Joint strengthening contour control method of robot milling system

Abstract

The invention discloses a joint strengthening contour control method of a robot milling machining system. The joint strengthening contour control method comprises the steps that the robot edge milling machining system is built; a contour error solving strategy based on a switching geometric method and projection factors is established to obtain a contour error compensation target point and a contour error in the motion process of the mechanical arm; an inner ring and outer ring double-layer cascade contour error control strategy is established, a flexible joint mechanical arm system is decomposed into a fast subsystem and a slow subsystem, mechanical arm dynamic system parameters are predicted, an inner ring guarantees the tracking precision of the flexible joint mechanical arm in a joint space based on the fast subsystem and slow subsystem control laws, and an outer ring corrects contour errors. The contour motion precision of the Cartesian space of the mechanical arm is ensured; and adopting a contour error solving strategy and an inner ring and outer ring double-layer cascade contour error control strategy to carry out double-ring cascade contour control on the robot edge milling processing system. The dynamic tracking precision is improved, and the contour precision of the mechanical arm in the moving process is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of the construction and precision control of industrial robotic arm processing systems, and particularly relates to a joint enhanced contour control method for a robot milling processing system. Background Art

[0002] In recent years, CFRP has been widely used in aerospace components, and edge milling is an essential process for such components. With the development of robot technology, mobile robotic arm systems have the advantages of a large working space and high flexibility, and are widely used in operations such as hole making, grinding, and assembly of large structural parts. Compared with numerically controlled systems that are large in size and expensive in cost for edge milling operations of large-sized parts, mobile robotic arm systems have more advantages in terms of construction cost and working space.

[0003] However, due to the influence of multi-source errors 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 running accuracy of the robot directly affects the geometric contour accuracy of the milled edge of the product. Simply improving the joint tracking performance of the robot cannot guarantee the contour accuracy. Therefore, it is necessary to study direct contour error estimation methods and contour error control methods. In addition, the oscillation and accuracy loss caused by joint flexibility resulting from the robot joint drive components lead to the inability of the robot motion accuracy to meet the requirements. There is an urgent need to propose a contour control method for a robot edge milling processing system.

[0004] The patent with publication number CN 201910314401.7 discloses a decoupled contour error control method for a five-axis numerically controlled machine tool. By decomposing the contour error into a contour error vector and a tangential tracking error vector, a normal contour error controller and a tangential contour error controller are respectively obtained for each drive axis, and the total control signal is obtained to control each drive axis. However, this method does not consider the influence of the tracking performance of a single axis on the tracking of the normal and tangential contour errors, and this link is the key to ensuring the contour tracking performance.

[0005] The patent with publication number CN 201910856025.4 discloses a contour error controller for a multi-axis motion system and its control method. 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 an extended state disturbance observer is proposed, effectively reducing the tracking error and contour error. However, this method mainly focuses on a three-axis system, specifically manifested as the driving motion direction of one axis. Compared with the end accuracy of a serial robotic arm system affected by multi-axis coupling, the control of the end contour accuracy is more complex.

[0006] The patent with the publication number CN 202210076416.6 discloses a method for controlling the path profile error at the end of a robot. For a two-degree-of-freedom system within the end effector of the robot, by superimposing a preset trajectory and a preset following error trajectory, a first trajectory is obtained as the starting signal for the trajectory. However, this method targets the end effector rather than the contour motion at the end of the robot.

[0007] The above patents only make discussions from the design of the controller and the control method, and do not involve the composition of the actual processing system and the construction of the hardware system of the closed-loop feedback system. They cannot be compatible with the application of the robotic arm system in the processing scenario, and do not combine the tracking error and the contour error of each axis of the system, which will lead to insufficient dynamic tracking performance of the system. There is less research on the contour error solution and contour error control of the six-axis serial robotic arm. Compared with the single-axis corresponding to a single direction in the Cartesian space of the machine tool system, the above method is not fully applicable to the robot system.

[0008] The literature "A novel hybrid contouring control method for 3-DOF robotic manipulators, 2016, (40): 178-193." designed a hybrid contour controller for a three-axis robotic arm system, which includes an independent joint controller and a Cartesian space sliding mode controller to enhance the dynamic tracking performance of the system. However, this method does not consider the joint flexibility caused by the joint drive mechanism of the large-load robot, and only uses the motor encoder as the feedback of the joint, which will lead to inaccurate estimation of the end position and requires an additional end position sensing and measurement system. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to provide, in view of the deficiencies of the above-mentioned prior art, a joint enhanced contour control method for a robot milling processing system, which combines grating compensation for joint flexibility, establishes a two-level cascade contour control strategy in the joint space and the Cartesian space, improves the dynamic tracking accuracy, and effectively enhances the contour accuracy during the movement of the robotic arm.

[0010] To achieve the above technical objectives, the technical solution adopted by the present invention is as follows:

[0011] A joint enhanced contour control method for a robot milling processing system, the control method comprising:

[0012] S1, building a robot milling edge processing system including a flexible process equipment for vacuum adsorption and clamping of large-size components, a modular and quickly replaceable milling edge end effector, and a flexible joint robotic arm with grating feedback;

[0013] S2. Establish a contour error solution strategy based on the switching geometry method and projection factor to obtain the contour error compensation target points and contour errors during the movement of the robotic arm.

