A polishing removal error compensation control method considering robot dynamic error

Abstract

The application discloses a polishing removal error compensation control method considering robot dynamic error, the method is used for predicting polishing removal depth by establishing a polishing removal depth prediction model considering robot dynamic error, solves the problem of nonlinearity of side blade contact pressure and relative slip speed distribution when the side blade is processed, breaks through the limitation of traditional Hertz model in narrow space side blade contact mechanics modeling, and realizes accurate prediction of polishing removal amount and surface topography; then, a hierarchical compensation mechanism of offline-online cooperation is proposed, a time-space transmission mechanism of robot error under time-varying dynamics is identified, accurate tracking of deterministic polishing trajectory is realized, and overall component polishing profile accuracy is improved.

Description

Technical Field

[0001] This invention relates to the field of robot grinding and polishing control technology, and in particular to a grinding and polishing removal error compensation control method that takes into account the dynamic error of the robot. Background Technology

[0002] Industrial robots, due to their low stiffness, joint clearances, and frequent posture adjustments, generate dynamic errors during grinding and polishing. Taking the grinding and polishing of an integral impeller as an example, the dynamic error fluctuation at the robot's end effector can reach the millimeter level, resulting in a material removal deviation of more than 30%.

[0003] Existing error compensation methods (such as joint stiffness calibration and geometric error compensation) are based on the assumption of stable operating conditions and do not consider the nonlinear effects of sudden velocity changes and force variations on dynamic errors. Furthermore, current research separates robot kinematic errors from grinding and polishing process parameters (such as contact pressure and feed rate), resulting in insufficient compensation accuracy. Finally, error compensation methods based on offline calibration cannot adapt to frequent pose adjustments within narrow flow channels, and real-time compensation delays lead to residual height deviations.

[0004] In summary, existing technologies lack real-time modeling of the coupling effect between robot dynamic errors and grinding and polishing process parameters, resulting in insufficient compensation accuracy and difficulty in meeting the contour accuracy requirements below 50μm. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a grinding and polishing error compensation control method that considers robot dynamic errors, primarily solving the problem of insufficient compensation accuracy in existing grinding and polishing error compensation methods.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0007] A grinding and polishing removal error compensation control method considering robot dynamic errors includes the following steps:

[0008] Step 1: Analyze the stress distribution in the side cutting area based on the processing constraints of the grinding and polishing tool. Use the stress distribution as the input of the Preston equation to construct a grinding and polishing removal depth prediction model for side cutting and polishing, which is used to predict the grinding and polishing removal depth of a single point in the grinding and polishing task.

[0009] Step 2: Construct a multibody dynamics model and a servo feed model based on the robot's static parameters. Design a dynamic error solver based on the multibody dynamics model and the servo feed model to calculate the dynamic deformation of the structure and the servo following error. Calculate the robot's actual polishing trajectory based on the dynamic deformation of the structure and the servo following error. Calculate the difference between the actual polishing trajectory and the preset polishing trajectory to obtain the dynamic error distribution.

[0010] Step 3: Analyze the offset and pressure center drift law caused by the dynamic error distribution to the side blade cutting area, and construct the mapping relationship between the dynamic error distribution and the grinding and polishing removal depth;

[0011] Step 4: Set up a hierarchical compensation mechanism, which includes an offline global optimization layer and an online dynamic control layer. The offline global optimization layer includes taking the robot's static parameters and the mapping relationship as input, and using a mirror iterative compensation method to cancel and iteratively correct the error between the mirror-symmetric actual grinding trajectory and the preset grinding trajectory to generate a globally optimized compensation trajectory. The online dynamic control layer includes building a model predictive controller based on the offline global optimization layer, taking the dynamic error distribution as a feedforward input, and combining it with the robot's real-time feedback data to form a closed-loop control, and calculating the optimal control input based on the compensation trajectory.

[0012] In some embodiments, the process of obtaining the stress distribution includes:

[0013] A side-edge cutting contact mechanical model was established based on the contact angle and contact area between the grinding and polishing tool and the workpiece. The cutting contact shape and corresponding stress distribution of the side edge with different types of curved surfaces under different tool tilt angles and pressure were analyzed.

