Polishing tcp calibration compensation method for robot flexible ball head
By establishing a kinematic model and a compression compensation model, the TCP of the flexible ball head tool was calibrated and corrected, solving the problem of uncontrollable contact pressure during robotic polishing and achieving constant contact pressure and high-precision trajectory control on surfaces with varying curvature.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHANGCHUN INST OF OPTICS FINE MECHANICS & PHYSICS CHINESE ACAD OF SCI
- Filing Date
- 2026-05-07
- Publication Date
- 2026-06-02
AI Technical Summary
In existing technologies, the contact pressure of flexible ball-end tools for industrial robots becomes uncontrollable due to changes in elastic displacement and contact mechanics during optical processing. It is difficult to achieve constant contact pressure on surfaces with varying curvature, and there is a lack of effective TCP calibration compensation models.
By establishing an accurate kinematic model and a compression compensation model, the contact pressure (TCP) of the flexible ball head tool is calibrated using the least squares method. Combining this with the Hertz contact model, compression compensation is performed to generate a polished TCP, thereby achieving stable control of the contact pressure.
It achieves stability of contact pressure and trajectory accuracy in the machining of surfaces with varying curvature, enhancing the adaptability and accuracy of robotic polishing of complex curved surfaces.
Smart Images
Figure CN122125730A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of optical processing technology, and in particular relates to a TCP calibration compensation method for polishing a robot flexible ball head. Background Technology
[0002] As modern optical systems evolve towards larger apertures, aspherical surfaces, and freeform surfaces, higher demands are placed on the manufacturing efficiency and surface accuracy of optical components. Six-degree-of-freedom industrial robots, with their advantages of large workspace, high flexibility, and low cost, have become an important platform for the efficient manufacturing of large-aperture optical components. In practical applications, to achieve full-aperture coverage of complex curved surfaces, a machining mode combining robots and flexible polishing tools is typically employed. This mode requires the motion system to possess the ability to achieve precise coupling of six degrees of freedom in three-dimensional space; that is, while ensuring the center of the flexible ball-head tool accurately reaches the predetermined dwell point, the coincidence of its tool axis and the local normal vector of the workpiece surface must be strictly controlled.
[0003] Currently, optical machining in industrial robots primarily relies on general-purpose industrial robot controllers for path planning. Common control methods are typically based on the robot's nominal kinematics model, assuming ideal parameters such as link lengths and joint angles. For tool center point (TCP) calibration, traditional four-point or six-point methods are often used, calibrating the geometric tip position of the tool. During machining, the robot drives a flexible ball-end tool along a preset trajectory, relying on the elastic deformation of the flexible ball-end tool to adapt to changes in the curvature of the workpiece surface.
[0004] The existing technology has the following main drawbacks: (1) The serial robot is an open chain cantilever structure with low end stiffness. Under the action of polishing contact force, the end of the robot will produce elastic displacement, which causes the actual indentation depth of the flexible ball tool to deviate from the theoretical value, resulting in instability of the removal function. (2) The traditional TCP calibration method only calibrates the geometric vertices of the flexible ball end tool. However, the flexible ball end tool must be pressed into the workpiece surface to a certain depth to produce effective polishing. If the geometric TCP is used directly for control, the compression change caused by contact mechanics is ignored, resulting in uncontrollable actual contact pressure. (3) The existing technology lacks a quantitative compensation model for the compression of flexible ball head tools, making it difficult to guarantee constant contact pressure throughout the entire path when machining surfaces with varying curvature. Summary of the Invention
[0005] In view of this, the present invention aims to provide a TCP calibration compensation method for polishing a robot flexible ball head. By establishing an accurate kinematic model, TCP calibration, and compression compensation model, the decoupled control of polishing force and processing position is achieved, ensuring constant contact pressure and high-precision trajectory execution during robot polishing.
[0006] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A method for TCP calibration compensation in the polishing of a robotic flexible ball head includes: S1: Install the flexible ball head tool at the end flange of the robot and control the robot's movement so that the geometric vertex of the flexible ball head tool contacts the fixed reference point in the activity space multiple times. S2: Based on the motion in step S1, calibrate the geometric TCP of the flexible ball head tool; S3: Based on the characteristics of the flexible ball end tool pressing into the workpiece surface in step S1, determine the mapping relationship between the normal load and the compression amount of the flexible ball end tool; S4: Using the compression amount determined in step S3 as a compensation value, the geometric TCP calibrated in step S2 is corrected to generate the polishing TCP for the robot during the polishing operation.
