A joint reinforcement contour control method of a robot milling system

Abstract

The application discloses a kind of joint reinforcement profile control methods of robot milling processing system, comprising: building robot milling edge processing system;Establish the profile error solving strategy based on switching geometry method and projection factor to obtain the profile error compensation target point and profile error of mechanical arm movement process;Establish double-layer cascaded profile error control strategy of inner loop and outer loop, flexible joint mechanical arm system is decomposed into fast subsystem and slow subsystem, and mechanical arm dynamics system parameters are predicted, inner loop based on fast subsystem and slow subsystem control law ensures the tracking accuracy of flexible joint mechanical arm in joint space, outer loop corrects profile error, ensures the profile motion accuracy of mechanical arm cartesian space;Using profile error solving strategy and inner loop and outer loop double-layer cascaded profile error control strategy to the robot milling edge processing system is carried out double-loop cascaded profile control.The application improves dynamic tracking accuracy, effectively improves the profile accuracy of mechanical arm movement process.

Description

Technical Field

[0001] This invention belongs to the field of industrial robotic arm processing system construction and precision control technology, specifically relating to a joint enhancement contour control method for a robot milling processing system. Background Technology

[0002] In recent years, CFRP has been widely used in aerospace components, with milling being an essential process for these parts. With the development of robotics technology, mobile robotic arm systems, with their advantages of large workspace and high flexibility, are widely used in operations such as drilling, grinding, and assembly of large structural components. Compared to bulky and expensive CNC systems, mobile robotic arm systems offer significant advantages in terms of construction cost and workspace for milling large components.

[0003] However, due to the influence of multiple sources of error, such as mechanical tolerances and joint flexibility, on the positioning accuracy of industrial robots, the absolute positioning accuracy of robots is only 2-3 mm. In edge milling, the robot's running accuracy directly affects the geometric contour accuracy of the milled product. Simply improving the robot's joint tracking performance cannot guarantee contour accuracy; therefore, it is necessary to study direct contour error estimation methods and contour error control methods. Furthermore, oscillations and accuracy loss caused by joint flexibility due to the robot's joint transmission components result in robot motion accuracy failing to meet requirements. Therefore, a contour control method for robot edge milling systems is urgently needed.

[0004] Patent publication CN 201910314401.7 discloses a decoupled contour error control method for five-axis CNC machine tools. This method decomposes the contour error into a contour error vector and a tangential tracking error vector, and then generates separate normal and tangential contour error controllers for each drive axis to obtain a total control signal that controls each drive axis. However, this method does not consider the impact of single-axis tracking performance on the tracking of normal and tangential contour errors, which is crucial for ensuring contour tracking performance.

[0005] Patent CN 201910856025.4 discloses a contour error controller and control method for a multi-axis motion system. For a multi-axis linkage control system driven by a three-axis permanent magnet linear synchronous motor servo, a contour error control algorithm based on extended state disturbance observation is proposed, effectively reducing tracking error and contour error. However, this method mainly targets a three-axis system, specifically one axis driving the motion direction. Compared to a serial robotic arm system where the end-effector accuracy is affected by multi-axis coupling, controlling the end-effector contour accuracy is more complex.

[0006] Patent CN 202210076416.6 discloses a method for controlling the path contour error of a robot's end effector. This method targets a two-degree-of-freedom system within the robot's end effector mechanism. It obtains a first trajectory as the starting signal by superimposing a preset trajectory with a preset following error trajectory. However, this method targets the end effector mechanism, not the robot's end effector contour motion.

[0007] The above patents only discuss the design of controllers and control methods, without addressing the actual processing system structure and the hardware system construction of closed-loop feedback systems. They are not compatible with the application of robotic arm systems in processing scenarios, and they do not combine the tracking errors of each axis of the system with the contour errors, which will lead to insufficient dynamic tracking performance of the system. There is little research on contour error solving and contour error control for six-axis serial robotic arms. Compared with the single axis of a machine tool system corresponding to a single direction in Cartesian space, the above methods are not entirely applicable to robot systems.

[0008] The paper "A novel hybrid contouring control method for 3-DOF roboticmanipulators, 2016, (40): 178-193" proposes a hybrid contouring controller for a three-axis robotic arm system, comprising independent joint controllers and a Cartesian space synovial controller to enhance the system's dynamic tracking performance. However, this method does not consider the joint flexibility caused by the joint transmission mechanism of the robot under heavy load, and only uses a motor encoder as the joint feedback, which leads to inaccurate end-effector position estimation, requiring the addition of an additional end-effector position sensing and measurement system. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a joint enhancement contour control method for a robotic milling system. By combining grating compensation for joint flexibility, a two-layer cascaded contour control strategy of joint space and Cartesian space is established, which improves dynamic tracking accuracy and effectively enhances the contour accuracy of the robotic arm movement process.