[0014] In some implementations, the grinding and polishing removal depth prediction model is:

[0015]

[0016] Where h is the grinding and polishing removal depth, K p denoted as the polishing removal coefficient, p(x,y) is the stress distribution in the side cutting contact area, v(x,y) is the relative velocity between the side cutting edge and the workpiece, Δd is the side cutting edge deformation, α is the side cutting edge deformation coupling coefficient, and ∈(x,y) is the residual formed by the random effect of abrasive particles.

[0017] In some implementations, the construction process of the multibody dynamics model includes:

[0018] Finite element modal analysis and frequency response experiments were used to calibrate the joint stiffness and link flexibility parameters of the robot. The Lagrange equation was constructed to quantify the dynamic deformation of the structure under the coupling action of grinding and polishing forces and inertial forces. Finally, the dynamic deformation of the structure was mapped to the end effector pose.

[0019] In some implementations, the construction process of the servo feed model includes:

[0020] The position loop, velocity loop gain, and friction parameters of the robot servo motor are identified using step response experiments and uniform speed no-load experiments. A dynamic equation for servo following error is constructed. The friction coefficient of the dynamic equation for servo following error is identified using the Coulomb-viscous friction model and no-load experiments. Combined with the preset polishing trajectory and the servo feed model, the servo following error of each axis of the servo motor is predicted.

[0021] In some implementations, the calculation process of the dynamic error distribution includes:

[0022] Based on the preset grinding and polishing trajectory, a command pose and a command velocity are generated, and the reference position of each joint under the command pose and the command velocity is calculated using inverse kinematics.

[0023] The reference position is input into the servo feed model to solve for the actual position of the servo motor and calculate the corresponding servo following error.

[0024] The actual position and the polishing force are input into the multibody dynamics model to obtain the dynamic deformation of the structure;

[0025] By integrating the servo following error and the dynamic deformation of the structure, the actual end-effector pose of the robot is solved using forward kinematics.

[0026] The dynamic error distribution is obtained by comparing the actual end pose with the commanded pose.

[0027] In some implementations, after step 2 is performed, the method further includes taking at least two control parameters among joint state, torque, contact force, and historical error as inputs, outputting error prediction values ​​that are not involved in the modeling of the multibody dynamics model and the servo feed model, and then using a Gaussian process regression algorithm to predict the error residuals of the error prediction values ​​in real time. The error residuals are then fused with the multibody dynamics model and the servo feed model through Kalman filtering.

[0028] The beneficial effects of this invention are as follows: By establishing a grinding and polishing removal depth prediction model that considers robot dynamic errors, the nonlinearity of the side edge contact pressure and relative sliding velocity distribution during side edge processing is solved, overcoming the limitations of the traditional Hertz model in side edge contact mechanics modeling in narrow spaces, and achieving accurate prediction of grinding and polishing removal amount and surface morphology; then, an offline-online collaborative hierarchical compensation mechanism is proposed to identify the spatiotemporal transmission mechanism of robot errors under time-varying dynamics, achieve accurate tracking of deterministic grinding and polishing trajectories, and improve the overall component grinding and polishing contour accuracy. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the grinding and polishing removal error compensation control method that considers robot dynamic errors as disclosed in an embodiment of the present invention.

[0030] Figure 2 This is a schematic diagram of the data flow direction in step 2 of the embodiment of the present invention regarding the dynamic error distribution;

[0031] Figure 3 This is a schematic diagram of trajectory optimization compensation in step 3 of the embodiment of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the content of this invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to this invention are shown in the accompanying drawings, not all of them.

[0033] This embodiment proposes a grinding and polishing removal error compensation control method that considers robot dynamic errors, such as... Figure 1 As shown, it includes the following steps:

[0034] Step 1: Analyze the stress distribution in the side-edge cutting area based on the processing constraints of the grinding and polishing tool. Use the stress distribution as the input of the Preston equation to construct a grinding and polishing removal depth prediction model for side-edge grinding and polishing, which is used to predict the grinding and polishing removal depth of a single point in the grinding and polishing task.

[0035] To improve accessibility, polishing tools often employ side-edge processing during the polishing of narrow flow channels in integral components. However, this method limits the contact angle and area, leading to nonlinear distributions of contact pressure and relative sliding velocity, making it impossible to characterize the cutting contact model using traditional Hertzian contact theory. Therefore, step 1 of this solution obtains the stress distribution in the side-edge cutting contact area and introduces side-edge deformation coupling and abrasive grain random effects to construct a polishing removal depth prediction model. This reveals the coupling law between the polishing tool-workpiece geometry and contact parameters, overcoming the limitations of the traditional Hertzian model in narrow-space side-edge contact and establishing a high-precision contact mechanics model.

