. For time-varying trajectory, the joints need to have a faster movement speed, and independent PD control is easy to produce tracking error. For this purpose, a nonlinear compensation can be introduced in the control loop first, which simplifies the robot into an easily controlled linear constant system (prior art), after eliminating the nonlinear term, that is:

[0105]

[0106]

[0107] Step 1D, M(q) is positive definite, so the system in step 1C is equivalent to a decoupled linear constant system:

[0108]

[0109] Step 1E, Since the desired trajectory q d (t) is twice differentiable, the desired velocity and acceleration are known. In order to make the system stable, PD control with bias is introduced again, which constitutes the corrected acceleration with the desired joint angle acceleration:

[0110]

[0111] Step 1F, Bring the model in step 1E into step 1D:

[0112]

[0113] Step 1G, For the proof of stability, take Lyapunov function as:

[0114]

[0115] By K p positive definite, V is globally positive, then

[0116]

[0117] The system is globally asymptotically stable in , that is, from any initial condition , there is always

[0118] Finally, bring the model in step 1F into the model in step 1C, that is:

[0119]

[0120] Step 2, establishing a robot position-based impedance control strategy model, specifically comprising the following steps:

[0121] Step 2A, simplifying the position-based impedance model:

[0122]

[0123] ΔX=X c -X r ,ΔF=F n -F d ;

[0124]

[0125] Considering that the robot control system is discrete in the time domain, further integration after discretization can be obtained:

[0126]

[0127] Where M d ,B d ,K d respectively represent the corresponding inertia matrix, damping matrix and stiffness matrix in the impedance model;

[0128] X c -robot end position;

[0129] X r -desired position;

[0130] respectively correspond to the velocity and acceleration of X c ,X r ;

[0131] F d -desired force of the end with the external environment contact;

[0132] F n -actual contact force, which can be measured by a force sensor.

[0133] Step 2B, mapping the robot end position variable in Cartesian space to the joint space:

[0134]

[0135] Where X1, X2, X3 are the coordinates of the robot end position xyz in three directions, and q1, q2, q3, q4, q5 are the joint positions of the five degrees of freedom of the robot.

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] From the prior art: Jacobian matrix The robot Jacobian matrix describes the relationship between joint variables (independent variables) and end Cartesian space coordinates (dependent variables).

[0142] Step 2C, the impedance model in step 2A, the mapping model in step 2B, into the control rate model in step 1, get the robot based on position impedance control control rate model:

[0143]

[0144] Where, ΔX=X c -X r ,ΔF=F n -F d Respectively, the output, input.

[0145] Desired acceleration, set by man.

[0146] Step 3, let m d ,b d ,k d M d ,B d ,K d Impedance parameters affect the analysis of control performance to determine the output parameters in the variable impedance control algorithm based on TD3.

[0147] Impedance parameter value range:

[0148] m d = [20, 50, 100, 500, 1000];

[0149] b d = [3500, 5000, 10000, 15000, 20000];

[0150] k d = [50, 100, 500, 1000, 1500].

[0151] (1) the influence of inertia coefficient m d On the performance of the system:

[0152] The simulation effect is as follows: Figure 14, performance indicators are shown in Table 1. Combined with chart analysis, it can be seen that overshoot, regulation time and steady-state error all increase with m d , while when m d ≥ 500, the end appears to contact the workpiece and then separate. It can be seen that the greater m d , the greater the inertia of the robot, which mainly affects the overshoot and response time of the system.

[0153] Table 1 Influence of inertia coefficient on system performance indicators

[0154]

[0155] (2) The influence of damping coefficient b d on system performance:

[0156] The simulation results are shown in Figure 15 , and the performance indicators are shown in Table 2. Combined with chart analysis, it can be seen that the overshoot and regulation time decrease with the increase of b d , and the change trend of steady-state error is not obvious. It can be seen that the damping coefficient b d mainly affects the overshoot and regulation time of the system.

[0157] Table 2 Influence of damping coefficient on system performance indicators

[0158]

[0159] (3) The influence of stiffness coefficient k d on system performance:

[0160] The simulation results are shown in Figure 16 , and the performance indicators are shown in Table 3. Combined with chart analysis, it can be seen that the overshoot and steady-state error increase with the increase of k d , the overshoot decreases, and the steady-state error increases, and the change trend of regulation time is not obvious. It can be seen that the damping coefficient k d mainly affects the overshoot and steady-state error of the system.

[0161] Table 3 Influence of stiffness coefficient on system performance indicators

[0162]

[0163]

[0164] In summary, compared with the change of m d , the influence on the performance indicators of the system is weak, and at the same time, it is shown in some literature that m dis set to a certain constant value or an identity matrix. Therefore, in the subsequent variable impedance control algorithm design, in order to improve the stability of the system, m d is considered in a variable range, m d = 20. For the parameters b d ,k d , the value range is limited according to the simulation above, so as to improve the convergence speed of the reinforcement learning algorithm.