[0014] S3. Establish a double-layer cascaded contour error control strategy for the inner and outer loops. This strategy decomposes the flexible joint robotic arm system into a fast subsystem and a slow subsystem through the singular perturbation theory, and uses an RBF neural network to predict the parameters of the robotic arm dynamics system as the feedforward term for the control of the slow subsystem. The inner loop is a flexible joint tracking controller, which, based on the control laws of the fast and slow subsystems, ensures the tracking accuracy of the flexible joint robotic arm in the joint space. The outer loop is a Cartesian space contour error controller, which is used to correct the contour error to obtain the corrected contour compensation points, thereby ensuring the contour motion accuracy of the robotic arm in the Cartesian space.

[0015] S4. Apply the contour error solution strategy and the double-layer cascaded contour error control strategy for the inner and outer loops to perform double-loop cascaded contour control on the robot milling-edge processing system.

[0016] To optimize the above technical solution, the specific measures taken also include:

[0017] The flexible process equipment described in S1 above includes 20 liftable pogo pins, forming the z-axis of the flexible tooling; every 4 pogo pins are installed on the crossbeam and can move on the crossbeam guide rails, forming the x-axis movement of the flexible tooling; the crossbeam is installed on the longitudinal guide rails, forming the y-axis of the flexible tooling; the flexible tooling can adaptively adjust the tooling state according to the shape of the product to be processed and use vacuum adsorption to ensure the stable clamping of the product.

[0018] 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, connecting the circuit and air path from the bottom of the robotic arm; the quick-change end is the actual processing end, equipped with a spindle and a machining milling cutter, with air cooling and dust suction functions; the fixed end and the quick-change end are connected by a quick-change joint, and the air path and circuit are conducted through the quick-change joint, ensuring that the quick-change end can be removed integrally without re-wiring.

[0019] The flexible joint robotic arm described in S1 above is located on an AGV. Angle feedback grating scales 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 real-time feedbacks the non-linear errors caused by joint flexibility during the movement and processing of the robotic arm.

[0020] The control system of the robotic arm described in S1 above realizes the closed-loop feedback control of the robotic arm based on a PC real-time controller, EtherCAT communication, and an industrial PLC. The control system includes a host computer, a slave computer, and an execution end. The host computer is used to parse the NC code for the movement of the robotic arm. The slave computer serves as the main controller and is used for trajectory planning, trajectory interpolation, and kinematic solution. The execution end is the drive motor of the robotic arm and the grating measurement system. The grating ruler accesses the signal into the control system through an EK1100 coupler and an EL5042 terminal.

[0021] The contour error solving strategy based on the switching geometric method and the projection factor described in S2 above is as follows:

[0022] (1) Based on the switching geometric method, the movement path of the robotic arm is discretized into continuous trajectories of straight lines and arcs;

[0023] (2) Calculate the projection factor, and determine the specific position of the contour point on the straight line segment or arc segment according to the projection factor, and use this as the contour error compensation target point;

[0024] The calculation formula for the projection factor is:

[0025]

[0026] where p a represents the actual point, h a represents the projection factor of the actual point on the current interpolation line segment, L s,i represents the start point of the i-th straight line segment, L e,i represents the end point of the i-th straight line segment;

[0027] Determining the position of the contour point according to the projection factor h a includes:

[0028] Case 1, if 0 ≤ h a ≤ 1, then the contour point p c is located on the current straight line segment;

[0029] Case 2, if h a > 1, when 0 ≤ h a+1 ≤ 1, h a+1 represents the projection factor of the actual point on the next interpolation line segment, then the contour point is located on the next straight line segment. When h a+1 < 0, the contour point is located on the current arc segment. When h a+1 > 1, then further solve the projection shadow until 0 ≤ h a+k ≤ 1 or h a+k< 0, determine the position where the contour point is located;

[0030] Case 3, if h a < 0, when 0 ≤ h a-1 ≤ 1, h a-1 represents the projection factor of the actual point on the previous interpolation line segment, then the contour point is located on the previous straight line segment. When h a-1 > 1, then the contour point is located on the previous circular arc segment. When h a-1 < 0, then further solve the projection shadow until 0 ≤ h a-k ≤ 1 or h a-k > 1, to determine the position where the contour point is located;

[0031] (3) Calculate the contour error according to the position where the contour point is located:

[0032] If the position where the contour point is located is a straight line segment, then the contour error is:

[0033] c e = -e t sinφ + e n cosφ

[0034] If the position where the contour point is located is a circular arc segment, then the contour error is:

[0035]

[0036] where, e n and e t are the tracking errors in the n-axis and t-axis directions in the local coordinate system respectively, φ is the angle between the moving tangent direction and the t-axis, and r is the radius of the circular arc.

