A robot polishing method based on posture recognition and iterative learning

Abstract

The present invention relates to the field of intelligent mechanical equipment and is a robot polishing method based on posture recognition and iterative learning, which solves the problem of poor generalization ability of the robot arm in the prior art. The present invention teaches trajectory reconstruction; posture recognition; when the posture of the workpiece changes, the robot arm calls the changed trajectory information and performs processing according to the trajectory information; and iterative learning of contact force. The present invention binds the robot arm path with the end posture and the point cloud data of the workpiece, compares the point cloud information before and after the posture of the workpiece changes, obtains the posture change of the workpiece through point cloud registration, and calls the new trajectory information for processing; the force sensor at the end records the interactive force data, and iteratively updates the path according to the set iterative learning algorithm update rate, so that the interactive force reaches the expected value and completes the precise polishing task.

Description

Technical Field

[0001] The present invention relates to the field of intelligent mechanical equipment, and in particular to a robot polishing method based on posture recognition and iterative learning. Background Art

[0002] In recent years, with advances in electronic hardware, image processing, and artificial intelligence, robotics has been gradually applied to a variety of fields, including home services, medical rehabilitation, firefighting, and disaster reduction. The application scope of traditional robotic arms has also expanded significantly, encompassing more complex processing, production, and testing processes. Path planning is the core operation of robotic arm motion control, and different path planning problems require different solutions. In addition to traditional direct programming methods, current path planning solutions primarily include teach-through programming, vision guidance, and brain-computer interfaces. These solutions address diverse tasks and are suitable for unique working environments.

[0003] There are two main ways to use teaching programming in industrial robotic arms:

[0004] Online teaching: In this method, technicians guide and control the movement of the robot arm, record the program points during the operation, and insert the necessary robot arm commands to complete the program writing.

[0005] Offline teaching: The operator does not directly teach the operating robot arm, but programs in an offline programming system or simulation environment, generates a teaching program, and indirectly controls the robot arm's control cabinet through a PC.

[0006] The limitation of online teaching lies in the difficulty of achieving precise tracking of a specific task path due to the limitations of human vision and control capabilities. As the operator drags the robotic arm along the target path, any slight jitter can cause the robotic arm controller to record incorrect path points, affecting the end-arm's ability to track the target path. Furthermore, during the drag-based teaching process, it is impossible to ensure precise spacing between the end-arm and the target path. This is especially true for high-precision tasks such as welding and laser cutting, where simple online teaching cannot meet these requirements.

[0007] Offline teaching requires the operator to set parameters such as the robot's working path in advance, which has certain advantages when performing simple and repetitive tasks. However, in scenarios where the work objectives frequently change, offline teaching is relatively inefficient because the robot's control program needs to be constantly updated as the work objectives change.

[0008] However, the above teaching method is not applicable to complex situations. For example, after the posture of the same workpiece changes, the previously taught trajectory cannot be used directly and needs to be re-taught. This low-generalization algorithm is not suitable for changing task scenarios.

[0009] There is an urgent need for a new robotic arm control method that can solve the above problems. Summary of the Invention

[0010] The present invention proposes a robot polishing method based on posture recognition and iterative learning, which solves the problem of poor generalization ability of the robot arm in the prior art.

[0011] The technical solution of the present invention is achieved as follows: a robot polishing method based on posture recognition and iterative learning, comprising the following steps:

[0012] 1. Taught trajectory reconstruction: The human partner teaches the polishing path for the current workpiece multiple times. The taught trajectory is reconstructed using dynamic time warping and a Gaussian mixture model. The depth camera mounted on the end of the robot's mechanical arm captures the workpiece's point cloud data and sends it to the information processing module of the microprocessor to generate machining trajectory information. The trajectory information and point cloud data are stored in the storage module.

[0013] 2. Posture recognition: The point cloud data of the workpiece is captured by the depth camera and sent to the microprocessor, which is then saved in the storage module. The information processing module then performs point cloud registration to determine whether the workpiece has undergone posture changes and saves the trajectory information generated after the posture change.

