Parallel solving method for calibration of robot measurement-grinding and polishing integrated system

Abstract

The application belongs to the technical field of robot measurement-grinding polishing automation processing, and relates to a parallel solving method for robot measurement-grinding polishing integrated system calibration. The method is based on a measurement-grinding polishing integrated system for large complex component integration, a measurement-component subsystem calibration model is established first, a dual quaternion and SVD are used to solve a rotation matrix and a translation matrix at the same time, and the closed-form solution is used as an initial value for iterative optimization solution to ensure the reliability of the optimization structure. Then, a measurement-machining subsystem calibration model is established, and the fixed pose transformation matrix solved in the measurement-component subsystem calibration model is used as a known quantity, and a re-projection error minimization is used to solve the pose transformation matrix in parallel. The method can effectively complete the collaborative work between multifunctional systems, has high calibration accuracy, and improves the processing quality of the robot measurement-grinding polishing integrated system.

Description

Technical Field

[0001] This invention belongs to the field of robot measurement-grinding and polishing automation technology, and relates to a parallel solution method based on the calibration of an integrated robot measurement-grinding and polishing system. Background Technology

[0002] The grinding and polishing of large and complex components for high-end equipment still relies on manual grinding and polishing. Its advantage lies in its strong adaptability to complex components, but the subjectivity of manual operation leads to poor consistency in grinding and polishing quality. Therefore, there is an urgent need to develop an integrated measurement-grinding and polishing system based on industrial robots. This system would replace human hands with highly flexible and rigid industrial robots, and replace human eyes with non-contact measurement systems that can achieve large-area, high-precision in-situ measurement, thereby realizing intelligent manufacturing of large and complex components.

[0003] Considering the discrepancy between the dimensions of large and complex component blanks after clamping and those of the digital model, direct machining planning based on the digital model is not feasible. In-situ measurement is necessary to obtain the actual shape of the component blank and guide machining. Currently, contact-based measuring devices such as coordinate measuring machines (CMMs), while offering high accuracy, have limited adaptability to complex components and are slow, resulting in poor applicability in intelligent automated machining processes. Non-contact measuring devices, such as structured light scanners, combined with collaborative robots, can perform real-time measurement of complex components across large spaces and areas, enabling automated measurement-polishing machining. Since the robot measurement-polishing integrated system has many sub-units, pose transformation calibration between units is a prerequisite for collaborative measurement-machining operations. The calibration process involves calibrating the pose transformation matrix between the measurement-component-machining integrated units, which is cumbersome, and calibration errors accumulate and amplify with each calibration step. Therefore, achieving accurate calibration of pose transformations between multiple units in the robot measurement-polishing integrated system is a pressing problem that needs to be solved.

[0004] Existing technical literature 1, "A general approach to hand-eye calibration through the optimization of atomic transformations", proposes a method for solving the pose transformation matrix based on the least squares method and uses reprojection error as an indicator to guide the optimization process. It can accurately predict the variance of the hand-eye matrix. However, this method is a step-by-step calibration. In the calibration process, the error of the first step is easily passed to the next step of the calibration process, causing the error accumulation problem, which makes it difficult to control the calibration accuracy of the robot measurement-grinding and polishing automatic processing system.

[0005] Existing technical document 2, "Probabilistic approaches to the AXB = YCZ calibration problem in multi-robot systems", combines the traditional solution method of the AXB = YCZ equation with the probabilistic estimation method of rigid body attitude. The method proposed in this document can reduce the impact of measurement noise on calibration accuracy. However, due to the introduction of a large number of iterative calculations, the solution process is time-consuming and difficult to apply to automated machining systems. Summary of the Invention

[0006] This invention addresses the unique structural requirements and high consistency in grinding and polishing of large, complex components in high-end equipment. It addresses the challenge of conventional CNC grinding machines in achieving CNC grinding of such components by establishing an integrated measurement-grinding / polishing system. A parallel solution algorithm based on minimizing reprojection error is invented to avoid error propagation and accumulation during step-by-step calibration, thereby improving system calibration accuracy. First, an integrated "in-situ measurement-automatic grinding / polishing" system is established, comprising a structured light scanner, a collaborative measurement robot, and a grinding / polishing industrial robot subunit. Second, a calibration model for the measurement-component subsystem is established, converting the pose transformation matrix into a dual quaternion that can simultaneously represent rotation and translation matrices, and performing a closed-form SVD solution. The closed-form calculation result is used as the initial value for iteratively solving the objective function, ensuring the accuracy and reliability of the iterative optimization process. Third, a calibration model for the measurement-machining subsystem is established, combining the minimization of reprojection error in the camera imaging model to solve the pose transformation matrix. This approach considers image point measurement errors while minimizing matrix calculation errors, further improving calibration accuracy. This method can effectively complete collaborative operations between multifunctional systems, and has high calibration accuracy. It has important guiding significance for low-damage grinding and polishing of large and complex components.

[0007] The technical solution adopted in this invention is a parallel solution method based on the calibration of a robot measurement-grinding and polishing integrated system. Its key feature is that, based on a measurement-grinding and polishing integrated system for large and complex components, it first establishes a calibration model for the measurement-component subsystem, using dual quaternions and SVD to simultaneously solve the rotation and translation matrices, and using the aforementioned closed-form solution as the initial value for iterative optimization to ensure the reliability of the optimization structure. Secondly, it establishes a calibration model for the measurement-processing subsystem, using the fixed pose transformation matrix solved in the measurement-component subsystem calibration model as a known quantity, and employs a parallel solution to minimize reprojection error, considering not only the matrix calculation error but also the calculation error of the scanner camera imaging, effectively improving the accuracy of the parallel calibration results. Finally, it achieves high-precision calibration of all global pose transformation matrices of the measurement-grinding and polishing integrated system.

[0008] The specific steps of the method are as follows:

[0009] Step 1: Build an integrated robotic measurement-grinding and polishing system based on non-contact measurement.