[0037] The above-mentioned S3 decomposes the flexible joint manipulator system into a fast subsystem and a slow subsystem through the singular perturbation theory, including:

[0038] Define the flexible joint manipulator system as:

[0039]

[0040] In the formula, q1, represent the actual angular position, velocity, and acceleration on the link side respectively, q2, are the actual angular position, velocity, and acceleration on the motor side respectively, is the inertia matrix of the manipulator, is the Coriolis force and centripetal force matrix, represents the gravity term matrix, K is the equivalent stiffness coefficient matrix of the flexible joint, J is the diagonal positive definite matrix of the driving motor at the joint, and u is the output torque of the driving motor at the joint;

[0041] Let \(x_1 = q_1\), \(x_3 = q_2\), The state - space expression of the flexible - joint manipulator system is:

[0042]

[0043] Based on singular - perturbation theory, the flexible - joint manipulator system is decomposed: Define the perturbation parameter \(0\lt\varepsilon\lt1\), let \(K\) ε \(=\varepsilon K\), and obtain the standard form of the singular - perturbation model:

[0044]

[0045] When \(\varepsilon = 0\), the control torque \(u\) becomes the control law \(u\) s , and Obtain the slow - subsystem as:

[0046]

[0047] where \(D(q_1)=M(q_1)+J = M(x_1)+J\), is the coupling inertia matrix of the manipulator and the motor;

[0048] Let the fast - time scale \(\tau=t / \varepsilon\), \(t\) is the slow - scale time, \(e\) f be the fast variable, and obtain the fast - subsystem of the manipulator:

[0049]

[0050] The method of using the RBF neural network to predict the parameters of the manipulator dynamic system is as follows:

[0051]

[0052] are the estimates of the parameters \(D(q_1)\), \(G(q_1)\) by the RBF neural network.

[0053] The slow - subsystem control law described in S3 above is:

[0054]

[0055] where and are the estimation matrices of \(D(q_1)\), and \(G(q_1)\) respectively, \(S\) is the link - position tracking error, then:

[0056]

[0057] \(\Lambda=\text{diag}(\lambda_1,\lambda_2,\cdots,\lambda\) n ) is a positive - definite matrix and \(\lambda\) i> 0, q 1r represents the reference position of q1, represents the deviation between the reference position and the actual position on the connecting rod side, represents the deviation between the reference speed and the actual speed on the connecting rod side;

[0058] The control law of the fast subsystem is:

[0059]

[0060] where K v is a diagonal positive definite matrix;

[0061] and x4 are obtained by estimation through a speed observer and

[0062]

[0063] where η1, η2 are the observer states, k1, k 01 , k 02 and k4 are all observer gains and are positive constants.

[0064] The Cartesian space contour error controller described above in S3 includes a real-time contour error estimator and a PD controller;

[0065] The real-time contour error estimator obtains the contour error compensation target point and the contour error during the movement of the robotic arm according to the contour error solution strategy;

[0066] The PD controller is based on the contour error compensation target point p c and can solve the contour error ε c = p c - p a , decomposes the movement of the robotic arm into four motion stages, is the basic parameter, a1 is the acceleration during the acceleration and deceleration stage, and different PD parameters are used for different stages, specifically as follows:

[0067]

[0068] The discrete-time control law of the contour error is:

[0069]

[0070] T = 0.002s is the operating cycle, k p is the proportional parameter, k d is the differential parameter, so as to obtain the corrected contour compensation point [p′ d , o′ d = [pd ,o d +u, o d represents the theoretical posture.

[0071] The present invention has the following beneficial effects:

[0072] (1) The present invention constructs a large-size component milling-edge system composed of a flexible process equipment, a modular end effector, and a mobile high-precision robotic arm. A real-time feedback measurement system is constructed using joint grating rulers, and a numerical control system for the robotic arm by parsing NC codes is proposed. Combining the traditional geometric contour error solving method with the projection factor ensures the speed and accuracy of contour error solving. Contour error points can be obtained within a single control cycle (2 ms), which provides a guarantee for the real-time control of contour error.

[0073] (2) A double-level cascaded contour error controller is designed. The inner-loop control improves the joint tracking performance of the flexible joint robotic arm. The robotic system is decomposed into a fast subsystem and a slow subsystem through the singular perturbation theory. Control laws are designed for the fast and slow subsystems, and the stability of the control laws designed for the control system is analyzed using the Lyapunov function method. The outer-loop control combines contour error estimation to design a Cartesian space contour error correction link, which is used to ensure the tracking accuracy of the Cartesian space contour, correct the interpolated output value, improve the dynamic tracking accuracy, and effectively enhance the contour accuracy during the movement of the robotic arm.

[0074] (3) A robotic arm large-size milling-edge platform composed of a flexible process equipment, an AGV, and a milling-edge end effector is developed. A secondary encoder sensor system is installed on each joint of the robotic arm, and joint closed-loop control is established. Each execution end is integrated into the same control system to solve the challenge of difficult integrated control. A method for improving the contour accuracy of the robot is designed, which can meet the accuracy requirements of product milling-edge processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 is a flowchart of a joint enhanced contour control method for a robotic arm milling and processing system of the present invention.

[0076] Figure 2 is a layout schematic diagram of the milling-edge processing system.

[0077] Figure 3 is a schematic diagram of the composition of the robotic arm control system and the robotic arm system with added grating rulers.

[0078] Figure 4 is a schematic diagram of the contour error estimation process combined with the projection factor.

[0079] Figure 5 is a schematic diagram of the control structure of the double-level cascaded contour controller.

[0080] Figure 6 It is a diagram showing the difference in contour error estimation between the traditional method and the switching geometric relationship method.

[0081] Figure 7 It is a diagram of the contour error result of contour error control using the method of the present invention. Detailed implementation manners

[0082] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present 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 only used to explain the present invention and are not used to limit the present invention.