[0014] 3. When the workpiece posture does not change, the robot's mechanical arm calls the trajectory information of the storage module and performs processing according to the trajectory information;

[0015] 4. When the posture of the workpiece changes, the robot's mechanical arm calls the trajectory information after the posture change in step 2 and performs processing according to the trajectory information;

[0016] 5. Iterative learning of contact force: The force sensor installed at the end of the robot arm sends the contact force information during the processing process to the information processing module; the information processing module iteratively updates the processing path according to the set iterative learning update rate and sends it to the end of the robot arm, and the cycle continues until the contact force meets the expected contact force.

[0017] The iterative learning update rate is designed as follows:

[0018]

[0019] The initial trajectory X r,0 =W′, the transformed trajectory is the initial value; i represents the number of iterations, L represents the iteration update rate, η i is the variable weight factor, F d represents the desired contact force, F e,i represents the real interaction force between the end of the manipulator and the workpiece at the i-th iteration, K erepresents the environmental stiffness, which can be calculated by Hooke's law in two iterations.

[0020] The step 2 is specifically as follows:

[0021] First, calibrate the depth camera to obtain its internal parameters and perform hand-eye calibration on the camera and robotic arm to obtain the transformation relationship between the robotic arm and the camera. Obtain two sets of point cloud data: point cloud data before and after posture transformation. Define a target optimization function as follows:

[0022]

[0023] where p s and p t Respectively represent the point cloud before and after posture transformation, R and t are the required rotation matrix R and translation matrix t between two point cloud lines, N is the total number of point clouds, and F(t) is the target optimization function;

[0024] Using the above two matrices, the trajectory W′=RW+t under the current posture is calculated, where W is the taught trajectory in step 1. After obtaining the trajectory, the information is sent to the robotic arm side through the software.

[0025] The dynamic model of the closed-loop system of the manipulator controller in the spatial domain is:

[0026]

[0027] Among them, M d 、C d , K d are the desired moment of inertia, damping matrix and stiffness matrix respectively; is the speed of the robot arm in the direction of movement; represents the spatial differential operator; E(s) is the tracking error vector; F h (s) is the interaction force.

[0028] The robotic arm is provided with a damping controller:

[0029]

[0030] where X r is the reference path of the robot, F d is the desired contact force, K is the equivalent stiffness parameter;

[0031] According to the robot-environment contact force model, considering the i-th iteration of path update, we have:

[0032] F e,i′ =K e (X i′ -X0)

[0033] Among them F e,i′ is the contact force, X i′ is the position of the end effector, K e and X0 are the stiffness and surface position of the environment respectively; considering two consecutive iterations, the stiffness of the environment is obtained:

[0034]

[0035] The DTW-ILC method is used to design the reference path update rule:

[0036]

[0037] The initial reference path is set to X r,0 =X r,p ,z is the unit matrix representing the path update direction, K e is the estimated equivalent stiffness, is the contact force; Q represents a discrete-time low-pass filter.

[0038] The expression of the Gaussian mixture model to reconstruct the teaching trajectory is:

[0039]

[0040] Where N(ξ j |u k ,∑k) is the probability function of the Gaussian mixture model, {α k ,∑k} are Gaussian mixture model parameters.

[0041] The present invention discloses a robot polishing method based on posture recognition and iterative learning. The method obtains the initial path and end posture of the workpiece to be polished based on teaching programming, uses a depth camera to obtain the point cloud data of the workpiece, and binds the robot arm path, end posture and workpiece point cloud data together; after the workpiece posture changes, the depth camera is used to obtain the point cloud information of the changed workpiece, and the posture change of the workpiece is obtained through point cloud registration; after obtaining the posture change, the previous teaching trajectory is called for polishing, and the force sensor at the end records the interaction force data. The path is iteratively updated according to the set iterative learning algorithm update rate, so that the interaction force reaches the expected value and the precise polishing task is completed. This method avoids the problem that the previous trajectory skill information cannot be reused due to changes in the workpiece posture, and introduces iterative learning in the polishing task, thereby enhancing the control of the contact force and improving the accuracy of polishing. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0043] Figure 1 : System module composition diagram;

[0044] Figure 2 : Control algorithm system flow chart;

[0045] Figure 3 : The teaching process uses dynamic time warping and Gaussian mixture model to reconstruct the before and after comparison images;

[0046] Figure 4 : Comparison of posture recognition and generalized trajectory information;

[0047] Figure 5 : Force tracking performance of the robot during iteration;

[0048] Figure 6 : Control framework of position-based impedance control method. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0050] The present invention discloses a robot polishing method based on posture recognition and iterative learning, comprising the following steps:

[0051] 1. Taught Trajectory Reconstruction: The human partner teaches the polishing path for the current workpiece multiple times. The taught trajectory is reconstructed through dynamic time warping and Gaussian mixture model to reduce the instability of the human partner's teaching. The depth camera mounted on the end of the robot's mechanical arm captures the point cloud data of the workpiece and sends it to the information processing module of the microprocessor to generate processing trajectory information. The trajectory information and point cloud data are stored in the storage module.