[0010] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows: A joint enhancement contour control method for a robotic milling system, the control method comprising: S1, Build a robotic milling system including flexible process equipment for vacuum adsorption and clamping of large-sized components, modular and quick-change milling end effectors, and flexible joint robotic arms equipped with grating feedback; S2, Establish a contour error solution strategy based on switching geometry method and projection factor to obtain the contour error compensation target point and contour error of the robotic arm motion process; S3. A two-layer cascaded contour error control strategy with inner and outer loops is established. This strategy decomposes the flexible joint manipulator system into fast and slow subsystems through singular perturbation theory, and uses RBF neural network to predict the parameters of the manipulator dynamic system as feedforward terms for the control of the slow subsystem. The inner loop is a flexible joint tracking controller based on the control laws of the fast and slow subsystems to ensure the tracking accuracy of the flexible joint manipulator in the joint space. The outer loop is a Cartesian space contour error controller to correct the contour error and obtain the corrected contour compensation point to ensure the contour motion accuracy of the manipulator in the Cartesian space. S4. A contour error solving strategy and a dual-loop cascaded contour error control strategy (inner and outer loops) are adopted to perform dual-loop cascaded contour control on the robot milling system.

[0011] To optimize the above technical solution, the specific measures also include: The flexible process equipment described in S1 above includes 20 liftable pogo columns, forming the z-axis of the flexible tooling; every 4 pogo columns are mounted on a crossbeam and can move on the crossbeam guide rail, forming the x-axis movement of the flexible tooling; the crossbeam is mounted on a longitudinal guide rail, forming the y-axis of the flexible tooling; the flexible tooling can adaptively adjust its state according to the shape of the product to be processed, and use vacuum adsorption to ensure stable clamping of the product.

[0012] The modular end effector described in S1 above is divided into a fixed end and a quick-change end. The fixed end is installed on the end flange of the robotic arm and connects to the circuit and air circuit from the bottom of the robotic arm. The quick-change end is the actual machining end, equipped with a spindle and a milling cutter, and has air cooling and dust extraction functions. The fixed end and the quick-change end are connected by a quick-change connector, and the air circuit and circuit are conducted through the quick-change connector to ensure that the quick-change end can be removed as a whole without rewiring.

[0013] The flexible joint robotic arm described in S1 above is located on the AGV. Angle feedback grating rulers are installed at each joint of the robotic arm. The grating measurement system uses a laser tracker measurement system to calibrate the grating readings and joint angles, and provides real-time feedback on nonlinear errors caused by joint flexibility during the movement and processing of the robotic arm.

[0014] The control system of the robotic arm described in S1 above is based on a PC real-time controller, EtherCAT communication, and an industrial PLC to realize closed-loop feedback control of the robotic arm. The control system includes a host computer, a slave computer, and an execution end. The host computer is used to parse the NC code of the robotic arm motion, the slave computer is used as the main controller for trajectory planning, trajectory interpolation, and kinematic calculation, and the execution end consists of the robotic arm drive motor and the grating measurement system. The grating ruler connects the signal to the control system through an EK1100 coupler and an EL5042 terminal.

[0015] The contour error solution strategy based on the switching geometry method and projection factor described in S2 above is as follows: (1) Based on the switching geometry method, the motion path of the robotic arm is discretized into a continuous trajectory of straight lines and circular arcs; (2) Calculate the projection factor and determine the specific location of the contour point on the straight line segment or arc segment based on the projection factor, and use it as the target point for contour error compensation. The formula for calculating the projection factor is: ; in, To indicate the actual point, This represents the projection factor of the actual point on the current interpolated line segment. This represents the starting point of the i-th line segment. This represents the end point of the i-th line segment; According to the projection factor Determining the location of the contour points includes: Case 1, if Then, the contour point. Located on the current straight segment; Case 2, if ,when , If the projection factor of the actual point in the next interpolation segment is given, then the contour point lies in the next line segment. The contour point is located on the current arc segment, when Then, the projected shadow is further solved until... or This determines the location of the contour points; Case 3, if ,when , If the projection factor of the actual point on the previous interpolation segment is given, then the contour point lies on the previous straight line segment. Then the contour point is located on the previous arc segment, when Then, the projected shadow is further solved until... or Determine the location of the contour points; (3) Calculate the contour error based on the location of the contour points: If the contour point is located on a straight line segment, then the contour error is: ; If the contour point is located on an arc segment, then the contour error is: ; in, and These represent the tracking errors along the n-axis and t-axis in the local coordinate system, respectively. Let be the angle between the direction of the tangent to the motion and the t-axis. The radius of the arc is denoted as .