[0083] Although the steps in the present invention are arranged with reference numerals, they are not used to limit the sequence of the steps. Unless the sequence of the steps is clearly stated or the execution of a certain step requires other steps as a basis, the relative sequence of the steps can be adjusted. It can be understood that the term "and / or" used herein relates to and encompasses any and all possible combinations of one or more of the associated listed items.

[0084] A joint enhanced contour control method for a robot milling system of the present invention is as Figure 1 shown. First, design a flexible process equipment for vacuum adsorption and clamping of large-size components, a modular and quickly replaceable milling edge end effector, and a moving high-precision robotic arm with grating feedback, and complete the hardware configuration and control software development to realize the construction of the robot milling system; secondly, design a contour error estimator based on the switching geometric method to directly solve the contour error and the contour error compensation target point during the movement of the robotic arm, providing a basis for contour error control; thirdly, design a double-level cascade contour error control method, where the inner loop ensures the tracking accuracy of the flexible joint robotic arm in the joint space, and the outer loop ensures the contour motion accuracy of the robotic arm in the Cartesian space; then, aiming at the joint flexibility problem in the inner loop joint space control, decompose the flexible joint robotic arm into a fast subsystem and a slow subsystem by the singular perturbation theory, and design control laws for the two subsystems respectively; finally, use the contour controller in the outer loop Cartesian space to correct the contour error target, and thus correct the interpolated output value. The specific introduction is as follows:

[0085] S1, construct a robot milling system including a flexible process equipment for vacuum adsorption and clamping of large-size components, a modular and quickly replaceable milling edge end effector, and a flexible joint robotic arm with grating feedback;

[0086] In the embodiment, in step S1, a large-size component milling-edge system composed of a flexible process equipment, a modular end effector, and a mobile high-precision robotic arm is constructed. The flexible process equipment is used to realize the adsorption and clamping of components with complex surfaces. A modular and quickly detachable multi-functional end effector is designed. Angle feedback grating scales are installed at the six joints of the industrial robot to real-time feedback the non-linear errors caused by joint flexibility during the movement of the robotic arm and the machining process. The large-size component milling-edge system established in step S1 provides a basis for the milling-edge contour control method constructed in S3;

[0087] Specifically, the construction of the robotic milling-edge processing system specifically includes the following steps:

[0088] S11, setup of the robotic milling-edge processing system and hardware configuration of the control system: A large-size component milling-edge system composed of a flexible process equipment, a modular end effector, and a mobile high-precision robotic arm is constructed. The flexible process equipment is used to realize the adsorption and clamping of components with complex surfaces. A modular and quickly detachable multi-functional end effector is designed:

[0089] According to the layout shown in Figure 2 , the flexible process equipment includes 20 liftable pogo pins, forming the z-axis of the flexible tooling; every 4 pogo pins are installed on the crossbeam and can move on the crossbeam guide rail, forming the x-axis movement of the flexible tooling; the crossbeam is installed on the longitudinal guide rail, forming the y-axis of the flexible tooling. The flexible tooling can adaptively adjust the tooling state according to the shape of the product to be machined and ensure the stable clamping of the product by using vacuum adsorption. The modular end effector is a drilling and milling end effector, which is divided into a fixed end and a quick-change end. The fixed end is installed on the end flange of the robot, and necessary circuits and gas paths are connected from the bottom of the robot; the quick-change end is the actual machining end, equipped with a spindle and a machining milling cutter, and has functions such as air cooling and dust suction. The fixed end and the quick-change end are connected by a quick-change joint, and the gas path and the circuit are conducted through the quick-change joint to ensure that the quick-change end can be integrally removed without re-wiring.

[0090] S12, establishment of a mobile high-precision robotic arm system. Angle feedback grating scales are installed at the six joints of the industrial robot to real-time feedback the non-linear errors caused by joint flexibility during the movement of the robotic arm and the machining process:

[0091] The robot is located on the AGV, effectively expanding the machining space of the robot. To solve the influence of the flexibility of the joint drive system of the industrial robot on the robot accuracy and realize the real-time measurement and compensation of the link angle, a grating measurement system is installed at the joint position of the robot to establish real-time joint position feedback. The grating measurement system consists of a reading head and a grating scale. The laser tracker measurement system is used to calibrate the grating reading and the joint angle to improve the measurement accuracy of the grating measurement system.

[0092] Develop as Figure 3The PC-controlled robot real-time control system shown is based on a PC real-time controller and high-real-time EtherCAT communication. It uses an industrial PLC to implement the control functions of complex control tasks, realizes real-time issuance of control instructions and rapid reception of feedback signals, and builds a robot closed-loop feedback control system.

[0093] The control structure is divided into the upper computer system, the lower computer system and the execution end.

[0094] The upper computer system is used to parse the robot motion NC code. The lower computer serves as the main controller and has functions such as trajectory planning, trajectory interpolation, and kinematic solution. The execution end is the robot drive motor and grating measurement system.

[0095] The grating ruler connects the signal to the system through the EK1100 coupler and EL5042 terminal, realizing the construction of the robot's real-time closed-loop feedback control system.