[0010] The non-contact measurement-polishing integrated robotic system consists of a collaborative measurement robot (1), a measurement scanner (2), a right camera of the scanner (3), a left camera of the scanner (4), a component clamping device (5), a component to be processed (6), a polishing robot (7), and a tool changer (8). It is divided into an in-situ measurement subunit, a component and clamping subunit, and a polishing subunit. The in-situ measurement subunit, combined with a structured light 3D measurement scanner mounted at the end of a six-degree-of-freedom robotic arm, enables large-space, large-area, and high-precision surface measurement of complex components. The component and clamping subunit handles component clamping and positioning, and provides support for in-situ measurement and polishing. The polishing subunit, composed of an industrial robot and polishing tools, performs polishing trajectory planning, position and attitude high-precision positioning control based on the actual profile of the in-situ measured component, and uses a floating grinding head mounted at the robot's end to perform constant-force polishing of the component. This automated polishing system integrates in-situ measurement, trajectory planning, and conformal polishing functions to achieve automated component polishing, developing an integrated measurement-processing system for large and complex components.

[0011] Step 2: Parallel solution of pose transformation matrix between measurement and component subsystems

[0012] 1) Establish a calibration model for the measurement-component subsystem.

[0013] A calibration model between the measurement and component subsystems is established based on a collaborative measurement robot, a structured light scanner, components, and a clamping device. After the component is fixed on the clamping device, marking points are affixed to the fixing column of the clamping device. The structured light 3D scanner is fixed to the end effector of the collaborative measurement robot and adjusted accordingly. Secondary robot pose, obtain Group scan measurement data, and The pose transformation relationship of the end effector of the collaborative robot relative to the base coordinate system is measured.

[0014] based on Set up measurement data and establish a base coordinate system for the collaborative robot. To the coordinate system of the end flange of the collaborative robot The pose transformation matrix is ​​A, and the coordinate system of the marked points on the fixed column of the clamping device is... To the scanner coordinate system The pose transformation matrix is ​​B, and the coordinate system of the end flange of the collaborative robot is measured. To the scanner coordinate system The pose transformation matrix is ​​X, and the measurement coordinate system of the collaborative robot is [missing information]. coordinate system of the marked point on the fixed column of the clamping device Let Y be the pose transformation matrix. The relationship between the pose transformation matrix of the collaborative robot and its components is constructed as follows:

[0015] (1)

[0016] in, , In order to be in The pose transformation matrix from the base coordinate system to the end flange coordinate system of the collaborative robot in each pose can be obtained from the forward kinematics of the collaborative robot. , It can be measured by collaborative robots. The coordinates of the calibration points acquired by the scanner in each pose can be used to solve the pose transformation matrix after the scanner reads the data.

[0017] 2) Parallel solution of model pose transformation matrix

[0018] Based on the calibration model of the collaborative robot-component subsystem, dual quaternions and iterative solving are used to solve the rotation and translation matrices in the pose transformation matrix in parallel. This avoids the error in the rotation matrix calculation during the sequential solution process from being introduced into the translation matrix calculation process, thus preventing the accumulation and amplification of errors in the calibration results. The pose transformation matrix in the model can be decomposed into two parts: the rotation matrix R and the translation matrix t. According to equation (1), we can obtain:

[0019] (2)

[0020] In the formula, These are the base coordinate systems for measuring collaborative robots. To the coordinate system of the end flange of the collaborative robot The rotation and translation matrices of the pose transformation matrix A are obtained by measuring the forward kinematics of the collaborative robot; The coordinate system of the marked points on the fixed column of the clamping device is respectively To the scanner coordinate system The rotation and translation matrices of the pose transformation matrix B can be calculated by scanning the point cloud. These are the coordinate systems of the end flange of the collaborative robot. To the scanner coordinate system The rotation and translation matrices of the pose transformation matrix X; The base coordinate system for measuring collaborative robots on components. coordinate system of the marked point on the fixed column of the clamping device The rotation and translation matrices of the pose transformation matrix Y.

[0021] By expanding the homogeneous transformation matrix of equation (2), we can derive:

[0022] (3)

[0023] (4)

[0024] To simultaneously solve for the rotation matrix R and translation matrix t of the pose transformation matrix, dual quaternions can be used to represent spatial rotation and translation simultaneously. The dual quaternion form of the pose transformation matrix is: ,in These are rotation unit quaternions and translation unit quaternions, respectively. For dual operators, satisfying Therefore, the homogeneous transformation matrices in equations (3) and (4) can be expressed in dual quaternion form as follows:

[0025] (5)

[0026] (6)

[0027] In the formula, These are the rotation unit quaternion and translation unit quaternion of the pose transformation matrix A, respectively. These are the rotation unit quaternion and translation unit quaternion of the pose transformation matrix B, respectively. These are the rotation unit quaternion and translation unit quaternion of the pose transformation matrix X, respectively. These are the rotation unit quaternion and translation unit quaternion of the pose transformation matrix Y, respectively.

[0028] Simplifying equations (5) and (6), we get:

[0029] (7)

[0030] Due to the movement of the calibration measurement robot Second, scanner acquisition The coordinates of the marker point under the next pose are therefore multiple sets of data. The multiple sets of measurements in equation (7) will be solved. Recorded as Unknown quantities to be determined Let q be the denoted q, then equation (7) can be simplified to:

[0031] (8)

[0032] in, It is a matrix composed of the dual quaternions of pose transformation matrices A and B. It is a matrix composed of the dual quaternions of the pose transformation matrices X and Y, and then the matrix is... Perform SVD decomposition, combined with dual quaternion constraints. It can simultaneously solve for the rotation unit quaternion and translation unit quaternion corresponding to the pose transformation matrices X and Y, denoted as , and used as the initial value for iterative solution.

[0033] Since the closed-loop solution process is easily affected by environmental disturbances and is therefore unstable, an iterative optimization solution method is adopted, and the closed-loop solution results are used. As initial values ​​for iterative solution, this improves the stability of the solution process and accelerates the convergence speed. First, the corresponding objective function is established. ,for The pose of the collaborative robot is measured, and the optimal cost function is constructed based on equations (5) and (6):

[0034] (9)

[0035] The objective function is solved using the LM method, and the result obtained in equation (8) is used as the initial value for the iterative solution process. Given initial parameter values, then follow the algorithm's iteration step size. Perform iterations:

[0036] (10)

[0037] In the formula, s is the number of iterations; let , For the objective function Jacobian matrix with respect to x; The damping coefficient; Let be the identity matrix. Solve using LM iteration; stop iterating when the iteration step size meets the condition, and output the objective function. optimal solution Then according to the formula Find the dual quaternions of pose transformation matrices X and Y, and convert the dual quaternions into pose transformation matrices to obtain the coordinate system of the end effector flange of the collaborative robot. To the scanner coordinate system Pose transformation matrix X, measuring the base coordinate system of the collaborative robot coordinate system of the marked point on the fixed column of the clamping device Pose transformation matrix Y.