[0016] The above-described S3 uses singular perturbation theory to decompose the flexible joint robotic arm system into fast and slow subsystems, including: The flexible joint robotic arm system is defined as: (1) ; In the formula, These represent the actual angular position, velocity, and acceleration on the connecting rod side, respectively. The actual rotational angle position, velocity, and acceleration on the motor side are respectively recorded. It is the inertia matrix of the robotic arm. It is the matrix of Coriolis force and centripetal force. Let represent the gravity term matrix, K be the equivalent stiffness coefficient matrix of the flexible joint, and J be the diagonal positive definite matrix of the drive motor at the joint. This refers to the output torque of the drive motor at the joint. make , , , The state-space expression of the flexible joint robotic arm system is: ; The flexible joint robotic arm system is decomposed based on singular perturbation theory: perturbation parameters are defined. ,make To obtain the standard form of the singular perturbation model: ; ; when At that time, control torque Becoming a slow subsystem control law ,and The slow subsystem is obtained as follows: ; In the formula, , where is the coupling inertia matrix between the robotic arm and the motor; Fast time scale , For slow-scale time, Assuming the variable is fast, we obtain the fast subsystem of the robotic arm: ; The method of using RBF neural networks to predict the parameters of the robotic arm's dynamic system is as follows: ; , , For RBF neural network pairs , , Parameter estimation.

[0017] The control law for the slow subsystem described in S3 above is: ; in , and They are respectively , and The estimated matrix, For the link position tracking error, then: ; ; It is a positive definite matrix and , , , express Reference position, This indicates the deviation between the reference position and the actual position on the connecting rod side. This indicates the deviation between the reference speed and the actual speed on the connecting rod side; The control law for the fast subsystem is: ; in, It is a diagonal positive definite matrix; and Using the velocity observer estimation and : ; ; in , For the observer state, , , and All are observer gains, which are positive constants.

[0018] The Cartesian space contour error controller described in S3 above includes a real-time contour error estimator and a PD controller; The real-time contour error estimator obtains the contour error compensation target point and contour error during the robotic arm's motion process based on the contour error solving strategy. The PD controller is based on the contour error compensation target point. Contour error can be solved The movement of the robotic arm is broken down into four motion stages. Basic parameters, To determine the acceleration during the acceleration and deceleration phases, different PD parameters are used for different phases, as detailed below: ; The discrete-time control rate of the contour error is: ; For the operating cycle, For proportional parameters, The differential parameters are used to obtain the corrected contour compensation points. , This indicates a theoretical stance.

[0019] The present invention has the following beneficial effects: (1) This invention constructs a large-size component milling system consisting of flexible process equipment, modular end effector and mobile high-precision robotic arm. It uses articulated grating ruler to construct a real-time feedback measurement system and proposes a robotic arm numerical control system for parsing NC code. It combines traditional geometric contour error solving methods with projection factors to ensure the speed and accuracy of contour error solving. The contour error point can be obtained within a single control cycle (2ms), which provides a guarantee for real-time control of contour error.

[0020] (2) A two-layer cascaded contour error controller was designed. The inner loop control improves the joint tracking performance of the flexible joint robot arm. The robot system is decomposed into fast subsystem and slow subsystem through singular perturbation theory. Control laws are designed for the fast subsystem and slow subsystem. The stability of the control law designed by the control system is analyzed by using the Lyapunov function method. The outer loop control is combined with contour error estimation to design a Cartesian space contour error correction link to ensure the tracking accuracy of the Cartesian space contour, correct the value of the interpolation output, improve the dynamic tracking accuracy, and effectively improve the contour accuracy of the robot arm movement process.

[0021] (3) A large-size milling platform consisting of a flexible process equipment, an AGV, and a milling end effector was developed. A secondary encoder sensor system was installed on each joint of the robotic arm, establishing a joint closed-loop control. The various actuators were integrated into the same control system, solving the challenge of integrated control. A method for improving the robot's contour accuracy was designed to meet the accuracy requirements of product milling. Attached Figure Description

[0022] Figure 1 This is a flowchart of a joint enhancement contour control method for a robot milling system according to the present invention.

[0023] Figure 2 This is a schematic diagram of the layout of the milling system.

[0024] Figure 3 This is a schematic diagram of the robotic arm control system and the robotic arm system with added grating rulers.

[0025] Figure 4 This is a schematic diagram of the contour error estimation process combined with the projection factor.

[0026] Figure 5 This is a schematic diagram of a two-layer cascaded contour controller control structure.

[0027] Figure 6 This is a diagram showing the difference between contour error estimation using the traditional method and the switching geometric relationship method.

[0028] Figure 7 This is a contour error result diagram obtained by using the contour error control method of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0030] Although the steps in this invention are arranged by reference numerals, this is not intended to limit the order of the steps. Unless the order of the steps is explicitly stated or the execution of a step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" as used herein refers to and covers any and all possible combinations of one or more of the associated listed items.