[0036] In one example, the process of obtaining the stress distribution described above includes:

[0037] A side-edge cutting contact mechanical model was established based on the contact angle and contact area between the grinding and polishing tool and the workpiece. The cutting contact shape and corresponding stress distribution of the side edge with different types of curved surfaces under different tool tilt angles and pressure were analyzed.

[0038] The Preston equation, after modification, yields the grinding and polishing removal depth prediction model referred to in this scheme. This grinding and polishing removal depth prediction model is as follows:

[0039]

[0040] Where h is the grinding and polishing removal depth, K p denoted as the polishing removal coefficient, p(x,y) is the stress distribution in the side cutting contact area, v(x,y) is the relative velocity between the side cutting edge and the workpiece, Δd is the side cutting edge deformation, α is the side cutting edge deformation coupling coefficient, and ∈(x,y) is the residual formed by the random effect of abrasive particles.

[0041] For the above grinding and polishing removal depth prediction model, the Gaussian process regression algorithm (GPR) is used to identify the residuals formed by the random effects of abrasive particles. GPR can perform nonlinear fitting on the grinding and polishing removal depth prediction model and give the confidence interval of the model output, thereby constructing a grinding and polishing removal depth prediction model that takes into account the uncertainty of grinding and polishing.

[0042] Step 2: Construct a multibody dynamics model and a servo feed model based on the robot's static parameters. Design a dynamic error solver based on these models to calculate the structural dynamic deformation and servo following error. Then, determine the robot's actual polishing trajectory based on these parameters and calculate the difference between the actual and preset polishing trajectories to obtain the dynamic error distribution. The aforementioned robot static parameters may include stiffness, geometric errors, joint clearances, etc. In principle, the more static parameters input, the more refined the constructed multibody dynamics model and servo feed model.

[0043] Dynamic tracking error of the robot is the core issue restricting the accuracy of grinding and polishing. Its root cause can be attributed to two key factors: ① Structural dynamic deformation: Insufficient robot stiffness leads to end-effector pose deviation under the coupling effect of processing force and inertial force, especially at time-varying speeds, where the dynamic deformation changes nonlinearly with acceleration; ② Servo following error: Response delay, parameter mismatch, and nonlinear friction in the servo systems of each axis cause the actual position to deviate from the commanded position, and the error accumulates dynamically with the rate of change of speed. Therefore, step 2 of this solution addresses the problem of large dynamic errors caused by time-varying pose and speed by fusing the body dynamics model and the servo feed model to calculate the dynamic error distribution.

[0044] In one example, the construction process of the above-mentioned multibody dynamics model includes:

[0045] Step 201 involves calibrating the robot's joint stiffness and link flexibility parameters using finite element modal analysis and frequency response experiments. A Lagrange equation is then constructed to quantify the dynamic deformation of the structure under the coupled action of grinding and inertial forces. Finally, the dynamic deformation is mapped to the end effector pose, thus describing the dynamic relationship between joint driving torque and end effector pose. Furthermore, the accuracy of the multibody dynamics model can be verified using experimental data from a laser tracker, forming a complete framework for predicting structural dynamic errors.

[0046] In one example, the construction process of the above servo feed model includes:

[0047] Step 202: The position loop, velocity loop gain and friction parameters of the robot servo motor are identified by step response experiment and uniform speed no-load experiment. The dynamic equation of servo following error is constructed. The friction coefficient of the dynamic equation of servo following error is identified by Coulomb-viscous friction model and no-load experiment. Combined with the preset polishing trajectory and servo feed model, the servo following error of each axis of the servo motor is predicted.

[0048] Based on the aforementioned multibody dynamics model and servo feed model, a dynamic error solver is designed to achieve efficient numerical solution of multiphysics coupled differential equations and obtain the dynamic error distribution, such as... Figure 2 As shown, the calculation process of the dynamic error distribution includes:

[0049] Step 203: Generate command pose and command velocity based on preset grinding and polishing trajectory, and use inverse kinematics to calculate the reference position of each joint under the command pose and command velocity;

[0050] Step 204: Input the reference position into the servo feed model, solve for the actual position of the servo motor, and calculate the corresponding servo following error;

[0051] Step 205: Input the actual position and polishing force into the multibody dynamics model to obtain the dynamic deformation of the structure;

[0052] Step 206: Integrate servo following error and structural dynamic deformation, and solve the robot's actual end-effector pose using forward kinematics.