[0165] Step 4, according to the simulation results, let the impedance parameter m d = 20, and the output parameter in the variable impedance control algorithm of TD3 is determined as the impedance parameter b d ,k d .

[0166] Step 5, improve the TD3 algorithm, and the improvement includes: replacing the Gaussian noise with the OU noise, and establishing a stage reward function.

[0167] The reward function design is divided into two parts: distance reward and contact force difference reward, and the reward function is:

[0168]

[0169] The main goal is to control the contact force during the surface treatment process. If the conventional TD3 algorithm is directly used for position control of the robot, the displacement of each rod is learned by strategy, which is theoretically feasible, but there are still the following problems in the actual process:

[0170] (1) The utilization efficiency of the MFRL algorithm on the interaction data is poor. In the learning process through trial and error, part of the sampling results cannot effectively help the current strategy to improve, that is, pure trial and error learning, part of the interaction sampling of the agent is invalid sampling. At the same time, the cost of training the robot in the real environment to obtain interaction data is undoubtedly high.

[0171] (2) The early learning strategy belongs to the random exploration of the actor, and this unstable action selection may cause the joint action of the robot to exceed the limit, directly leading to the damage of the components. In addition, under the condition of unknown external environment stiffness, the method of directly outputting displacement in the action space also further increases the safety risk of the system.

[0172] (3) The reward function is a key indicator to guide the strategy learning, and a good reward function can accelerate the convergence process of the strategy to a certain extent and improve the learning efficiency. How to design a practical reward function in connection with the surface treatment process is also a problem to be solved.

[0173] On the basis of comprehensive consideration of the above problems, the traditional TD3 algorithm is combined with the position-based impedance control algorithm to design a composite force control algorithm. This algorithm no longer directly learns the strategy of the robot's end position or joint displacement, but uses the exploration characteristics of the reinforcement learning algorithm to dynamically adjust the impedance parameters, thereby indirectly achieving the purpose of force control. At the same time, in order to improve the efficiency of data utilization, the selection range of impedance parameters can be limited in combination with the above simulation experiments to ensure that each action selection of the actor is within the effective range of force control; for problem 2, the OU (Ornstein-Uhlenbeck) process noise can be selected to replace the original Gaussian process. Compared with Gaussian noise, OU noise is more effective and more suitable for real-world control tasks; for problem 3, a segmented reward function can be used to guide agent training.

[0174] Compared with Gaussian noise, OU noise is more suitable for inertial systems

[65] For robot force control, the robot itself has a large inertia, and the use of independent noise can cause a large difference between the previous and next steps, causing a sudden change in the robot's displacement or speed. The autocorrelation characteristics of OU noise can make the control signal continuous, although the adjustment period is longer, but it can ensure the safety of the robot.

[0175] As a function defined in the state space and action space, the reward function can give an actual reward value according to the current state and action of the robot to guide the subsequent behavior of the robot and achieve the desired control goal.

[0176] In a machining process, the motion state of the robot can be divided into two types, namely the free space state and the contact state. When in the free space state, it is necessary to ensure fast tracking of the desired trajectory; when in the contact state, it is necessary to ensure the tracking accuracy of the desired contact force. Therefore, it is more reasonable to design a phased reward function according to the actual situation to guide the behavior. The reward function design in this paper is divided into two parts: distance reward and contact force difference reward.

[0177] (1) Distance reward r d When there is no contact, r d guides the robot's end to move towards the desired position. At this time, the end is in the free space and there is no contact force feedback. The distance between the end and the environment can be used as an evaluation index:

[0178] r d =-c1*d(x t ,x d ) 2

[0179] where c1 is a weight index and is positive; d(xt x r represents the Euclidean distance between the actual position x t and the desired position x d .

[0180] (2) Contact force difference reward r f After contacting the external environment, the end effector changes from moving in free space to moving in a constrained space. Considering that the displacement space generated by fluctuations around the desired position at the current stage is small, a more intuitive contact force is selected as the evaluation index. At the same time, in order to improve the tracking accuracy and reduce fluctuations, a positive reward is given according to the distance from 0N when the contact force difference enters the range of 1N, guiding the robot to approach 0N as much as possible:

[0181]

[0182] In the formula, c2, c3, and c4 are weight indexes and are positive numbers; Δf = |f n -f d | represents the difference between the actual contact force and the desired force.