[0096] S13, the system is integrated into the same control software to ensure the coordination of various components:

[0097] The PC-based robot control decomposes the robot into six motor controls, and integrates the robot control with the end effector and flexible tooling into the same integrated control system, ensuring the coordination of each component and realizing the construction of a robot milling platform for large-size components.

[0098] 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 robot arm motion process;

[0099] In the embodiment, S2 designs a contour error solution method of switching geometric relationship method, calculates the projection factor from the actual position to the theoretical contour, and then ensures the solution accuracy of the contour error value and the contour error target point, combines the traditional geometric contour error solution method with the projection factor, ensures the solution rate while taking into account the solution accuracy, and provides a basis for the Cartesian space contour control link in the double-layer cascade contour control in S3;

[0100] Specifically, a contour error solution method of switching the geometric relationship method is designed, which combines the traditional geometric contour error solution method with the projection shadow to ensure the solution rate while taking into account the solution accuracy, including the following steps:

[0101] S21, discretize the robot's motion path into straight line and circular arc continuous trajectories:

[0102] like Figure 4As shown, the non-parametric path in the robot machining process is difficult to be represented by a function. Using continuous short straight lines to fit the non-parametric path is a common method. The arcs are used to transition between the short straight lines to smooth the trajectory and speed, and then the non-parametric trajectory is transformed into a continuous straight line and arc transition trajectory, providing a basis for the contour error estimation of the proposed switching geometric relationship method.

[0103] S22. The geometric method for solving the contour error combines the projection factor to ensure both the solution rate and the solution accuracy:

[0104] Based on the solution of the contour error of the straight line and arc trajectories, the contour error of the straight line trajectory is:

[0105] c e =-e t sinφ+e n cosφ

[0106] The contour error of the arc trajectory is:

[0107]

[0108] e n and e t are the tracking errors in the n-axis and t-axis directions in the local coordinate system respectively, φ is the angle between the moving tangent direction and the t-axis, and r is the radius of the arc.

[0109] For the non-parametric contour fitted by straight lines and arcs, a projection factor is introduced to improve the accuracy of the contour error point and the solution of the contour error. The projection factor h a is expressed as the difference between the vector connecting the start and end points of the current interpolation segment of the actual point and the vector connecting the start point of the trajectory and the actual point, and is defined as:

[0110]

[0111] p a represents the actual point, L s,i represents the start point of the i-th straight line, and L e,i represents the end point of the i-th straight line. If 0≤h a ≤1, the actual point is located in the projection area of the current straight line segment. If h a <0, the actual point is located before the current straight line segment. If h a >1, the actual point is located after the current straight line segment. Therefore, it is necessary to solve h a+1 to represent the projection factor of the actual point on the next interpolation line segment, and h a-1Indicates the projection factor of the actual point on the previous interpolation line segment, and further determines the interval where the nearest contour error point projected by the actual point is located. Specifically, it can be subdivided into the following three cases:

[0112] Case 1, if 0 ≤ h a ≤ 1, the contour point p c is located on the current straight line segment.

[0113] Case 2, if h a > 1, when 0 ≤ h a+1 ≤ 1, the contour point is located on the next straight line segment, when h a+1 < 0, the contour point is located on the current circular arc segment, when h a+1 > 1, it is necessary to further solve the projection shadow until it is determined that 0 ≤ h a+k ≤ 1 or h a+k < 0, and the position where the contour point is located is determined.

[0114] Case 3, if h a < 0, when 0 ≤ h a-1 ≤ 1, the contour point is located on the previous straight line segment, when h a-1 > 1, the contour point is located on the previous circular arc segment, when h a-1 < 0, it is necessary to further solve the projection shadow until it is determined that 0 ≤ h a-k ≤ 1 or h a-k > 1, and the position where the contour point is located is determined.

[0115] S3. Establish a double - layer cascaded contour error control strategy. This strategy decomposes the flexible - joint manipulator system into a fast subsystem and a slow subsystem through singular perturbation theory, and uses an RBF neural network to predict the dynamic system parameters of the manipulator as the feed - forward term for slow - subsystem control. The inner loop is a flexible - joint tracking controller, which is used to run the control laws of the fast subsystem and the slow subsystem to ensure the tracking accuracy of the flexible - joint manipulator in the joint space. The outer loop is a Cartesian - space contour error controller, which is used to correct the contour error to obtain the corrected contour compensation point to ensure the contour motion accuracy of the manipulator in the Cartesian space;

[0116] In the embodiment, S3 designs a double - layer cascaded contour control method. The inner loop uses an RBF neural network to establish the dynamic model of the manipulator system, decomposes the flexible - joint robot into a fast subsystem and a slow subsystem through singular perturbation theory, and the outer loop combines the contour error estimation to design a Cartesian - space contour error correction link. The structure of the control method is expressed in step S3, and the detailed control method is described below.