[0031] The present invention provides a joint enhancement contour control method for a robotic milling system, such as... Figure 1As shown, firstly, a flexible process equipment for vacuum adsorption and clamping of large-sized components, a modular and quickly replaceable milling end effector, and a high-precision mobile robotic arm equipped with grating feedback are designed. Hardware configuration and control software development are completed to build the robotic milling system. Secondly, a contour error estimator using a switching geometry method is designed to directly solve for the contour error and the contour error compensation target point during the robotic arm's motion, providing a foundation for contour error control. Thirdly, a two-layer cascaded contour error control method is designed, with the inner loop ensuring the tracking accuracy of the flexible joint robotic arm in joint space and the outer loop ensuring the contour motion accuracy of the robotic arm in Cartesian space. Next, addressing the joint flexibility problem in the inner loop joint space control, the flexible joint robotic arm is decomposed into a fast subsystem and a slow subsystem using singular perturbation theory, and control laws are designed for each subsystem. Finally, the contour controller in the outer loop Cartesian space is used to correct the contour error target, thereby correcting the interpolation output value. Details are as follows:

[0032] S1, Build a robotic milling system including flexible process equipment for vacuum adsorption and clamping of large-sized components, modular and quick-change milling end effectors, and flexible joint robotic arms equipped with grating feedback;

[0033] In this embodiment, step S1 constructs a large-size component milling system consisting of flexible process equipment, a modular end effector, and a mobile high-precision robotic arm. The flexible process equipment is used to achieve the adsorption and clamping of complex-shaped components. A modular and quickly detachable multi-functional end effector is designed. An angle feedback grating ruler is installed at the six joints of the industrial robot to provide real-time feedback on the nonlinear errors caused by the joint flexibility during the movement of the robotic arm and the processing. The large-size component milling system established in step S1 provides the foundation for the milling contour control method constructed in S3.

[0034] Specifically, building a robotic milling system includes the following steps:

[0035] S11, Robotic Milling System Construction and Control System Hardware Configuration: A large-size component milling system was constructed, consisting of flexible process equipment, modular end effectors, and a mobile high-precision robotic arm. The flexible process equipment is used to achieve the adsorption and clamping of complex-shaped components, and a modular, quickly detachable, multi-functional end effector is designed.

[0036] According to the actual processing scenario Figure 2The layout shown includes 20 liftable pogo posts, forming the z-axis of the flexible tooling; every four pogo posts are mounted on a crossbeam and can move along the crossbeam guide rails, forming the x-axis movement of the flexible tooling; the crossbeam is mounted on a longitudinal guide rail, forming the y-axis of the flexible tooling. The flexible tooling can adaptively adjust its state according to the shape of the product to be processed, using vacuum adsorption to ensure stable clamping of the product. The modular end effector is a drilling and milling end effector, consisting of a fixed end and a quick-change end. The fixed end is mounted on the robot's end flange, connecting to the necessary electrical and pneumatic sources from the bottom of the robot; the quick-change end is the actual machining end, equipped with a spindle and milling cutter, and features air cooling and dust extraction functions. The fixed end and quick-change end are connected via a quick-change connector, with the pneumatic and electrical circuits conducted through the quick-change connector, ensuring that the quick-change end can be removed as a whole without rewiring.

[0037] S12, Establish a high-precision mobile robotic arm system, and install angle feedback grating rulers at the six joints of the industrial robot to provide real-time feedback on nonlinear errors caused by joint flexibility during the robotic arm's movement and processing:

[0038] The robot, mounted on an AGV, effectively expands its processing space. To address the impact of the flexibility of the industrial robot's joint transmission system on robot accuracy and to achieve real-time measurement and compensation of link angles, a grating measurement system is installed at the robot's joint positions to establish real-time joint position feedback. The grating measurement system consists of a reading head and a grating ruler. A laser tracker measurement system is used to calibrate the grating readings and joint angles, improving the measurement accuracy of the grating measurement system.

[0039] Development such as Figure 3 The PC-based robot real-time control system shown is based on a PC real-time controller and uses EtherCAT communication with high real-time performance. It employs an industrial PLC to realize the control functions of complex control tasks, realizes the real-time issuance of control commands and the rapid reception of feedback signals, and constructs a robot closed-loop feedback control system.

[0040] The control structure is divided into a host computer system, a slave computer system, and an execution terminal.

[0041] The host computer system is used to parse the robot's motion NC code, while the slave computer acts as the main controller, with functions such as trajectory planning, trajectory interpolation, and kinematics calculation. The execution end consists of the robot drive motor and the grating measurement system.

[0042] The grating ruler connects the signal to the system through the EK1100 coupler and EL5042 terminal, realizing the construction of a real-time closed-loop feedback control system for the robot.