[0183] As Figure 17 shown in the simulation experiment, the end effector of the robot mainly uses a grinding disc, a chuck, and a motor as the driving device; the chuck is an elastic cylinder chuck; the motor clamp is a clamping device composed of a and b, and the inside is composed of two different radius circles to form a groove line to be buckled with the motor tail groove; the force sensor is a force feedback device, which is on the same central axis as the motor, ensuring that the normal contact force can be directly measured by a one-dimensional force sensor; the flange extension, flange connection, and connecting flange are main connection devices, which are fixed to the B shaft to increase the reachable range of the end effector.

[0184] As Figure 4 shown, the “forward kinematics module” converts the joint variables into the end position;

[0185] The “environmental impedance characteristic module” converts the end position into the actual contact force, and the specific principle is:

[0186] F n = K e (X c -X e );

[0187] K e is the equivalent stiffness of the external environment; X e is the position of the external environment.

[0188] As Figure 3As shown, from the beginning to the end of the operation, the contact state between the robot end and the external environment can be generally divided into three types: free state without contact in space, critical contact state with external environment, and stable contact state finally reached. When in the free state, as shown in Figure 3 (a), the external environment does not deform under force, at which time F n = 0, the impedance controller forces the end to move to the desired position; when the transition to the critical contact state, as shown in Figure 3 (b), the end just contacts the external environment, at which time F n = 0, if the desired force F r = 0, then from the formula , it can be known that ΔX = 0, i.e. X c = X e , the trajectory tracking control of the external environment will be achieved; if F r ≠ 0, the system will be converted from trajectory tracking to contact force control, thereby entering the stable contact state, as shown in Figure 3 (c), the external environment deforms to generate a reaction force, at which time ΔF ≠ 0, the impedance controller starts to calculate the position deviation ΔX according to the contact force deviation ΔF, thereby compensating the robot end position, so as to indirectly control the contact force.

[0189] The "impedance controller module" outputs the displacement correction amount;

[0190] The "inverse kinematics module" converts the end position into joint variables.

[0191] The "position controller module" combines the joint variables, the first derivative of the joint variables, generates the second derivative of the joint variables, and finally outputs the joint torque matrix.

[0192] From the prior art, it can be known that the joint torque is related to the first derivative of the joint variables and the second derivative of the joint variables.

[0193] The "robot module" converts the joint torque into joint variables and the first derivative of the joint variables, and re-enters the "position controller module", and finally outputs the joint variables corrected by the "position controller module".

[0194] As shown in Figure 5 , the "position control module" is equivalent to the "position controller module" + "robot module" in Figure 4 .

[0195] I. Planar workpiece experiment design and result analysis:

[0196] For Figure 7The actual contact force described by the blue curve fluctuates significantly overall, with the variable impedance fluctuating within the range of -8±2N. This is partly due to interference from the buzzing of the robot's linkage motor and the noise of the electric spindle, and partly due to the slight vibration of the electric spindle during the machining process. Figure 7 The paper also presents the force measured by the XY inspection platform during the surface treatment process. When the Z-axis normal contact force is constant, the XY axis force is generally close to a certain value because the electric spindle speed and robot feed speed are kept constant. However, due to factors such as electric spindle vibration, the specific value fluctuates around the fixed value.

[0197] for Figure 8 The comparison effect of point cloud of medium workpiece is as follows Figure 9 As shown in Table 1, the specific 3D comparison values ​​are as follows. According to the national standard GB / T11337-2004, the cloud map tolerance is set to ±0.1mm. Figure 9 It can be seen that the majority of the defective areas in both methods are located at the edges of the workpiece. Traditional impedance control primarily results in undercutting, accounting for approximately 13.59%, while variable impedance control primarily results in overcutting, accounting for approximately 12.63%. The acceptable areas (green areas) for both methods account for a significantly larger proportion, at 76.47% and 85.6%, respectively. Combining the above analysis with Table 1, it can be seen that both methods can ensure a certain degree of surface flatness during surface treatment, but comparatively, the variable impedance control method is more effective.

[0198] Table 1 Comparison of Point Cloud Values ​​(Thickness) for Planar Workpieces

[0199]

[0200] II. Experimental Design and Result Analysis of Curved Surface Workpieces:

[0201] Depend on Figure 10 As shown by the red curves, both methods perform worse than those using a planar workpiece in terms of overshoot and average error after stabilization. Specifically, the overshoot of traditional impedance control is approximately 5.7127 N, while that of variable impedance control is approximately 1.6221 N. After stabilization, the average error of traditional impedance control is approximately 1.315 N, while that of variable impedance control is approximately 0.4352 N, indicating that variable impedance control is more effective. The actual contact force (blue in the figure) is affected by the external environment and still fluctuates within a certain range.