[0117] Specifically, a double - level cascade contour control method is designed, a flexible - joint robot model is established. The inner loop decomposes the flexible - joint robot into fast and slow subsystems through singular perturbation theory, and uses an RBF neural network to establish the dynamic model of the manipulator system. The outer loop combines contour error estimation to design a Cartesian - space contour error correction link, including the following steps:

[0118] Structure of the double - level cascade contour error control method:

[0119] As Figure 5 shown in the double - level cascade contour control strategy, the robot motion instruction is input in the form of NC code. Through the trajectory planning module (GCS trajectory planner), the path points are converted into a continuous linear - arc transition form, and the position information and speed information of the output trajectory are obtained. The real - time interpolation module is used to discretize the trajectory to obtain the real - time interpolation Cartesian - space target points, and then the motion reference positions of each joint are obtained through inverse kinematics. The inner loop is a flexible - joint tracking controller, which consists of a speed observer, an RBF neural network prediction model, and a singular perturbation controller, to improve the tracking accuracy and dynamic response ability of the flexible - joint robot. The outer loop is a Cartesian - space contour error controller, which consists of a contour error estimator and a PD controller, and is used to correct the Cartesian - space target contour position.

[0120] Based on the singular perturbation control theory, the flexible - joint robot is decomposed into a fast subsystem and a slow subsystem. The feedback measurement systems are the motor encoder and the 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 as the feed - forward term of the slow - subsystem controller to improve the system dynamic response.

[0121] The flexible - joint robot system is defined as:

[0122]

[0123] In the formula, q1, respectively represent the actual rotation angle position, speed, and acceleration on the link side, q2, respectively represent the actual rotation angle position, speed, and acceleration on the motor side, is the inertia matrix of the robot, is the Coriolis force and centripetal force matrix, represents the gravity - term matrix, K is the equivalent stiffness - coefficient matrix of the flexible joint, J is the diagonal positive - definite matrix of the driving motor at the joint, u is the output torque of the driving motor at the joint, and K(q2 - q1) is the coupling relationship between the link dynamic system and the motor dynamic system. Let the variable x1 = q1, x3 = q2, The state - space expression is defined as:

[0124]

[0125] Based on singular perturbation theory, the system is decomposed, and the perturbation parameter \(0 < \varepsilon < 1\) is defined. Let \(K\) ε \(=\varepsilon K\), and the standard form of the singular perturbation model is obtained:

[0126]

[0127] When \(\varepsilon = 0\), the control torque \(u\) becomes the control law \(u\) of the slow subsystem s , and The slow subsystem is obtained as:

[0128]

[0129] where \(D(q_1)=M(q_1)+J = M(x_1)+J\) is the coupling inertia matrix of the manipulator and the motor. Let the fast time scale \(\tau = t / \varepsilon\), \(t\) is the slow scale time, and \(e\) f is the fast variable, and the fast subsystem of the robot is obtained:

[0130]

[0131] The fast and slow subsystems of the flexible joint robot are obtained.

[0132] Use the RBF neural network to predict the dynamic model parameters:

[0133] The output of the RBF neural network is:

[0134] \(y = w\) T \(h = w_1h_1+w_2h_2+\cdots+w\) m \(h\) m

[0135] where \(w\) is the value of the network, and \(h = [h\) j \) T is the output of the hidden layer.

[0136] The following design is carried out for the dynamic model parameters

[0137]

[0138] is the estimation of the parameters \(D(q_1)\), \(G(q_1)\) by the neural network.

[0139] (1) For the inner-loop joint space tracking controller, control laws are designed for the fast and slow subsystems. The grating encoder is used as the link-side position feedback, and the motor encoder is used as the joint-side position feedback. The tracking accuracy of the link is the premise to ensure the Cartesian space contour accuracy. The stability of the control laws designed for the control system is analyzed using the Lyapunov function method;

[0140] Design the tracking controller for the joint space of the inner-ring flexible joint robot, and design the control laws for the fast subsystem and the slow subsystem, including the following steps:

[0141] 1) The control law for the slow subsystem is:

[0142]

[0143] Let \(S\) define the tracking error of the link position.

[0144]

[0145] \(\Lambda=\text{diag}(\lambda_1,\lambda_2,\ldots,\lambda_{ n )\) is a positive definite matrix and \(\lambda_{ i >0\). \(q_{ 1r \) represents the reference position of \(q_1\). represents the deviation between the reference position and the actual position on the link side. represents the deviation between the reference velocity and the actual velocity on the link side.

[0146] 2) The control law for the fast subsystem is:

[0147]

[0148] \(K_{ v \) is a diagonal positive definite matrix. Design a velocity observer to estimate \({{ }}\) and \(x_4\).

[0149] Design the velocity observer to provide velocity estimation for the perturbation controller, avoiding the error influence caused by directly differentiating the position signal. Among them, \(\eta_1\) and \(\eta_2\) are the observer states, and \(k_1,k_{ 01 ,k_{ 02 \) and \(k_4\) are all observer gains, which are positive constants. and are the observer outputs.

[0150]

[0151] 3) Design the Lyapunov function to analyze the system stability.

[0152] For the tracking controller, define the Lyapunov function:

[0153]

[0154] Among them, Take the derivative of \(V\) to get:

[0155]

[0156] Among them, According to the skew symmetry property of the matrix, and So there is

[0157]

[0158] Combining the slow subsystem and its control law, we get

[0159]

[0160] in

[0161] Combining the above two equations, we get

[0162]

[0163] exist

[0164]

[0165] therefore, is simplified to

[0166]

[0167] By debugging K D Parameters, can guarantee Therefore, the system is asymptotically stable, and the conditions for the asymptotic stability of the system are adjustable.