[0038] Step 3: The measurement-machining subsystem optimizes the parameters based on minimizing the reprojection error.

[0039] 1) Establish a calibration model for the measurement collaborative robot-grinding and polishing subsystem.

[0040] A calibration model of the measurement-machining subsystem is established based on a collaborative measurement robot, a grinding tool, and a polishing robot. First, a model of the pose transformation relationship between the collaborative measurement robot, the scanner, the polishing robot, and the grinding tool is established. A calibration plate is placed at the end effector of the polishing tool on the industrial robot, and a structured light 3D scanner is fixed to the end effector of the collaborative measurement robot. The model is then modified... The collaborative robot's pose is measured, and the grinding and polishing industrial robot changes accordingly. The pose of the secondary grinding and polishing robot was obtained. Group scanning calibration plate measurement data, simultaneously acquire Group measurement of the pose transformation relationship of the end effector of the collaborative robot relative to the base coordinate system and The pose transformation relationship of the end effector of the grinding and polishing industrial robot relative to the base coordinate system.

[0041] Based on n sets of measurement data, let the base coordinate system of the collaborative measurement robot be defined. To the coordinate system of the end flange of the collaborative robot Let the pose transformation matrix be A, and the scanner coordinate system be... coordinate system of end-effector grinding tools in industrial grinding and polishing robots The pose transformation matrix is ​​D, and the base coordinate system of the grinding and polishing industrial robot is... To the end flange coordinate system of the grinding and polishing industrial robot The pose transformation matrix is ​​E, and the coordinate system of the end flange of the grinding and polishing industrial robot is... coordinate system of end-effector grinding tools in industrial grinding and polishing robots The pose transformation matrix is ​​P, and the measurement coordinate system of the collaborative robot is [missing information]. To the base coordinate system of the grinding and polishing industrial robot The pose transformation matrix is ​​Z, which is derived from the coordinate system of the end flange of the collaborative robot obtained from the calibration model of the collaborative robot-component subsystem in step 2. To the scanner coordinate system The pose transformation matrix X is fixed and does not change with the movement of the measurement collaborative robot. Therefore, matrix X is used as a known quantity in solving the calibration model of the measurement-machining subsystem, and the pose transformation matrix relationship between the measurement-machining system is constructed as follows:

[0042] (11)

[0043] in, , To measure the base coordinate system of a collaborative robot in n poses To the coordinate system of the end flange of the collaborative robot The pose transformation matrix can be obtained by measuring the forward kinematics of the collaborative robot. , Let the base coordinate system of the grinding and polishing industrial robot be defined in n poses. To the end flange coordinate system of the grinding and polishing industrial robot The pose transformation matrix can be obtained from the forward kinematics of the grinding and polishing industrial robot; , To measure the coordinate system of the scanner as the collaborative robot moves n times. coordinate system of end-effector grinding tools in industrial grinding and polishing robots The pose transformation matrix can be solved by reading data from the scanner; matrix X is obtained from the measurement collaborative robot-component subsystem calibration model in step 2 and is used as a known quantity in the measurement-machining system calibration model; P is the coordinate system of the end flange of the grinding and polishing industrial robot. coordinate system of end-effector grinding tools in industrial grinding and polishing robots Pose transformation matrix; Z is the base coordinate system of the collaborative robot. To the base coordinate system of the grinding and polishing industrial robot Pose transformation matrix.

[0044] Let G be the known quantity on the left side of equation (11), that is... and order Equation (11) can be written as:

[0045] (12)

[0046] In the formula, the pose transformation matrices A and E can be directly obtained by reading and calculating from the teach pendant based on the forward motion of the collaborative robot and the grinding and polishing industrial robot. The pose transformation matrix D can be solved by the scanner measurement data. The pose transformation matrix X between the end flange and the tool of the collaborative robot is obtained from step 2, and the two are rigidly fixed.

[0047] 2) Solving the parameter optimization model based on minimizing reprojection error

[0048] Due to the actual position coordinates of a point in space under the world coordinate system Calculated values ​​on the imaging plane of the scanner camera There is an error The optimal pose transformation matrix is ​​solved by minimizing the projection error, where K is the intrinsic parameter of the scanner camera and T is the pose transformation matrix between the scanner coordinate system and the world coordinate system. Equation (12) is solved by minimizing the reprojection error parameter optimization method, and the cost function is minimized. To simultaneously solve for the rotation matrix of pose transformation matrix Q and Z Translation matrix ,make Based on equation (12), the objective function for minimizing reprojection error is constructed as follows:

[0049] (13)

[0050] In the formula, To measure the number of moves of the collaborative robot; k is the number of checkerboard grid points on the calibration plate of the grinding tool within the scanner's field of view; Let be the actual position coordinates of the k chessboard grid points measured in the world coordinate system at the j-th pose. Let d be the pixel coordinates of the measurement point projected onto the scanner camera's imaging plane, and d be the depth of the measurement point in the scanner coordinate system.

[0051] Repeat step 2 of the parallel solution algorithm to obtain the pose transformation matrix in equation (12) based on the dual quaternion closed-form solution method. And as the initial value of the objective function to minimize the reprojection error, given parameters d and K, for the minimized objective function The coordinate system of the end flange of the grinding and polishing industrial robot is obtained by performing LM iterative solution. coordinate system of end-effector grinding tools in industrial grinding and polishing robots Pose transformation matrix and measuring the base coordinate system of collaborative robots To the base coordinate system of the grinding and polishing industrial robot Pose transformation matrix Z.