[0052] 2. Posture recognition: The point cloud data of the workpiece is captured by the depth camera and sent to the microprocessor, which is then saved in the storage module. The information processing module then performs point cloud registration to determine whether the workpiece has undergone posture changes and saves the trajectory information generated after the posture change.

[0053] 3. When the workpiece posture does not change, the robot's mechanical arm calls the trajectory information of the storage module and performs processing according to the trajectory information;

[0054] 4. When the workpiece posture changes, the previously taught trajectory will not be applicable to the new posture. The robot's mechanical arm calls the trajectory information after the posture change in step 2 and performs processing according to the trajectory information;

[0055] 5. Iterative Learning of Contact Force: The force sensor at the end of the robotic arm sends contact force information during machining to the information processing module. The information processing module iteratively updates the machining path at the set iterative learning update rate and sends it to the robotic arm, repeating the cycle until the contact force meets the expected contact force. Due to the instability of human partner teaching and errors in posture recognition, the interaction force between the robotic arm end and the workpiece during actual machining is not necessarily the expected contact force. Accurate contact force is a prerequisite for ensuring the polishing effect.

[0056] The iterative learning update rate is designed as follows:

[0057]

[0058] The initial trajectory X r,0 =W′, the transformed trajectory is the initial value; i represents the number of iterations, L represents the iteration update rate, η i is the variable weight factor, F d represents the desired contact force, F e,i represents the real interaction force between the end of the manipulator and the workpiece at the i-th iteration, K e represents the environmental stiffness, which can be calculated by Hu Ke's law during the two iterations; according to the above iterative update rate design, the trajectory X that meets the expected interaction force is obtained r,i+1 .

[0059] The step 2 is specifically as follows:

[0060] First, calibrate the depth camera to obtain its internal parameters and perform hand-eye calibration on the camera and robotic arm to obtain the transformation relationship between the robotic arm and the camera. Obtain two sets of point cloud data: point cloud data before and after posture transformation. Define a target optimization function as follows:

[0061]

[0062] where p s and p tThey represent the point cloud before and after posture transformation, R and t are the rotation matrix R and translation matrix t required between the two point cloud lines, N is the total number of point clouds, and F(t) is the target optimization function. Ideally, when F(t) = 0, the ideal rotation matrix and translation matrix are found. In practical applications, when F(t) is the global minimum, the optimal rotation matrix R and translation matrix t can be obtained.

[0063] Using the above two matrices, the trajectory W′=RW+t under the current posture is calculated, where W is the taught trajectory in step 1. After obtaining the trajectory, the information is sent to the robotic arm side through the software.

[0064] The dynamic model of the closed-loop system of the manipulator controller in the spatial domain is:

[0065]

[0066] Among them, M d 、C d , K d are the desired moment of inertia, damping matrix and stiffness matrix respectively; is the speed of the robot arm in the direction of movement; represents the spatial differential operator; E(s) is the tracking error vector; F h (s) is the interaction force.

[0067] The robotic arm is provided with a damping controller:

[0068]

[0069] where X r is the reference path of the robot, D d is the desired contact force, K is the equivalent stiffness parameter;

[0070] According to the robot-environment contact force model, considering the i-th iteration of path update, we have:

[0071] F e,i′ =K e (X i′ -X0)

[0072] Among them F e,i′ is the contact force, X i′ is the position of the end effector, K e and X0 are the stiffness and surface position of the environment respectively; considering two consecutive iterations, the stiffness of the environment is obtained:

[0073]

[0074] In order to improve the contact force tracking performance, the DTW-ILC method is used to design the reference path update rule by combining the impedance control model and the environmental stiffness estimation:

[0075]

[0076] The initial reference path is set to X r,0 =X r,p ,z is the unit matrix representing the path update direction, K e is the estimated equivalent stiffness, is the contact force; Q represents a discrete-time low-pass filter. The proposed path learning method and GMM / GMR approach can learn the operator's desired robot path and posture. Therefore, using the designed ILC update law, the reference path is updated only in the axial direction of the robot end-effector, thereby compensating for force tracking errors.