[0043] S13, the system is integrated into the same control software, ensuring the coordination of all components:

[0044] PC-based robot control decomposes the robot into six motor controls and integrates the robot control, end effector, and flexible tooling into the same integrated control system, ensuring the coordination of each component and enabling the construction of a robot milling platform for large-sized components.

[0045] S2, Establish a contour error solution strategy based on switching geometry method and projection factor to obtain the contour error compensation target point and contour error of the robotic arm motion process;

[0046] In the embodiment, S2 designs a contour error solution method using a switching geometric relationship method, calculates the projection factor from the actual position to the theoretical contour, thereby ensuring the solution accuracy of the contour error value and the contour error target point. It combines the traditional geometric contour error solution method with the projection factor, ensuring both the solution rate and the solution accuracy, and provides a foundation for the Cartesian space contour control link in the two-layer cascade contour control in S3.

[0047] Specifically, a contour error solution method using a switching geometric relationship approach is designed, combining the traditional geometric contour error solution method with projection shadows to ensure both solution speed and accuracy. The method includes the following steps:

[0048] S21, Discretize the robot's motion path into continuous straight line and circular arc trajectories:

[0049] like Figure 4 As shown, non-parametric paths in robot machining processes are difficult to represent using functions. Fitting non-parametric paths with continuous short straight lines is a common method. The trajectory and velocity are smoothed by transitioning between short straight lines with circular arcs, thereby transforming the non-parametric trajectory into a continuous straight-arc transition trajectory, which provides a basis for contour error estimation using the proposed switching geometric relationship method.

[0050] S22, Geometric method for contour error calculation combined with projection factor, ensures both solution speed and solution accuracy:

[0051] Based on the solution of the contour errors of straight line and circular arc trajectories, the contour error of the straight line trajectory is: ;

[0052] The error of the circular arc trajectory profile is: ; and These represent the tracking errors along the n-axis and t-axis in the local coordinate system, respectively. Let be the angle between the direction of the tangent to the motion and the t-axis. The radius of the arc is denoted as .

[0053] For non-parametric contours fitted by straight lines and circular arcs, a projection factor is introduced to improve the accuracy of contour error point and contour error solution. Projection factor The difference between the vector connecting the start and end points of the current interpolation segment's trajectory to the vector connecting the start point and the actual point is defined as: ; To indicate the actual point, This represents the starting point of the i-th straight line segment. This represents the end point of the i-th straight line segment. If... The actual point is located within the projection area of ​​the current line segment. The actual point is located before the current line segment, if The actual point is located after the current line segment, therefore it is necessary to solve for it. The projection factor of the actual point on the next interpolated line segment, and This indicates the projection factor of the actual point on the previous interpolation segment, further determining the interval containing the nearest contour error point projected by the actual point. Specifically, this can be subdivided into the following three cases:

[0054] Case 1, if Contour point Located on the current line segment.

[0055] Case 2, if ,when The contour point is located on the next line segment, when The contour point is located on the current arc segment, when Further calculations are needed to determine the projected shadow until it is determined. or This determines the location of the contour points.

[0056] Case 3, if ,when The contour point is located on the upper straight line segment, when The contour point is located on the previous arc segment, when Further calculations are needed to determine the projected shadow until it is determined. or Determine the location of the contour points.

[0057] S3. A two-layer cascaded contour error control strategy with inner and outer loops is established. This strategy decomposes the flexible joint manipulator system into fast and slow subsystems through singular perturbation theory, and uses RBF neural network to predict the parameters of the manipulator dynamic system as feedforward terms for the control of the slow subsystem. The inner loop is a flexible joint tracking controller used to run the control laws of the fast and slow subsystems to ensure the tracking accuracy of the flexible joint manipulator in the joint space. The outer loop is a Cartesian space contour error controller used to correct the contour error and obtain the corrected contour compensation point to ensure the contour motion accuracy of the manipulator in the Cartesian space.

[0058] In this embodiment, S3 designs a two-layer cascaded contour control method. The inner loop uses an RBF neural network to establish a dynamic model of the robotic arm system and decomposes the flexible joint robot into a fast subsystem and a slow subsystem through singular perturbation theory. The outer loop combines contour error estimation to design a Cartesian space contour error correction link. Step S3 expresses the structure of the control method, and the detailed control method is described below.

[0059] Specifically, a two-layer cascaded contour control method is designed, and a flexible joint robot model is established. The inner loop decomposes the flexible joint robot into fast and slow variable subsystems through singular perturbation theory, and uses RBF neural network to establish the dynamic writing model of the robotic arm system. The outer loop combines contour error estimation to design a Cartesian space contour error correction stage, including the following steps:

[0060] Structure of the two-layer cascaded contour error control method:

[0061] like Figure 5 The diagram illustrates a two-layer cascaded contour control strategy. Robot motion commands are input in NC code form. The trajectory planning module (GCS trajectory planner) transforms path points into continuous straight-line and circular-arc transitions, outputting the trajectory's position and velocity information. A real-time interpolation module discretizes the trajectory to obtain the Cartesian space target point, and then inverse kinematics is used to obtain the motion reference position of each joint. The inner loop is a flexible joint tracking controller, consisting of a velocity observer, an RBF neural network prediction model, and a singular perturbation controller, improving the tracking accuracy and dynamic response capability of the flexible joint robot. The outer loop is a Cartesian space contour error controller, consisting of a contour error estimator and a PD controller, used to correct the Cartesian space target contour position.