[0202] For XY-axis force measurement, in the feed direction, i.e., the X-axis, the initial normal contact force F n The resultant force F along the X-axis m In the opposite direction, later F n With F m In the same direction, it presents a transition from pressure to tension, while the Y-axis is mainly affected by the rotation of the grinding head and the vibration of the motor, and the overall trend tends to a certain value.

[0203] for Figure 11 The comparison effect of point cloud of medium workpiece is as follows Figure 12 As shown in Table 2, the specific 3D comparison values ​​are set with a tolerance of ±0.1mm. According to the detection cloud map, the acceptable areas for the two methods are 49.14% and 67.08%, respectively, which are lower than those for planar methods. The unacceptable areas are mainly the workpiece edges and areas with significant curvature. Traditional impedance control primarily involves undercutting in the middle, accounting for approximately 33.03%, while variable impedance control primarily involves overcutting on the left and right edges, accounting for approximately 20.47%. Overall, the variable impedance control method has a larger acceptable area and better accuracy in controlling the normal contact force during processing.

[0204] Table 2 Comparison of 3D values ​​for curved surface workpieces

[0205]

[0206] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A modeling method of a variable impedance based robot surface treatment contact force control model, characterized by, Comprise the following steps: Step 1, according to Newton Euler method to establish the ideal state of the robot dynamics model, design its calculation torque control rate model: where q is the joint variable; the first and second derivatives of q in sequence; Torque matrix on the Z component of the joint; are both [5xl] matrices; M(q) - inertia matrix, symmetric matrix; - coupling matrix of centrifugal and Coriolis forces; G(q) - gravity matrix; K d ,K p - positive definite matrix; - desired acceleration; Step 2, the establishment of robot impedance control strategy model based on position, specifically including the following steps: Step 2A, simplify the impedance model based on position: ΔX = X c - X r , ΔF = F n - F d ; wherein M d , B d , K d respectively represent the corresponding inertia matrix, damping matrix and stiffness matrix in the impedance model; X c - robot end position; X r - desired position; corresponding to X c , X r velocity and acceleration; F d - desired force at the end to contact the outside environment; F n - actual contact force, as measured by the force sensor; Step 2B, the robot end position X in Cartesian space is mapped into joint space: c The variables are mapped into joint space: wherein L -1 (X) - inverse kinematics; J -1 inverse Jacobian matrix; Step 2C, the impedance model in step 2A, step 2B mapping model, into step 1 in the control rate model, get robot impedance control control rate model based on position: Step 3, let m d ,b d ,k d represent M d ,B d ,K d , the impedance parameter m d ,b d ,k d The impact analysis of the control performance determines the output parameters in the variable impedance control algorithm based on TD3; Step 4, according to the simulation results, let the impedance parameter m d = 20, the output parameter in the variable impedance control algorithm of TD3 is determined as the impedance parameter b d ,k d ; Step 5, improve TD3 algorithm, the improvement includes: the OU noise instead of Gaussian noise, the establishment of stage reward function.

2. The modeling method of claim 1, wherein, In step 2B, the solution process is as follows: Wherein, X1, X2, X3 in turn for the robot end position in x, y, z three direction coordinates; Q1, q2, q3, q4, q5 in turn for the robot five degrees of freedom corresponding to the joint position.

3. The modeling method of claim 1, wherein, Step 1 in the control rate model modeling steps include: Step 1A, the introduction of the ideal state of the robot dynamics model: Step IB, ignore joint friction and external force disturbances, rewrite the robot dynamics model: Step 1C, the robot is simplified as an easy to control linear system: Step 1D, step 1C in the system equivalent to a decoupled linear system: Step 1E, the introduction of the PD control with bias, and its with the expected joint angular acceleration constitutes the modified acceleration: Step 1F, step 1E in the model into step 1D: Step 1G, step 1F in the model into step 1C in the model.

4. The modeling method of claim 1, wherein, In step 3, the range of impedance parameters: m d ＝[20,50,100,500,1000]； b d ＝[3500,5000,10000,15000,20000]； k d ＝[50,100,500,1000,1500]。 5. The modeling method of claim 1, wherein, In step 5, the reward function design is divided into two parts: distance reward and contact force difference reward, the reward function is:

6. The modeling method of claim 1, wherein, The end effector of the robot comprises: Chuck and grinding disc, and the output shaft of the motor is connected in turn; The force sensor is a force feedback device for monitoring the actual contact force F n The sensing end penetrates through the motor clamp and contacts the motor shell, which is fixed to the connecting flange and is on the same central axis with the motor, thereby ensuring the normal contact force F n The one-dimensional force sensor can directly measure the force. The connecting flange is fixedly connected with the B shaft and connected with the flange extension.

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