[0077] The expression of the Gaussian mixture model to reconstruct the teaching trajectory is:

[0078]

[0079] Where N(ξ j |u k ,∑k) is the probability function of the Gaussian mixture model, {α k ,∑k} are Gaussian mixture model parameters.

[0080] The robot arm used in the experiment is a Sawyer 7-axis collaborative robot arm, the depth camera is an interrealsense D435i camera, and the force sensor is a Robotiq FT300.

[0081] The human partner teaches the polishing path of the current workpiece multiple times. The software algorithm reconstructs the teaching trajectory through dynamic time warping and Gaussian mixture model to reduce the instability of the human partner's teaching. The depth camera mounted on the end of the robotic arm captures the point cloud data of the workpiece and sends it to the information processing module of the microprocessor to generate processing trajectory information, and stores the trajectory information and the point cloud data in the storage module; when the posture of the workpiece changes, the depth camera at the end of the robotic arm obtains the point cloud data of the workpiece in the current posture and sends it to the information processing module of the microprocessor to generate processing trajectory information, and stores the trajectory information and the point cloud data in the storage module; the optimal rotation matrix R and translation matrix t are obtained through point cloud registration, and the trajectory W′=R□+t in the current posture is calculated through the above two matrices, where W is the teaching trajectory in step one. After obtaining the trajectory, the information is sent to the robotic arm side through the software; after obtaining the trajectory information, the robotic arm side processes according to the trajectory information, and the force sensor at the end records the contact force information during the processing process and sends it to the information processing module of the microprocessor. The machining path is iteratively updated according to the set iterative learning update rate and sent to the robot arm end, and the cycle is repeated until the contact force meets the expected contact force.

[0082] In step 1, the initial workpiece machining path is obtained through multiple teachings by the human partner. First, the human partner drags the end of the robotic arm to teach the desired machining path three times. The robotic arm records the taught trajectory and sends it to the information processing module of the microprocessor. The information processing module first aligns the experimental data of different experimental lengths using dynamic time warping. After the data is aligned, a Gaussian mixture model is used to reconstruct the three teaching data to reduce the instability of the human partner's teaching. The following expression is the Gaussian mixture model to reconstruct the taught trajectory:

[0083]

[0084] Where N(ξ j |u k ,∑k) is the probability function of the Gaussian mixture model, {α k ,∑k} is the Gaussian mixture model parameter. Step 2 of the present invention is posture recognition and processing trajectory mapping based on point cloud data matching. After obtaining two sets of point cloud data ① and ②, first define a target optimization function as follows:

[0085]

[0086] where p s and p t Denote point clouds ① and ② respectively, R and t are the rotation matrix and translation matrix required between the two point clouds, N is the total number of point clouds, and F(t) is the target optimization function. Represent the centroids of the original point cloud ① and the target point cloud ② respectively, and let Perform SVD decomposition on this 3×3 matrix to obtain H=U∑V T , then the optimal rotation matrix is ​​R = VU T , the optimal translation matrix is At this point, the optimal rotation matrix R and translation matrix t are obtained, and the new trajectory of the mapping is: W′=RW+t, where W is the teaching trajectory in step 1.

[0087] Contact force adjustment, first of all, the underlying control of the present invention involves specifically:

[0088] First, we introduce the dynamic model of the system. The dynamic model of the robotic arm in Cartesian space is as follows:

[0089]

[0090] in X(t) represents the acceleration, velocity and position of the end effector respectively; C x and G x Represent the Coriolis force matrix coefficient and gravity term respectively; u(t) represents the joint torque of the manipulator, j represents the mapping relationship between the terminal velocity, angular velocity and joint angular velocity, that is, the Jacobian matrix; F h (t) represents the external force applied by the human partner and can be measured by a force sensor.

[0091] Let E = x(t) - x r (t), represents the expected trajectory x r The error between (t) and the true trajectory x(t) is Represent the velocity and acceleration errors respectively. Combined with the dynamic model in Cartesian space, we can get:

[0092]

[0093] In the above formula, H e =H x , C e =C x , F(t)=J -T u(t).