[0052] Step 4, Global calibration based on the robot measurement-grinding and polishing integrated system

[0053] First, based on the established robot measurement-grinding and polishing integrated system, the pose transformation relationships between various devices in the integrated system are obtained according to the solution results of the calibration models of the measurement-component subsystem and the measurement-processing subsystem. Then, the complete profile of the measured component 6, guided by the measurement collaborative robot 1 and the scanner 2, is transformed into the coordinate system of the end flange of the measurement collaborative robot through the pose transformation matrix X. The coordinates are then transformed to the base coordinate system of the collaborative measurement robot via the pose transformation matrix A. The system then plans the grinding and polishing trajectory for different areas based on the component's structure and shape. This planned trajectory is then transformed into a readable processing path by the grinding and polishing robot 7. Finally, the processing path is converted to the robot's base coordinate system using the pose transformation matrix Z. The coordinates are then transformed to the end-effector coordinate system of the grinding and polishing industrial robot based on the pose transformation matrices E and P. Next, the data between the measurement, component and processing sub-units is unified to realize multi-functional collaborative processing; finally, the processing path is input into the control terminal of the grinding and polishing industrial robot and the processing speed and acceleration are set to realize automatic grinding and polishing processing of the robot measurement-grinding and polishing integrated system.

[0054] The significant effects and benefits of this invention are as follows: Based on the constructed integrated measurement-grinding and polishing system, the proposed parallel solution algorithm employs dual quaternions to simultaneously represent the rotation and translation matrices of the pose transformation relationship during the calibration process of the measurement-component subsystem model. This avoids the cumulative effect of errors during the sequential solution of matrices. Combined with the closed-loop solution of the calibration model using SVD, and using the above results as the initial value for the iterative solution of the objective optimization function, a reliable initial point is provided for the objective function, avoiding the optimization solution from getting trapped in local optima. Simultaneously, the fixed pose transformation matrix solved in the measurement-component subsystem calibration model is applied to the calibration process of the measurement-processing subsystem model. The initial value of the objective function is calculated using a closed-loop solution method. Combined with the camera imaging principle, a coordinate transformation relationship for solving the objective function based on minimizing reprojection error is established. This not only considers the calculation error of the matrix but also the measurement error of the scanner camera imaging, effectively improving the accuracy of the parallel calibration results. This enables accurate robotic hand-eye collaborative processing of large and complex components in the constantly changing in-situ measurement-automatic grinding and polishing system. This method, based on simultaneously solving the rotation and translation matrices of the pose transformation relationship, introduces the minimization of reprojection error for optimization, coordinates the operational stability of in-situ measurement and grinding and polishing, can effectively complete collaborative operations between multifunctional systems, give full play to the performance of automated processing, and thus improve the processing quality of the robot measurement-grinding and polishing integrated system. Attached Figure Description

[0055] Figure 1 —Flowchart of a parallel solution method based on the calibration of a robot measurement-grinding and polishing integrated system.

[0056] Figure 2 —Model diagram of a robot measurement-grinding and polishing integrated system based on non-contact measurement; where 1—measuring collaborative robot, 2—measuring scanner, 3—right camera of scanner, 4—left camera of scanner, 5—component clamping device, 6—component to be processed, 7—grinding and polishing robot, 8—tool changer.

[0057] Figure 3 —Measurement-component subsystem model diagram; where Oxyz is the world coordinate system and A is the base coordinate system of the measurement collaborative robot. To the coordinate system of the end flange of the collaborative robot The pose transformation matrix, X—the coordinate system of the end flange of the collaborative robot. To the scanner coordinate system The pose transformation matrix, B—coordinate system of the marked points on the fixed column of the clamping device. To the scanner coordinate system The pose transformation matrix, Y—the base coordinate system of the collaborative robot. coordinate system of the marked point on the fixed column of the clamping device The pose transformation matrix.

[0058] Figure 4 —Diagram of the measurement-machining subsystem; where Oxyz is the world coordinate system and A is the base coordinate system of the measurement collaborative robot. To the coordinate system of the end flange of the collaborative robot The pose transformation matrix, X—the coordinate system of the end flange of the collaborative robot. To the scanner coordinate system Pose transformation matrix, D-scanner coordinate system coordinate system of end-effector grinding tools in industrial grinding and polishing robots P—pose transformation matrix of the end flange coordinate system of the grinding and polishing industrial robot coordinate system of end-effector grinding tools in industrial grinding and polishing robots The pose transformation matrix, E—base coordinate system of the grinding and polishing industrial robot. To the end flange coordinate system of the grinding and polishing robot The pose transformation matrix, Z—the base coordinate system of the collaborative robot. To the base coordinate system of the grinding and polishing industrial robot The pose transformation matrix.

[0059] Figure 5 —Schematic diagram of reprojection error calculation principle; where Oxyz —world coordinate system. —Scanner coordinate system P—Measurement point in the world coordinate system —The pixel projected by point P onto the imaging plane of the scanner's left camera. —The pixel projected by point P onto the imaging plane of the scanner's right camera. —The calculated number of pixels, e—reprojection error, which is the number of pixels projected onto the imaging plane by the measurement point. and the calculated pixel points The difference, R, T—are the rotation and translation matrices of the pose transformation matrix from the scanner coordinate system to the world coordinate system, respectively. Detailed Implementation

[0060] The specific embodiments of the present invention are described in detail below with reference to the technical solutions and accompanying drawings.

[0061] Because the robot measurement-grinding and polishing integrated system has many sub-units, the calibration accuracy of the pose transformation matrix between each functional unit directly affects the machining accuracy. To solve this problem, achieve accurate calibration between functional units, and improve the quality of automated machining, a parallel solution method based on the calibration of the robot measurement-grinding and polishing integrated system is invented.

[0062] Appendix Figure 1This is a flowchart of a parallel solution method for calibration based on a robot measurement-grinding and polishing integrated system, as per the present invention. Figure 2 This is a model diagram of a robot measurement-grinding and polishing integrated system. (According to the attached diagram...) Figure 1 The overall process of the method shown involves parallel solution of the calibration model of the robot measurement-grinding and polishing integrated system. The specific steps of the method process are as follows:

[0063] Step 1: Build a robot measurement-grinding and polishing integrated system based on non-contact measurement.