[0053] Step 207: Compare the actual end-effector pose with the commanded pose to obtain the dynamic error distribution.

[0054] It also includes step 208, which takes at least two of the control parameters among joint state, torque, contact force and historical error as input, outputs the error prediction value that is not involved in the modeling of the multibody dynamics model and the servo feed model, and then uses the Gaussian process regression algorithm to predict the error residual of the error prediction value in real time. The error residual is then fused with the multibody dynamics model and the servo feed model through Kalman filtering.

[0055] Step 3: Analyze the offset caused by the dynamic error distribution to the side blade cutting area and the drift law of the pressure center, and construct the mapping relationship between the dynamic error distribution and the grinding and polishing removal depth.

[0056] Step 3 of this scheme addresses the unclear coupling mechanism between the dynamic error distribution (obtained in step 2) and the grinding and polishing removal depth (obtained in step 1) during the grinding and polishing process. First, it analyzes the impact of dynamic error on key grinding and polishing parameters, and then constructs and verifies the mapping relationship between the dynamic error distribution and the grinding and polishing removal depth.

[0057] Specifically, including:

[0058] Step 301: Based on the dynamic error distribution output by the dynamic error solver, and combined with the grinding and polishing contact mechanics model and geometric contact analysis, analyze the transmission path of dynamic error (end position offset, attitude angle deviation) on grinding and polishing force distribution, tool tilt angle, and dwell time.

[0059] Step 302: Construct a geometric mapping model of the side blade-workpiece contact area based on the above transmission path, and analyze the side blade cutting area offset and pressure center drift caused by dynamic error distribution. The pressure center drift law mentioned above can be quantified by statistical methods.

[0060] Step 303: Based on the offset of the side blade cutting area and the drift law of the pressure center, the accuracy of the above transmission path is verified by comparing the grinding force fluctuation of the preset grinding trajectory (predicted by the theoretical model) with the actual grinding trajectory (obtained by actual measurement) through robot dynamics simulation and static contact simulation.

[0061] Step 304: Input the dynamic error prediction results into the grinding and polishing removal depth prediction model constructed in Step 1 to construct a material removal amount error-robot error coupling mapping model.

[0062] Step 305 focuses on analyzing the changes in the side blade contact area caused by the dynamic error through the grinding and polishing angle offset, as well as the cumulative effect of the removal amount caused by the residence time deviation, and constructs a mapping relationship between the dynamic error distribution and the grinding and polishing removal depth.

[0063] Step 4: Set up a tiered compensation mechanism, which includes an offline global optimization layer and an online dynamic control layer. The offline global optimization layer includes, for example: Figure 3 As shown, the robot's static parameters and mapping relationship are used as inputs. The mirror iterative compensation method is used to cancel and iteratively correct the error between the actual grinding and polishing trajectory and the preset grinding and polishing trajectory, generating a globally optimized compensation trajectory. The online dynamic control layer includes a model predictive controller built on the basis of the offline global optimization layer. The dynamic error distribution is used as the feedforward input and combined with the robot's real-time feedback data to form a closed-loop control, and the optimal control input based on the compensation trajectory is calculated.

[0064] In this step, the difference between the actual polishing trajectory and the preset polishing trajectory can be calculated based on Euclidean distance or normal error.

[0065] In step 4, based on the grinding and polishing removal depth prediction model, a model predictive controller is constructed. This solution takes the MPC controller as an example. Specifically, the model predictive controller includes:

[0066]

[0067] Where, x k+1 To predict the state, x ref For reference trajectory, u k Q and R are weight matrices used to control the input.

[0068] The optimization process of equation (2) first calculates the error change in the next N steps using the grinding and polishing depth prediction model constructed in step 1, and then uses the rolling optimization method to solve for the optimal control input u. k By utilizing error feedback, the MPC control parameters are dynamically adjusted. Different compensation strategies are compared and analyzed to optimize the MPC control parameters and improve the dynamic error compensation effect. Furthermore, by comparing the control performance of different compensation strategies, the parameters of the MPC controller are optimized to ensure the robot's accurate tracking of the deterministic grinding and polishing trajectory. Finally, a collaborative compensation method for offline and online layers based on the error confidence level of the model residual variance is proposed. Weight allocation and adjustment are performed according to the model residual variance to balance the efficiency and accuracy of collaborative compensation.