[0094] The controller of the robotic arm is as follows:

[0095]

[0096] Where M d 、C d , K d are the desired inertia matrix, damping matrix and stiffness matrix respectively.

[0097] Then we can get the expression of the closed-loop dynamic system in the time domain:

[0098]

[0099] So far, we have obtained the closed-loop system's interaction force F h The expressions of the tracking error E(t) and its derivatives in the time domain are given below. The specific control method will be given in combination with the actual operation environment of the robot arm.

[0100] The impedance control model, a common impedance model in robotic arm control, was proposed by Hogan. It approximately simulates the process of the robot's contact with the outside world into a second-order system of mass-spring-damper. In order to achieve ideal control performance, the stiffness information of the environment and the surface position information of the environment in the robot's base coordinate system need to be pre-specified before the actual operation of the robot. Then, the dynamic characteristics of the robot's contact with the environment can be adjusted by adjusting the inertia, damping and stiffness parameters in the impedance model, thereby indirectly achieving control of the contact force.

[0101] like Figure 1 As shown, the entire system module composition of the present invention is specifically described. It mainly includes a visual system, namely a depth camera, a robotic arm workbench, a control algorithm system and a robotic arm body. The visual system is specifically a depth camera; the robotic arm workbench is specifically a human-computer interaction interface, a microprocessor or a server computer; the control algorithm system includes a coordinate generalization module, a motor control module, and an inverse kinematics module, that is, the dynamic model of the closed-loop system of the robotic arm controller in the spatial domain; the relationship between the four parts is explained in detail. The visual system is responsible for collecting point cloud data, the control algorithm system is responsible for processing point cloud information and controlling the movement of the robotic arm, the robotic arm workbench is responsible for displaying point cloud data and human-computer interaction, and the robotic arm body is responsible for polishing the workpiece.

[0102] like Figure 2 As shown in the figure, the specific process of the control algorithm system is described in detail, which is divided into two parts. The first part is responsible for teaching, GMM / GMR teaching trajectory reconstruction and initial point cloud acquisition. The second part is to calculate the initial path using point cloud information after the workpiece posture is transformed, and use iterative learning to calculate the final path, combined with the inverse kinematics of the robot arm and motor control to achieve the final grinding / polishing task.

[0103] like Figure 3 The comparison figure before and after the teaching process using dynamic time warping and Gaussian mixture model reconstruction is shown. The red curve represents the experimental result of the teaching process using GMM / GMR reconstruction, and the other three curves represent the three-dimensional teaching trajectory curves. As can be seen from these two figures, after GMM / GMR reconstruction, the trajectory data is more stable and smooth, and the robot arm can better represent the teaching intention when executing.

[0104] like Figure 4As shown in the comparison chart between posture recognition and generalized trajectory information, the black curve represents the machining trajectory before the workpiece posture change and the teaching trajectory of step one. The red curve represents the generalized trajectory after posture recognition and the result of step two. The blue curve represents the expected result after posture change. The error between the two is within 5 mm, which meets the polishing machining accuracy.

[0105] The polishing experiment was carried out under the same experimental conditions using the method proposed in the present invention. The force tracking performance of the robot at the 0th, 2nd, 4th and 7th iterations was as follows: Figure 3 As shown in the figure, despite the use of different polishing feed speeds (variable robot operating speed), the robot can effectively track the required force as the iterations proceed using the proposed force tracking method, where the mean and standard deviation of the force tracking error are reduced to 0.18N and 0.12N, respectively, at the 7th iteration, meeting the required polishing force tracking requirements.

[0106] The present invention discloses a robot polishing method based on posture recognition and iterative learning. The method obtains the initial path and end posture of the workpiece to be polished based on teaching programming, uses a depth camera to obtain the point cloud data of the workpiece, and binds the robot arm path, end posture and workpiece point cloud data together; after the workpiece posture changes, the depth camera is used to obtain the point cloud information of the changed workpiece, and the posture change of the workpiece is obtained through point cloud registration; after obtaining the posture change, the previous teaching trajectory is called for polishing, and the force sensor at the end records the interaction force data. The path is iteratively updated according to the set iterative learning algorithm update rate, so that the interaction force reaches the expected value and the precise polishing task is completed. This method avoids the problem that the previous trajectory skill information cannot be reused due to changes in the workpiece posture, and introduces iterative learning in the polishing task, thereby enhancing the control of the contact force and improving the accuracy of polishing.