[0064] The non-contact measurement robot-grinding and polishing integrated system consists of a collaborative measurement robot 1, a measurement scanner 2, a right camera of the scanner 3, a left camera of the scanner 4, a component clamping device 5, a component to be processed 6, a grinding and polishing robot 7, and a tool changer 8. It is divided into an in-situ measurement subunit, a component and clamping subunit, and a grinding and polishing subunit, as shown in the attached diagram. Figure 2 As shown. The component and clamping subunit is used to fix and position the components. A ground rail is designed at the bottom to accommodate components of different sizes. It also has rotation and flipping functions to adapt to the full-surface grinding and polishing of complex components. The in-situ measurement subunit includes a collaborative measurement robot, a structured light 3D scanner, a computer, and other components. The structured light 3D measurement scanner is installed at the end effector of the six-degree-of-freedom collaborative measurement robot to expand the scanner's field of view, enabling in-situ measurement of large-sized components. The grinding and polishing subunit includes an industrial robot, an end-effector grinding tool, a tool changer, and other components. Combining the high degrees of freedom, large workspace, and strong flexibility of serial robots, the grinding tool is integrated into the end effector of the six-degree-of-freedom industrial robot, enabling efficient processing of large and complex components.

[0065] Step 2: Parallel solution of pose transformation between measurement and component subsystems

[0066] First, the pose transformation matrix of the measurement-component subsystem is calibrated. A schematic diagram of the pose transformation between subsystems is attached. Figure 3 As shown, marking points are affixed to the fixed column in the clamping fixture, and then the structured light 3D scanner fixed to the end of the measuring collaborative robot is used to change the position. The robot's pose was then assessed, and point cloud data of scanned marker points were acquired in five different poses. It can be read by computer-controlled scanner software, and the pose transformation matrix can be solved using the PnP algorithm. ,according to Obtain the coordinate system of the marked points on the fixed column of the clamping device. To the scanner coordinate system Pose transformation matrix B; and 5 sets of coordinate systems for the end effector of the collaborative measurement robot. Relative to the base coordinate system of the collaborative robot attitude The pose transformation matrix can be obtained by measuring the forward kinematics of the collaborative robot. ,through Calculate the base coordinate system of the collaborative robot To the coordinate system of the end flange of the collaborative robot Pose transformation matrix A.

[0067] Then, based on the point cloud data of the 5 sets of scanned marker points... Robot end-effector pose data The corresponding 5 sets of pose transformation matrices were obtained respectively. and Further calculate multiple sets of relative motion matrices A and B between adjacent measured poses, and substitute matrices A and B into formula (1) to obtain a two-variable linear equation for the pose transformation matrix between the measurement and the component. Relationship with dual quaternion transformation The pose transformation matrices A and B can be converted into dual quaternion form as follows: ,

[0068] The transformation matrix calculated from the five pose measurements of the collaborative robot Substituting into equation (7), for the matrix Perform singular value decomposition ,because Given that, the left singular matrix can be obtained. Right singular matrix and eigenvalues The column vectors with zero singular values ​​in the right singular matrix Substituting into equation (8) yields Combining the properties of dual quaternions Initial values ​​can be solved simultaneously .

[0069] Will As the initial value for the iterative solution of equation (9), the LM iterative solution is then performed according to the algorithm iterative step size equation (10). When the iterative step size is small enough, the iteration stops and the objective function is output. optimal solution The specific solution process is as follows:

[0070] 1) Given initial values Find the Jacobian matrix. Damping coefficient , Take 10 -6 Termination conditions The initial number of iterations s=0, and the coefficients .

[0071] 2) When termination condition 1 is met: If the distance to the target is too far, it means that the next step size needs to be calculated. If the step size satisfies termination condition 2: This indicates that even if termination condition 1 is not met, the iteration step size is already small enough, and the optimal result can be determined at this point; when termination condition 1 is met: If the condition is met, it means the function has reached its optimal state and the optimal result has been obtained; otherwise, continue to step 3).

[0072] 3) Calculate the new step size ,in Damping coefficient It also needs to be updated, including The adjustment is made by the gain rate To control, if This indicates that the optimization effect is good, and the updated damping coefficient is: ;like This indicates that the optimization effect has deteriorated, and the damping coefficient has been updated to: Then return to step 2) to continue iterating until the condition is met.

[0073] Finally, based on the five sets of calibration data collected in the specific embodiment, the rotation matrix of the unknowns in the measurement-component subsystem calibration model was solved using the dual quaternion and LM method iterative solution method. Translation matrix Parallel solution, then according to the formula Find the dual quaternions of pose transformation matrices X and Y, and convert the dual quaternions into pose transformation matrices to obtain the coordinate system of the end effector flange of the collaborative robot. To the scanner coordinate system Pose transformation matrix X, measuring the base coordinate system of the collaborative robot coordinate system of the marked point on the fixed column of the clamping device Pose transformation matrix Y.

[0074] Step 3: Optimize the parameters of the measurement-machining subsystem based on minimizing reprojection error.

[0075] First, establish a model of the pose transformation relationship between the collaborative measurement robot, the measurement scanner, the grinding and polishing industrial robot, and the grinding tools, such as... Figure 4 As shown. A calibration plate is placed at the end of the industrial robot's grinding tool, and a structured light 3D scanner is fixed to the end of the collaborative robot for measurement. The calibration plate is then adjusted. The pose of the collaborative robot was measured, and five sets of coordinate systems of the robot's end effector under different poses were obtained. Relative to the base coordinate system of the collaborative robot attitude The pose transformation matrix can be obtained by measuring the forward kinematics of the collaborative robot. ,through The pose transformation matrix A is calculated; the scanner measures the point cloud data of the calibration plate. The pose transformation matrix is ​​obtained by directly linearly transforming the point cloud data read by the computer-based scanner control software. ,through The pose transformation matrix D is calculated. The grinding and polishing industrial robot changes its pose five times accordingly, and five sets of coordinate systems of the end flange of the grinding and polishing industrial robot are obtained. Relative to the base coordinate system of grinding and polishing industrial robots attitude Five pose transformation matrices can be obtained from the forward kinematics of the grinding and polishing industrial robot. ,through The pose transformation matrix E is calculated. Since the pose transformation relationship X between the end flange coordinate system of the measurement collaborative robot and the scanner coordinate system is fixed, and the matrix X is obtained from the measurement-component subsystem calibration model, it is used as a known quantity in the measurement-machining system calibration model.