[0168] (2) The outer loop Cartesian space contour controller (outer loop contour error controller) includes a real-time contour error estimator and a PD controller. It uses a grating to measure the actual joint position and combines it with the forward kinematics of the robot arm to solve the actual end position of the robot, which is then brought into the contour error controller to output the contour error correction and feedback the corrected interpolation output value.

[0169] The outer ring contour error controller includes a real-time contour error estimator and a PD controller, and the controller corrects the interpolation output value and includes the following steps:

[0170] 1) Using the grating measured connecting rod side angle value as input, the forward kinematics model is established using the identified kinematic parameters to obtain the actual position of the end, which is then brought into the contour error solver to obtain the contour error compensation target point p c And solve the contour error

[0171] c =p c -p a .

[0172] 2) Construct a PD controller. For the trapezoidal velocity curve during the linear motion of the robot, decompose the robot's trajectory into acceleration, constant velocity, and deceleration phases, and adopt uniform motion for the circular arc segments. Decompose the robot's motion into four motion phases. Taking [parameters] as the basic parameters and a1 as the acceleration during the acceleration and deceleration phases, adopt different PD parameters for different phases. The constructed parameter relationships are as follows:

[0173]

[0174] The discrete-time control rate of the contour error is

[0175]

[0176] With T = 0.002 s as the operation period, k p as the proportional parameter and k d as the differential parameter, thus obtaining the corrected contour compensation point [p′ d , o′ d = [p d , o d + u, where o d represents the theoretical pose.

[0177] In S4, adopt the contour error solving strategy and the double-loop cascade contour error control strategy of the inner loop and the outer loop to perform double-loop cascade contour control on the robot edge milling processing system.

[0178] Build the above-mentioned robot edge milling processing platform, plan an S-shaped curve in the robot's working space, and use the contour error estimation and contour error control methods proposed by the present invention. The contour error estimation accuracy and contour error control accuracy of the spatial S-shaped curve are as Figure 6 and Figure 7 shown.

[0179] Figure 6 In (a), it shows the comparison between the contour error estimated value solved by the traditional geometric method and the contour error true value and the contour error estimated value solved by the method of the present invention and the contour error true value. (b) shows the estimation error between the two, and (c) shows the estimation error between the two in the form of a heat map. The maximum contour error estimation error of the method proposed by the present invention is 0.3 μm, and the operation time is 0.1 ms. Compared with the maximum contour error of 0.28 mm of the traditional geometric estimation method, this method effectively improves the estimation accuracy. After adopting the control method proposed by the present 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 the joint flexible tracking performance (0.4 mm), the position contour error is improved by more than 90% and 60% respectively, as shown in (a) of Figure 7 . Figure 7In (b), it shows the contour error heat map of the S-shaped curve using this method.

[0180] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention. Any reference signs in the claims should not be construed as limiting the claimed invention.

[0181] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard 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 joint strengthening contour control method for a robot milling system, characterized in that, The control method includes: S1. Build a robotic milling-edge processing system including a flexible process equipment for vacuum adsorption and clamping of large-sized components, a modular and quickly replaceable milling-edge end effector, and a flexible-joint robotic arm with grating feedback. S2. Establish a contour error solving strategy based on the switching geometric method and projection factor to obtain the contour error compensation target points and contour error during the movement of the robotic arm. S3. Establish a double-layer cascaded contour error control strategy for the inner and outer loops. This strategy decomposes the flexible-joint robotic arm system into a fast subsystem and a slow subsystem through the singular perturbation theory, and uses an RBF neural network to predict the dynamic system parameters of the robotic arm as the feedforward term for the slow subsystem control. The inner loop is a flexible-joint tracking controller, which ensures the tracking accuracy of the flexible-joint robotic arm in the joint space based on the control laws of the fast and slow subsystems. The outer loop is a Cartesian-space contour error controller used to correct the contour error and obtain the corrected contour compensation points to ensure the contour motion accuracy of the robotic arm in the Cartesian space. S4. Use the contour error solving strategy and the double-layer cascaded contour error control strategy for the inner and outer loops to perform double-loop cascaded contour control on the robotic milling-edge processing system.

2. The joint strengthening contour control method of a robot milling system according to claim 1, characterized in that The flexible process equipment in S1 includes 20 liftable pogo pins, forming the z-axis of the flexible tooling; every 4 pogo pins are installed on the cross beam and can move on the cross beam guide rail, forming the x-axis movement of the flexible tooling; the cross beam is installed on the longitudinal guide rail, forming the y-axis of the flexible tooling; the flexible tooling can adaptively adjust the tooling state according to the shape of the product to be processed and ensure the stable clamping of the product by vacuum adsorption.

3. The joint strengthening contour control method of a robot milling system according to claim 1, characterized in that The modular end effector in S1 is divided into a fixed end and a quick-change end. The fixed end is installed on the end flange of the robotic arm, connecting the circuit and air circuit from the bottom of the robotic arm; the quick-change end is the actual processing end, equipped with a spindle and a processing milling cutter, with air cooling and dust suction functions; the fixed end and the quick-change end are connected by a quick-change joint, and the air circuit and the circuit are conducted through the quick-change joint to ensure that the quick-change end can be removed integrally without rewiring.