[0107] Of course, without departing from the spirit and essence of the present invention, technicians familiar with the field should be able to make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A robot polishing method based on posture recognition and iterative learning, characterized by: The following steps are involved:

1. Taught trajectory reconstruction: The human partner teaches the polishing path for the current workpiece multiple times. The taught trajectory is reconstructed using dynamic time warping and a Gaussian mixture model. The depth camera mounted on the end of the robot's mechanical arm captures the workpiece's point cloud data and sends it to the information processing module of the microprocessor to generate machining trajectory information. The trajectory information and point cloud data are stored in the storage module.

2. Posture recognition: The point cloud data of the workpiece is captured by a depth camera and sent to the microprocessor, which is then stored in the storage module for storage. The information processing module then performs point cloud registration to determine whether the workpiece has undergone posture changes and saves the trajectory information generated after the posture changes. This process includes the following steps: First, calibrate the depth camera to obtain its internal parameters and perform hand-eye calibration on the camera and robotic arm to obtain the transformation relationship between the robotic arm and the camera. Obtain two sets of point cloud data: point cloud data before and after posture transformation. Define a target optimization function as follows: ； in and Respectively represent the point cloud before and after posture transformation, and is the rotation matrix required between two point cloud verses and translation matrices , is the total number of point clouds, Optimize the function for the target; Through the above two matrices, calculate the trajectory under the current posture ,in This is the teaching trajectory in step 1. After obtaining the trajectory, the information is sent to the robotic arm side through the software; 3. When the workpiece posture does not change, the robot's mechanical arm calls the trajectory information of the storage module and performs processing according to the trajectory information; 4. When the workpiece posture changes, the previously taught trajectory will not be applicable to the new posture. The robot's mechanical arm calls the trajectory information after the posture change in step 2 and performs processing according to the trajectory information; 5. Iterative learning of contact force: The force sensor installed at the end of the robot arm sends the contact force information during the processing process to the information processing module; the information processing module iteratively updates the processing path according to the set iterative learning update rate and sends it to the end of the robot arm, and the cycle continues until the contact force meets the expected contact force.

2. The robot polishing method based on posture recognition and iterative learning according to claim 1, characterized in that: The iterative learning update rate is designed as follows: The initial trajectory , the transformed trajectory is taken as the initial value; represents the number of iterations, represents the iterative update rate, is the variable weight factor, represents the desired contact force, Indicates the The real interaction force between the end of the robot arm and the workpiece, represents the environmental stiffness, which can be calculated by Hooke's law in two iterations.

3. The robot polishing method based on posture recognition and iterative learning according to claim 2, characterized in that: include: Vision system: responsible for collecting point cloud data; Control algorithm system: responsible for processing point cloud information and controlling the movement of the robotic arm; Robotic arm workbench: responsible for displaying point cloud data and human-computer interaction; Robotic arm body: responsible for grinding the workpiece; The control algorithm system includes a coordinate generalization module, a motor control module, and an inverse kinematics module, i.e., a dynamic model of the closed-loop system of the manipulator controller in the spatial domain: in 、 、 are the desired moment of inertia, damping matrix and stiffness matrix respectively; is the speed of the robot arm in the direction of movement; represents the spatial differential operator; is the tracking error vector; For interactive force.

4. The robot polishing method based on posture recognition and iterative learning according to claim 3, characterized in that: The robotic arm is provided with a damping controller: in is the reference path of the robot, is the desired contact force, is the equivalent stiffness parameter; According to the robot-environment contact force model, the path update is considered iterations, there are: in is the contact force, is the position of the end effector, and are the stiffness of the environment and the surface position respectively; considering two adjacent iterations, the stiffness of the environment is obtained: The DTW-ILC method is used to design the reference path update rule: The initial reference path is set to , is the identity matrix representing the path update direction, is the estimated equivalent stiffness, is the contact force; represents a discrete-time low-pass filter.

5. The robot polishing method based on posture recognition and iterative learning according to claim 4, characterized in that: The expression of the Gaussian mixture model to reconstruct the teaching trajectory is: in is the probability function of the Gaussian mixture model, are the Gaussian mixture model parameters.

Images