[0076] Then, following the parallel solution method of dual quaternions in step two, the obtained pose transformation matrices A, D, E, and X are substituted into equation (12), where G = AXD, to perform a closed-form solution for the pose transformation model of the measurement-machining subsystem in equation (12). First, the pose transformation matrix corresponding to equation (12) is converted into dual quaternion form. Establish the matrix equations formed by the five movements of the measuring robot and the grinding and polishing industrial robot. Then for the matrix Perform singular value decomposition By combining the properties of dual quaternions, the solution can be obtained simultaneously. Then the dual quaternion is converted into a pose transformation matrix. The pose transformation matrix is ​​obtained by calculating the closed-form result. As the initial values ​​of the parameter optimization model for minimizing reprojection error, and given the initial parameters d and K, the LM method is used to solve formula (13). According to the LM method solution process in step two, based on the five sets of calibration data collected in the specific embodiment, the coordinate system of the end flange of the grinding and polishing industrial robot is obtained. coordinate system of end-effector grinding tools in industrial grinding and polishing robots Pose transformation matrix and measuring the base coordinate system of collaborative robots To the base coordinate system of the grinding and polishing industrial robot Pose transformation matrix Z.

[0077] Step 4: Global Calibration of the Robot Measurement-Grinding and Polishing Integrated System

[0078] Based on the global pose transformation matrix calibration model of the measurement-grinding and polishing integrated system in steps one through three, and targeting complex components to be processed, the measurement collaborative robot 1 first guides the measurement scanner 2 to scan the marked points on the fixed column of the clamping device 3 multiple times to obtain the measurement mark point data and the movement posture of the measurement collaborative robot. The base coordinate system of the measurement collaborative robot can then be calculated. To the end flange coordinate system Pose transformation matrix A, coordinate system of marker points on the fixed column of the clamping device To the scanner coordinate system The pose transformation matrix B is used to solve the coordinate system of the end flange of the collaborative robot using the measurement-component subsystem calibration model. To the scanner coordinate system The pose transformation matrix X will transform the scanner coordinate system. The actual profile point cloud data of the component measured by the downscan is converted to the base coordinate system of the measurement collaborative robot. Based on the measured point cloud data, combined with the component structure and shape, the zonal grinding and polishing trajectory is planned and then set as a processing path that can be read by the control system of the grinding and polishing robot 5. Then, the measurement collaborative robot 1 guides the measurement scanner 2 to scan the calibration plate on the end-effector of the grinding and polishing industrial robot multiple times to obtain the measurement calibration plate data and the movement posture of the measurement collaborative robot and the grinding and polishing robot. According to the calculation, the base coordinate system of the measurement collaborative robot can be obtained. To the coordinate system of the end flange of the collaborative robot Pose transformation matrix A, base coordinate system of grinding and polishing industrial robot To the end flange coordinate system of the grinding and polishing industrial robot The pose transformation matrix E is used to solve the coordinate system of the end flange of the grinding and polishing industrial robot using the calibration model of the measurement-machining subsystem. coordinate system of end-effector grinding tools in industrial grinding and polishing robots Pose transformation matrix P, measuring the base coordinate system of the collaborative robot To the base coordinate system of the grinding and polishing industrial robot The pose transformation matrix Z transforms the robot processing path in the scanner coordinate system to the end coordinate system of the grinding and polishing industrial robot 5 grinding tool. The transformation matrix Z is then input into the grinding and polishing industrial robot controller, and the processing speed and acceleration are set to realize in-situ measurement and automatic grinding and polishing functions, ultimately forming a robot measurement-grinding and polishing integrated processing system.

[0079] In summary, the parallel solution method based on the calibration of the robot measurement-grinding and polishing integrated system proposed in this invention provides a foundation for in-situ measurement-grinding and polishing, enabling the determination of pose transformation relationships between devices such as the end effector of the measurement collaborative robot and the scanner, the scanner and the component, and the scanner and the end effector of the grinding and polishing industrial robot. This method, based on simultaneously solving the rotation and translation matrices of the pose transformation relationships, introduces the minimization of reprojection error for optimization, coordinating the operational stability of in-situ measurement and grinding and polishing, fully leveraging the performance of automated processing, and thus improving the processing quality of the robot measurement-grinding and polishing integrated system.