[0062] Based on singular perturbation control theory, the flexible joint robot is decomposed into a fast subsystem and a slow subsystem. The feedback measurement systems are a motor encoder and a grating encoder, respectively, which can provide the actual rotation angles on the motor side and the link side. An RBF neural network is used to construct the dynamic system parameters, which serve as feedforward terms for the slow subsystem controller, thereby improving the system's dynamic response.

[0063] The flexible joint robot system is defined as:

[0064] (1)

[0065] ; In the formula, These represent the actual angular position, velocity, and acceleration on the connecting rod side, respectively. The actual rotational angle position, velocity, and acceleration on the motor side are respectively recorded. It is the inertia matrix of the robotic arm. It is the matrix of Coriolis force and centripetal force. Let represent the gravity term matrix, K be the equivalent stiffness coefficient matrix of the flexible joint, and J be the diagonal positive definite matrix of the drive motor at the joint. This refers to the output torque of the drive motor at the joint. This represents the coupling relationship between the linkage dynamics system and the motor dynamics system. Let the variables... , , , Define the state-space expression as follows: ;

[0066] Based on the singular perturbation theory, the system is decomposed, and perturbation parameters are defined. ,make To obtain the standard form of the singular perturbation model: ; ;

[0067] when At that time, control torque Becoming a slow subsystem control law ,and The slow subsystem is obtained as follows: ; In the formula, Let be the coupling inertia matrix of the robotic arm and the motor, and let the fast time scale , For slow-scale time, Assuming fast variables, we obtain the robot's fast subsystem: ; The fast and slow subsystems of the flexible joint robot were obtained.

[0068] Predicting dynamic model parameters using RBF neural networks:

[0069] The output of the RBF neural network is: ; in For the value of the network, This is the output of the hidden layer.

[0070] The following design is made for the parameters of the dynamic model. ;

[0071] , , For neural network pairs , , Parameter estimation.

[0072] (1) For the inner ring joint space tracking controller, control laws are designed for the fast subsystem and the slow subsystem. The grating encoder is used as the position feedback on the link side and the motor encoder is used as the position feedback on the joint side. The tracking accuracy of the link is the premise of ensuring the accuracy of the Cartesian space contour. The stability of the control law designed for the control system is analyzed by using the Lyapunov function method.

[0073] Design a joint space tracking controller for an inner-loop flexible joint robot, and design control laws for the fast and slow subsystems, including the following steps:

[0074] 1) The control law for the slow subsystem is: ;

[0075] Define the link position tracking error. ; ; It is a positive definite matrix and , , , express Reference position, This indicates the deviation between the reference position and the actual position on the connecting rod side. This indicates the deviation between the reference speed and the actual speed on the connecting rod side.

[0076] 2) The control law for the fast subsystem is: ; It is a diagonal positive definite matrix. A velocity observer is designed to estimate... and .

[0077] The design of the velocity observer provides velocity estimation for the perturbation controller, avoiding the error caused by direct differentiation of the position signal. , For the observer state, , , and All are observer gains, which are positive constants. and For observer output ; ;

[0078] 3) Design Lyapunov functions to analyze system stability.

[0079] For the tracking controller, define the Lyapunov function: ; in , right Taking the derivative, we get: ; in According to the property of matrix skew symmetry, we have ,and , , Therefore there is ; By combining the slow subsystem with its control law, we obtain... ; in .;

[0080] Combining the above two equations, we get ; exist ; therefore, Simplified to ; Through debugging Parameters that can guarantee Therefore, the system is asymptotically stable, and the conditions for asymptotic stability are adjustable.

[0081] (2) The outer ring Cartesian space contour controller (outer ring contour error controller) includes a real-time contour error estimator and a PD controller. It uses grating to measure the actual joint position, combines the positive kinematics of the robotic arm, solves the actual end position of the robot, inputs it into the contour error controller, outputs the contour error correction, and feeds back the corrected interpolation output value.

[0082] The outer ring contour error controller includes a real-time contour error estimator and a PD controller. The value of the interpolation output is corrected by the controller through the following steps:

[0083] 1) Using the angle value of the connecting rod measured by the grating as input, and utilizing the identified kinematic parameters, a positive kinematic model is established to obtain the actual position of the end effector. Substituting this into the contour error solver yields the contour error compensation target point. And solve for the profile error .