4. The joint strengthening contour control method of a robot milling system according to claim 1, characterized in that The flexible-joint robotic arm in S1 is located on an AGV, and corner feedback grating rulers are installed at each joint of the robotic arm. The grating measurement system calibrates the grating readings and joint angles using a laser tracker measurement system, and real-time feedbacks the non-linear errors caused by joint flexibility during the movement and processing of the robotic arm.

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

6. The joint strengthening contour control method of a robot milling system according to claim 1, characterized in that, The contour error solving strategy based on the switching geometric method and projection factor in S2 is as follows: (1) Based on the switching geometric method, discretize the motion path of the robotic arm into continuous trajectories of straight lines and arcs. (2) Calculate the projection factor, and determine the specific position of the contour point on the straight line segment or circular arc segment according to the projection factor, and use this as the contour error compensation target point; The calculation formula of the projection factor is: Among them, p a represents the actual point, h a represents the projection factor of the actual point on the current interpolation line segment, L s,i represents the starting point of the i-th straight line segment, L e,i represents the end point of the i-th straight line segment; Said according to the projection factor h a Determine the specific position of the straight line segment or circular arc segment where the contour point is located, including: Case 1, if 0 ≤ h a ≤ 1, the contour point is located on the current line segment; Case 2, if h a > 1, when 0 ≤ h a+1 ≤ 1, h a+1 represents the projection factor of the actual point on the next interpolation line segment, then the contour point is located on the next straight line segment. When h a+1 < 0, the contour point is located on the current circular arc segment. When h a+1 > 1, then further solve the projection shadow until 0 ≤ h a+k ≤ 1 or h a+k < 0 to determine the position of the contour point; Case 3, if h a < 0, when 0 ≤ h a-1 ≤ 1, h a-1 represents the projection factor of the actual point on the previous interpolation line segment, then the contour point is located on the previous straight line segment. When h a-1 > 1, then the contour point is located on the previous circular arc segment. When h a-1 < 0, then further solve the projection shadow until 0 ≤ h a-k ≤ 1 or h a-k > 1 to determine the position of the contour point; (3) Calculate the contour error according to the specific position of the contour point on the straight line segment or circular arc segment: If the position where the contour point is located is a straight line segment, the contour error is: c e = -e t sinφ + e n cosφ If the position where the contour point is located is a circular arc segment, the contour error is: where e n and e t are the tracking errors in the directions of the n-axis and the t-axis in the local coordinate system, φ is the angle between the moving tangent direction and the t-axis, and r is the radius of the circular arc.

7. The joint strengthening contour control method of a robot milling system according to claim 1, characterized in that The flexible joint manipulator system is decomposed into a fast subsystem and a slow subsystem through the singular perturbation theory in S3, including: The flexible joint manipulator system is defined as: wherein, respectively represent the actual angular position, velocity and acceleration on the connecting rod side, respectively represent the actual angular position, velocity and acceleration on the motor side, is the inertia matrix of the robotic arm, is the Coriolis force and centripetal force matrix, represents the gravity term matrix, K is the equivalent stiffness coefficient matrix of the flexible joint, J is the diagonal positive definite matrix of the driving motor at the joint, and u is the output torque of the driving motor at the joint; Let the variable x1 = q1, x3 = q2, The state - space expression of the flexible - joint manipulator system is as follows: Decompose the flexible-joint manipulator system based on singular perturbation theory: Define the perturbation parameter \(0 < \varepsilon < 1\), and let \(K\ ε =\varepsilon K\) to obtain the standard form of the singular perturbation model: When ε = 0, the control torque u becomes the control law u of the slow subsystem s , and the slow subsystem is obtained as: In the formula, D(q1) = M(q1) + J = M(x1) + J, which is the coupled inertia matrix of the manipulator and the motor; Let the fast time scale τ = t / ε, where t is the slow-scale time and ε is the fast variable, to obtain the fast subsystem of the robotic arm: f ​ The parameters of the manipulator dynamics system are predicted by using the RBF neural network as follows: The estimation of the parameters of D(q1) by the RBF neural network, G(q1).

8. The joint reinforcement contour control method of a robot milling system according to claim 7, characterized in that The control law of the slow subsystem in S3 is: Where S is the link position tracking error, then: Λ = diag(λ1, λ2, …, λ n ) is a positive definite matrix and λ i > 0, q 1r represents the reference position of q1, represents the deviation between the reference position and the actual position on the connecting rod side, represents the deviation between the reference speed and the actual speed on the connecting rod side; The control law of the fast subsystem is: where K v is a positive definite diagonal matrix; and x4 are obtained by estimation through a speed observer and where η1 and η2 are the observer states, and k1, k 01 , k 02 and k4 are all observer gains.

9. The joint strengthening contour control method of a robot milling system according to claim 1, characterized in that The Cartesian space contour error controller in S3 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 the contour error in the motion process of the manipulator according to the contour error solving strategy; The PD controller compensates the target point p based on the contour error c to solve the contour error ε c = p c - p a , and decomposes the motion of the robotic arm into four motion stages, and different PD parameters are adopted for different stages, specifically as follows: Among them, is the basic parameter, and a1 is the acceleration in the acceleration and deceleration stages; The discrete-time control law of the contour error is: T = 0.002s is the operating period, k p is the proportional parameter, k d is the differential parameter, thus obtaining the corrected profile compensation point [p′ d , o′ d = [p d , o d + u, o d represents the theoretical attitude.

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