Claims

1. A parallel solution method based on the calibration of a robot measurement-grinding and polishing integrated system, characterized in that, This method is based on an integrated measurement-grinding and polishing system for large and complex components. First, a calibration model for the measurement-component subsystem is established. Dual quaternions and SVD are used to simultaneously solve for the rotation and translation matrices. A closed-form solution is used as the initial value for iterative optimization to ensure the reliability of the optimized structure. Second, a calibration model for the measurement-machining subsystem is established. Using the fixed pose transformation matrix solved in the measurement-component subsystem calibration model as known quantities, the pose transformation matrix is ​​solved in parallel by minimizing the reprojection error. Finally, high-precision calibration of all global pose transformation matrices of the integrated measurement-grinding and polishing system is achieved. The specific steps of the method are as follows: Step 1: Build a robot measurement-grinding and polishing integrated system based on non-contact measurement. The non-contact measurement robot measurement-grinding and polishing integrated system consists of a measurement collaborative robot (1), a measurement scanner (2), a scanner right camera (3), a scanner left camera (4), a component clamping device (5), a component to be processed (6), a grinding and polishing robot (7), and a tool changer (8). It is divided into an in-situ measurement subunit, a component and clamping subunit, and a grinding and polishing processing subunit. The in-situ measurement subunit, combined with a structured light 3D measurement scanner mounted at the end of a six-degree-of-freedom robotic arm, enables large-space, large-area, and high-precision surface measurement of complex components. The component and clamping subunit enables component clamping and positioning, and provides support for in-situ measurement and grinding / polishing. The grinding / polishing subunit consists of a grinding / polishing robot and grinding tools. Based on the actual profile of the in-situ measured component, it performs grinding / polishing trajectory planning, position and attitude high-precision positioning control, and a floating grinding head mounted at the end of the robot performs constant-force grinding of the component. The automatic grinding / polishing system integrates in-situ measurement, trajectory planning, and conformal grinding functions to realize automatic grinding / polishing of components, and develops an integrated measurement-processing system for large and complex components. Step 2: Parallel solution of pose transformation matrix between measurement and component subsystems 1) Establish a calibration model for the measurement-component subsystem. A calibration model between the measurement and component subsystems is established based on a collaborative measurement robot, a structured light scanner, components, and a clamping device. After the component is fixed on the clamping device, marking points are affixed to the fixing column of the clamping device. The structured light 3D scanner is fixed to the end effector of the collaborative measurement robot by changing... Secondary robot pose, obtain Group scan measurement data, and The pose transformation relationship of the collaborative robot's end effector relative to the base coordinate system was measured. based on Set up measurement data and establish a base coordinate system for the collaborative robot. To the coordinate system of the end flange of the collaborative robot The pose transformation matrix is ​​A, and the coordinate system of the marked points on the fixed column of the clamping device is... To the scanner coordinate system The pose transformation matrix is ​​B, and the coordinate system of the end flange of the collaborative robot is measured. To the scanner coordinate system The pose transformation matrix is ​​X, and the measurement coordinate system of the collaborative robot is [missing information]. coordinate system of the marked point on the fixed column of the clamping device Let Y be the pose transformation matrix. The relationship between the pose transformation matrix of the collaborative robot and its components is constructed as follows: (1) in, , In order to be in The pose transformation matrix from the base coordinate system to the end flange coordinate system of the collaborative robot in each pose is obtained from the forward kinematics of the collaborative robot. , It can be measured by collaborative robots. The coordinates of the calibration points acquired by the scanner in each pose are used to solve the pose transformation matrix after the scanner reads the data. 2) Parallel solution of model pose transformation matrix Based on the calibration model of the collaborative robot-component subsystem, dual quaternions and iterative solutions are used to solve the rotation and translation matrices in the pose transformation matrix in parallel, avoiding the introduction of rotation matrix calculation errors into translation matrix calculations during sequential solutions, thus preventing the accumulation and amplification of calibration results errors. The pose transformation matrix in the model can be decomposed into two parts: rotation matrix R and translation matrix t, which are obtained according to equation (1): (2) In the formula, These are the base coordinate systems for measuring collaborative robots. To the coordinate system of the end flange of the collaborative robot The rotation and translation matrices of the pose transformation matrix A are obtained by measuring the forward kinematics of the collaborative robot; The coordinate system of the marked points on the fixed column of the clamping device is respectively To the scanner coordinate system The rotation and translation matrices of the pose transformation matrix B are calculated by the scanner after measuring the point cloud. These are the coordinate systems of the end flange of the collaborative robot. To the scanner coordinate system The rotation and translation matrices of the pose transformation matrix X; The base coordinate system for measuring collaborative robots on components. coordinate system of the marked point on the fixed column of the clamping device The rotation and translation matrices of the pose transformation matrix Y; By expanding the homogeneous transformation matrix of equation (2), we can derive: (3) (4) To simultaneously solve for the rotation matrix R and translation matrix t of the pose transformation matrix, dual quaternions are used to represent spatial rotation and translation simultaneously. The dual quaternion form of the pose transformation matrix is: ,in These are rotation unit quaternions and translation unit quaternions, respectively. For dual operators, satisfying Therefore, the homogeneous transformation matrices in equations (3) and (4) are expressed in dual quaternion form as follows: (5) (6) In the formula: These are the rotation unit quaternion and translation unit quaternion of the pose transformation matrix A, respectively. These are the rotation unit quaternion and translation unit quaternion of the pose transformation matrix B, respectively. These are the rotation unit quaternion and translation unit quaternion of the pose transformation matrix X, respectively. These are the rotation unit quaternion and translation unit quaternion of the pose transformation matrix Y, respectively; Rearranging equations (5) and (6), we get: (7) Due to the movement of the calibration measurement robot Second, scanner acquisition The coordinates of the marker point under the next pose are therefore multiple sets of data. The multiple sets of measurements in equation (7) will be solved. Recorded as Unknown quantities to be determined Let q be the denoted q, then equation (7) can be simplified to: (8) in, It is a matrix composed of the dual quaternions of pose transformation matrices A and B. It is a matrix composed of the dual quaternions of the pose transformation matrices X and Y, and then the matrix is... Perform SVD decomposition, combined with dual quaternion constraints. It can simultaneously solve for the rotation unit quaternion and translation unit quaternion corresponding to the pose transformation matrices X and Y, denoted as , and use them as initial values ​​for iterative solution; An iterative optimization method is used to solve the problem, and the results are obtained using a closed-form solution. As the initial value for iterative solution; firstly, establish the corresponding objective function. ,for The pose of the collaborative robot is measured, and the optimal cost function is constructed based on equations (5) and (6): (9) The objective function is solved using the LM method, and the result obtained in equation (8) is used as the initial value for the iterative solution process. Given initial parameter values, then follow the algorithm's iteration step size. Perform iterations: (10) In the formula: s is the number of iterations; let , For the objective function Jacobian matrix with respect to x; The damping coefficient; The identity matrix is ​​used; the objective function is solved through LM iteration. The iteration stops when the step size meets the condition, and the objective function is output. optimal solution Then according to the formula Find the dual quaternions of pose transformation matrices X and Y, and convert the dual quaternions into pose transformation matrices to obtain the coordinate system of the end effector flange of the collaborative robot. To the scanner coordinate system Pose transformation matrix X, measuring the base coordinate system of the collaborative robot coordinate system of the marked point on the fixed column of the clamping device Pose transformation matrix Y; Step 3: Optimize the parameters of the measurement-machining subsystem based on minimizing reprojection error. 