[0069] The above embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made based on the essence of the content of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A polishing removal error compensation control method considering robot dynamic error, characterized in that, The method comprises the following steps: Step 1: analyzing the stress distribution of the side blade contact area according to the machining and polishing tool processing restricted condition, taking the stress distribution as the input of the Preston equation, and constructing a polishing removal depth prediction model of the side blade polishing for predicting the polishing removal depth of a single point in the polishing task; the polishing removal depth prediction model is: wherein, is the polishing removal depth, is the polishing removal coefficient, is the stress distribution of the side edge contact area, is the relative velocity of the side edge and the workpiece, is the side edge deformation amount, is the side edge deformation coupling coefficient, is the residual error formed by the random effect of the abrasive particles; Step 2: constructing a multi-body dynamics model and a servo feed model according to the robot static parameters, designing a dynamic error solver based on the multi-body dynamics model and the servo feed model, respectively calculating the structural dynamic deformation and the servo following error, and calculating the actual polishing trajectory of the robot according to the structural dynamic deformation and the servo following error, calculating the difference between the actual polishing trajectory and the preset polishing trajectory to obtain the dynamic error distribution; the construction process of the multi-body dynamics model comprises: The joint stiffness and link flexibility parameters of the robot are calibrated by adopting finite element modal analysis and frequency response experiments, the structural dynamic deformation under the coupling action of polishing force and inertial force is quantified by constructing the Lagrange equation, and finally the structural dynamic deformation is mapped to the end position and posture; the construction process of the servo feed model comprises: the position loop, the speed loop gain and the friction parameters of the robot servo motor are identified by adopting step response experiments and uniform speed no-load experiments, the servo following error dynamic equation is constructed, the friction coefficient of the servo following error dynamic equation is identified by adopting the Coulomb-viscous friction model and the no-load experiment, and the servo following error of each axis of the servo motor is predicted in combination with the preset polishing trajectory and the servo feed model; Step 3: analyzing the offset and pressure center drift rule caused by the dynamic error distribution to the side blade contact area, and constructing the mapping relationship between the dynamic error distribution and the polishing removal depth; Step 4: setting a hierarchical compensation mechanism, the hierarchical compensation mechanism comprises an offline global optimization layer and an online dynamic regulation layer, wherein the offline global optimization layer comprises: taking the robot static parameters and the mapping relationship as inputs, and using the mirror iterative compensation method to offset and iteratively correct the mirror-symmetrical actual polishing trajectory and the preset polishing trajectory to generate a globally optimized compensation trajectory, and the online dynamic regulation layer comprises: constructing a model predictive controller based on the offline global optimization layer, taking the dynamic error distribution as a feedforward input, combining with the real-time feedback data of the robot to form a closed-loop control, and calculating the optimal control input based on the compensation trajectory.

2. The polishing removal error compensation control method considering robot dynamic errors according to claim 1, wherein, The stress distribution acquisition process comprises: A side blade contact mechanics model is established based on the contact angle and contact area of the polishing tool and the workpiece, and the contact shape and corresponding stress distribution of the side blade under different tool inclination angles and down pressure are analyzed.

3. The polishing removal error compensation control method considering robot dynamic errors according to claim 1, wherein, The dynamic error distribution calculation process comprises: According to the preset polishing trajectory, an instruction position and an instruction speed are generated, and the reference position of each joint under the instruction position and the instruction speed is calculated by using inverse kinematics; The reference position is input into the servo feed model to solve the actual position of the servo motor, and the corresponding servo following error is calculated; inputting the actual position and the polishing force into the multi-body dynamics model to obtain the structural dynamic deformation; fusing the servo following error and the structural dynamic deformation, and solving the actual end position and posture of the robot by forward kinematics; comparing the actual end position and posture with the command position and posture to obtain the dynamic error distribution.

4. The polishing removal error compensation control method considering robot dynamic errors according to claim 3, wherein, After step 2 is executed, further comprising: inputting at least two control parameters of joint state, torque, contact force and historical error, outputting error prediction value of error not involved in modeling of the multi-body dynamics model and the servo feed model, and then using a Gaussian process regression algorithm to predict error residual of the error prediction value in real time, and fusing the error residual with the multi-body dynamics model and the servo feed model by Kalman filtering.

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