[0084] 2) Construct a PD controller, and determine the trapezoidal velocity curve during the robot's linear motion. Decompose the robot trajectory into acceleration, constant velocity, and deceleration stages, with the circular arc segments using constant velocity motion. Decompose the robot's motion into four motion stages. Basic parameters, To determine the acceleration during the acceleration and deceleration phases, different PD parameters are applied for different phases. The parameter relationships are constructed as follows: ; The discrete-time control rate of the contour error is ;

[0085] For the operating cycle, For proportional parameters, The differential parameters are used to obtain the corrected contour compensation points. , This indicates a theoretical stance.

[0086] S4. A contour error solving strategy and a dual-loop cascaded contour error control strategy (inner and outer loops) are adopted to perform dual-loop cascaded contour control on the robot milling system.

[0087] The aforementioned robotic milling platform is constructed, and an S-shaped curve is planned within the robot's workspace. The contour error estimation and control methods proposed in this invention are then applied. The contour error estimation accuracy and contour error control accuracy of the spatial S-shaped curve are as follows: Figure 6 and Figure 7 As shown.

[0088] Figure 6In the diagram, (a) represents a comparison between the contour error estimate obtained by the traditional geometric method and the true contour error, and the contour error estimate obtained by the method of this invention. (b) represents the estimation error between the two methods. (c) uses a heatmap to represent the estimation error between the two methods. The maximum contour error estimation error of the method proposed in this invention is 0.3 μm, and the computation time is 0.1 ms. Compared with the maximum contour error of 0.28 mm in the traditional geometric estimation method, this method effectively improves the estimation accuracy. After adopting the control method proposed in this invention, the contour error of the robot is reduced from 2.2 mm to 0.15 mm. Compared with the control method that only considers contour control and does not combine joint flexible tracking performance (0.4 mm), the position contour error is improved by more than 90% and 60%, respectively. Figure 7 As shown in (a), Figure 7 (b) represents the contour error heatmap of the S-shaped curve using this method.

[0089] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0090] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for joint enhancement contour control in a robotic milling system, characterized in that, The control method includes: S1, Build a robotic milling system including flexible process equipment for vacuum adsorption and clamping of large-sized components, modular and quick-change milling end effectors, and flexible joint robotic arms equipped with grating feedback; S2, Establish a contour error solution strategy based on switching geometry method and projection factor to obtain the contour error compensation target point and contour error of the robotic arm motion process; The contour error solution strategy based on the switching geometry method and projection factor is as follows: (1) Based on the switching geometry method, the motion path of the robotic arm is discretized into a continuous trajectory of straight lines and circular arcs; (2) Calculate the projection factor and determine the specific location of the contour point on the straight line segment or arc segment based on the projection factor, and use it as the target point for contour error compensation. The formula for calculating the projection factor is: ； in, To indicate the actual point, This represents the projection factor of the actual point on the current interpolated line segment. This indicates the starting point of the i-th line segment. This represents the endpoint of the i-th line segment; According to the projection factor Determine the specific location of the contour point on the straight line segment or circular arc segment, including: Case 1, if If the contour point is located on the current line segment, then the contour point is located on the current line segment. Case 2, if ,when , If the projection factor indicates that the actual point is on the next interpolation segment, then the contour point is on the next line segment. The contour point is located on the current arc segment, when Then, the projected shadow is further solved until... or This determines the location of the contour points; Case 3, if ,when , Indicates the projection factor of the actual point on the previous interpolation segment, then the contour point lies on the previous straight line segment. Then the contour point is located on the previous arc segment, when Then, the projected shadow is further solved until... or Determine the location of the contour points; (3) Calculate the contour error based on the specific location of the contour point on the straight line segment or arc segment: If the contour point is located on a straight line segment, then the contour error is: ； If the contour point is located on an arc segment, then the contour error is: ； in, and These represent the tracking errors along the n-axis and t-axis in the local coordinate system, respectively. Let be the angle between the direction of the tangent to the motion and the t-axis. The radius of the arc; S3. A two-layer cascaded contour error control strategy with inner and outer loops is established. This strategy decomposes the flexible joint manipulator system into fast and slow subsystems through singular perturbation theory, and uses RBF neural network to predict the parameters of the manipulator dynamic system as feedforward terms for the control of the slow subsystem. The inner loop is a flexible joint tracking controller based on the control laws of the fast and slow subsystems to ensure the tracking accuracy of the flexible joint manipulator in the joint space. The outer loop is a Cartesian space contour error controller to correct the contour error and obtain the corrected contour compensation point to ensure the contour motion accuracy of the manipulator in the Cartesian space. The Cartesian space contour error controller includes a real-time contour error estimator and a PD controller; The real-time contour error estimator obtains the contour error compensation target point and contour error during the robotic arm's motion process based on the contour error solving strategy. The PD controller is based on the contour error compensation target point. Solving for contour error The robotic arm's motion is decomposed into four motion stages, and different PD parameters are used for each stage, as follows: ； in, , , , These correspond to the acceleration, constant speed, deceleration, and circular motion stages, respectively. Basic parameters, This refers to the acceleration during the acceleration / deceleration phase. The discrete-time control rate of the contour error is: ； For the operating cycle, For proportional parameters, The differential parameters are used to obtain the corrected contour compensation points. , Indicates a theoretical stance; S4. A contour error solving strategy and a dual-loop cascaded contour error control strategy (inner and outer loops) are adopted to perform dual-loop cascaded contour control on the robot milling system.