1) Establish a calibration model for the measurement collaborative robot-grinding and polishing subsystem. A calibration model of the measurement-processing subsystem is established based on a collaborative measurement robot, a grinding tool, and a polishing robot. First, a model of the pose transformation relationship between the collaborative measurement robot, the scanner, the polishing robot, and the grinding tool is established. A calibration plate is placed at the end of the polishing tool of the industrial robot, and a structured light 3D scanner is fixed to the end of the collaborative measurement robot. The model is then modified... The collaborative robot's pose is measured, and the grinding and polishing industrial robot changes accordingly. The pose of the secondary grinding and polishing robot was obtained. Group scan calibration plate measurement data, and simultaneously acquire Group measurement of the pose transformation relationship of the end effector of the collaborative robot relative to the base coordinate system and The pose transformation relationship of the end effector of a grinding and polishing industrial robot relative to the base coordinate system; based on Set up measurement data and establish a base coordinate system for the collaborative robot. To the coordinate system of the end flange of the collaborative robot Let the pose transformation matrix be A, and the scanner coordinate system be... coordinate system of end-effector grinding tools in industrial grinding and polishing robots The pose transformation matrix is ​​D, and the base coordinate system of the grinding and polishing industrial robot is... To the end flange coordinate system of the grinding and polishing industrial robot The pose transformation matrix is ​​E, and the coordinate system of the end flange of the grinding and polishing industrial robot is... coordinate system of end-effector grinding tools in industrial grinding and polishing robots The pose transformation matrix is ​​P, and the measurement coordinate system of the collaborative robot is [missing information]. To the base coordinate system of the grinding and polishing industrial robot The pose transformation matrix is ​​Z, which is derived from the coordinate system of the end flange of the collaborative robot obtained from the calibration model of the collaborative robot-component subsystem in step 2. To the scanner coordinate system The pose transformation matrix X is fixed and does not change with the movement of the measurement collaborative robot. Therefore, matrix X is used as a known quantity in solving the calibration model of the measurement-machining subsystem, and the pose transformation matrix relationship between the measurement-machining system is constructed as follows: (11) in, , In order to be in Measurement of collaborative robot base coordinate system at each pose To the coordinate system of the end flange of the collaborative robot The pose transformation matrix can be obtained by measuring the forward kinematics of the collaborative robot. , In order to be in The coordinate system of the grinding and polishing industrial robot in each position To the end flange coordinate system of the grinding and polishing industrial robot The pose transformation matrix is ​​obtained from the forward kinematics of the grinding and polishing industrial robot; , For measuring the movement of collaborative robots Secondary scanner coordinate system coordinate system of end-effector grinding tools in industrial grinding and polishing robots The pose transformation matrix is ​​obtained by solving the pose transformation matrix after reading the data from the scanner; matrix X is obtained from the calibration model of the collaborative robot-component subsystem in step 2 and is used as a known quantity in the calibration model of the measurement-machining system; P is the coordinate system of the end flange of the grinding and polishing industrial robot. coordinate system of end-effector grinding tools in industrial grinding and polishing robots Pose transformation matrix; Z is the base coordinate system of the collaborative robot. To the base coordinate system of the grinding and polishing industrial robot Pose transformation matrix; Let G be the known quantity on the left side of equation (11), that is... and order Equation (11) can be written as: (12) In the formula, the pose transformation matrices A and E can be directly obtained by reading and calculating from the teach pendant based on the forward motion of the collaborative robot and the grinding and polishing industrial robot. The pose transformation matrix D is solved by the scanner measurement data. The pose transformation matrix X between the end flange and the tool of the collaborative robot is obtained by step 2, and the two are rigidly fixed. 2) Solving the parameter optimization model based on minimizing reprojection error Due to the actual position coordinates of a point in space under the world coordinate system Calculated values ​​on the imaging plane of the scanner camera There is an error The optimal pose transformation matrix is ​​solved by minimizing the projection error, where K is the intrinsic parameter of the scanner camera and T is the pose transformation matrix between the scanner coordinate system and the world coordinate system. Equation (12) is solved by minimizing the reprojection error parameter optimization method, and the cost function is minimized. To simultaneously solve for the rotation matrix of pose transformation matrix Q and Z Translation matrix ,make Based on equation (12), the objective function for minimizing reprojection error is constructed as follows: (13) In the formula, To measure the number of moves of the collaborative robot; k is the number of checkerboard grid points on the calibration plate of the grinding tool within the scanner's field of view; Let be the actual position coordinates of the k chessboard grid points measured in the world coordinate system at the j-th pose. d represents the pixel coordinates of the measurement point projected onto the scanner camera's imaging plane, and d represents the depth of the measurement point in the scanner coordinate system. Repeat step 2 of the parallel solution algorithm to obtain the pose transformation matrix in equation (12) based on the dual quaternion closed-form solution method. And as the initial value of the objective function to minimize the reprojection error, given parameters d and K, for the minimized objective function The coordinate system of the end flange of the grinding and polishing industrial robot is obtained by performing LM iterative solution. coordinate system of end-effector grinding tools in industrial grinding and polishing robots Pose transformation matrix and measuring the base coordinate system of collaborative robots To the base coordinate system of the grinding and polishing industrial robot Pose transformation matrix Z; Step 4: Global calibration based on the robot measurement-grinding and polishing integrated system First, based on the established robot measurement-grinding and polishing integrated system, the pose transformation relationship between each device in the integrated system is obtained according to the solution results of the calibration model of the measurement-component subsystem and the calibration model of the measurement-processing subsystem. Then, the complete profile of the in-situ measured component (6) guided by the measurement collaborative robot (1) and the scanner (2) is transformed into the coordinate system of the end flange of the measurement collaborative robot through the pose transformation matrix X. The coordinates are then transformed to the base coordinate system of the collaborative measurement robot via the pose transformation matrix A. The system then plans the grinding and polishing trajectory according to the component structure and shape, and uses the planned trajectory as the processing path read by the grinding and polishing robot (7). The processing path is then transformed into the base coordinate system of the grinding and polishing robot (7) using the pose transformation matrix Z. The coordinates are then transformed to the end-effector coordinate system of the grinding and polishing industrial robot based on the pose transformation matrices E and P. Next, the data between the measurement, component and processing sub-units is unified to realize multi-functional collaborative processing; finally, the processing path is input into the control terminal of the grinding and polishing industrial robot and the processing speed and acceleration are set to realize automatic grinding and polishing processing of the robot measurement-grinding and polishing integrated system.

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