2. The joint enhancement contour control method for a robotic milling system according to claim 1, characterized in that, The flexible process equipment described in S1 includes 20 liftable pogo columns, forming the z-axis of the flexible tooling; every 4 pogo columns are mounted on a crossbeam and can move on the crossbeam guide rail, forming the x-axis movement of the flexible tooling; the crossbeam is mounted on a longitudinal guide rail, forming the y-axis of the flexible tooling; the flexible tooling can adaptively adjust its state according to the shape of the product to be processed, and use vacuum adsorption to ensure stable clamping of the product.

3. The joint enhancement contour control method for a robotic milling system according to claim 1, characterized in that, The modular, quick-change milling end effector described in S1 consists of a fixed end and a quick-change end. The fixed end is mounted on the end flange of the robotic arm and connects to the circuitry and pneumatic system from the bottom of the robotic arm. The quick-change end is the actual machining end, equipped with a spindle and milling cutter, and features air cooling and dust extraction functions. The fixed end and quick-change end are connected via a quick-change connector, and the pneumatic and electrical systems are conducted through the quick-change connector, ensuring that the quick-change end can be removed as a whole without rewiring.

4. The joint enhancement contour control method for a robot milling system according to claim 1, characterized in that, The flexible joint robotic arm described in S1 is located on the AGV. Angle feedback grating rulers are installed at each joint of the robotic arm. The grating measurement system uses a laser tracker measurement system to calibrate the grating readings and joint angles, and provides real-time feedback on nonlinear errors caused by joint flexibility during the movement and processing of the robotic arm.

5. The joint enhancement contour control method for a robotic milling system according to claim 1, characterized in that, The control system of the robotic arm described in S1 is based on a PC real-time controller, EtherCAT communication, and an industrial PLC to realize closed-loop feedback control of the robotic arm. The control system includes a host computer, a slave computer, and an execution end. The host computer is used to parse the NC code of the robotic arm motion, the slave computer is used as the main controller for trajectory planning, trajectory interpolation, and kinematic calculation, and the execution end consists of the robotic arm drive motor and the grating measurement system. The grating ruler connects the signal to the control system through an EK1100 coupler and an EL5042 terminal.

6. The joint enhancement contour control method for a robotic milling system according to claim 1, characterized in that, S3 describes the decomposition of the flexible joint robotic arm system into fast and slow subsystems using singular perturbation theory, including: The flexible joint robotic arm system is defined as: (1) ； In the formula, These represent the actual angular position, velocity, and acceleration on the connecting rod side, respectively. The actual rotational angle position, velocity, and acceleration on the motor side are respectively recorded. It is the inertia matrix of the robotic arm. It is the matrix of Coriolis force and centripetal force. Let represent the gravity term matrix, K be the equivalent stiffness coefficient matrix of the flexible joint, and J be the diagonal positive definite matrix of the drive motor at the joint. This refers to the output torque of the drive motor at the joint. Let the variable , , , The state-space expression of the flexible joint robotic arm system is: ； The flexible joint robotic arm system is decomposed based on singular perturbation theory: perturbation parameters are defined. ,make To obtain the standard form of the singular perturbation model: ； ； when At that time, control torque Becoming a slow subsystem control law ,and The slow subsystem is obtained as follows: ； In the formula, , where is the coupling inertia matrix between the robotic arm and the motor; Fast time scale , For slow-scale time, Assuming the variable is fast, we obtain the fast subsystem of the robotic arm: ； The method of using RBF neural networks to predict the parameters of the robotic arm's dynamic system is as follows: ； , , For RBF neural network pairs , , Parameter estimation.

7. The joint enhancement contour control method for a robot milling system according to claim 6, characterized in that, The control law for the slow subsystem described in S3 is: ； in For the link position tracking error, then: ； ； It is a positive definite matrix and , , , express Reference position, This indicates the deviation between the reference position and the actual position on the connecting rod side. This indicates the deviation between the reference speed and the actual speed on the connecting rod side; The control law for the fast subsystem is: ； in, It is a diagonal positive definite matrix; and Using the velocity observer estimation and : ； ； in , For the observer state, , , and All are observer gains.

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