[0007] Furthermore, prior to step S1, the system also includes constructing the forward kinematic equations from the robot's base coordinate system to the robot's end flange coordinate system.
[0008] Furthermore, the forward kinematic equations are: ; Among them, T n Let A represent the pose matrix of the robot with respect to the nth axis and the robot's base. i This represents the transformation matrix between the coordinate systems of two adjacent links in a robot.
[0009] Furthermore, step S2 includes: determining the vector identity between the geometric TCP and the fixed reference point based on the position and orientation of the robot's end flange; and solving the vector identity by least squares to obtain the geometric TCP.
[0010] Furthermore, the vector identity is: R j ×P tcp +P base,j =P ref ; Among them, P ref R represents the position vector of a fixed reference point. j P represents the rotation matrix of the end flange when the j-th geometric vertex of the flexible ball end tool contacts the fixed reference point. tcpRepresents geometric TCP, P base,j This represents the position vector of the end flange at the j-th contact. The least squares solution is obtained using the following formula: ; Among them, J(P tcp ) denotes the least squares objective function constructed with geometric TCP as the independent variable, ∑ denotes the summation over N measurements, and ‖·‖ denotes the Euclidean norm of the vector.
[0011] Furthermore, the mapping relationship in step S3 is as follows: ; Where δ represents the compression amount when the flexible ball end tool is pressed into the workpiece, F represents the normal load, R represents the geometric radius of the flexible ball end tool, and E represents the equivalent elastic modulus of the contact system formed by the flexible ball end tool and the workpiece.
[0012] Furthermore, in step S4, the geometric TCP is corrected using the following formula to obtain the polished TCP: Ptcp' = Ptcp - δ × n; Among them, P tcp Represents geometric TCP, P tcp ' represents polishing TCP, δ represents the compression amount when the flexible ball end tool is pressed into the workpiece, and n represents the axial direction vector of the flexible ball end tool.
[0013] Furthermore, the methods also include: S5: Based on the polishing TCP obtained in step S4, perform polishing trajectory planning, and avoid the robot's wrist singularity, elbow singularity and shoulder singularity areas during the polishing trajectory planning process.
[0014] Furthermore, in step S5, the geometric symmetry of the flexible ball-head tool rotating around its own axis is used to monitor the condition number of the robot's kinematic Jacobian matrix, and the angles of the robot's joints are actively adjusted to avoid the robot's wrist singularity, elbow singularity and shoulder singularity regions.
[0015] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention presents a method for calibrating and compensating the TCP (Technical Contact Error) of a robot flexible ball head for polishing. It accurately calibrates the TCP of the flexible ball head tool set using the least squares method, eliminating the impact of mechanical installation errors and encoder reading errors on trajectory accuracy. By combining the Hertz contact model with compression compensation of the flexible ball head tool, it transforms the difficult-to-control contact pressure into position control, which the robot excels at, achieving contact force stability in open-loop force control mode. Based on the axial direction vector of the flexible ball head tool, the polishing TCP is corrected, effectively solving the pressure fluctuation problem caused by curvature mismatch in the machining of surfaces with varying curvature, and enhancing the adaptability of polishing complex curved surfaces. Attached Figure Description
[0016] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic flowchart of the polishing TCP calibration compensation method for the flexible ball head of a robot as described in an embodiment of the present invention. Detailed Implementation
[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other.
[0018] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0019] The invention will now be described in detail with reference to the accompanying drawings and embodiments.
[0020] like Figure 1 As shown in the embodiment of the present invention, the polishing TCP calibration compensation method for a robot flexible ball head includes: S1: Install the flexible ball head tool at the end flange of the robot and control the robot's movement so that the geometric vertex of the flexible ball head tool contacts a fixed reference point in the working space multiple times.
[0021] In some embodiments, prior to step S1, the system further includes constructing the forward kinematic equations from the robot's base coordinate system to the robot's end flange coordinate system, specifically: ; Among them, T n Let A represent the pose matrix of the robot with respect to the nth axis and the robot's base. i This represents the transformation matrix between the coordinate systems of two adjacent links in a robot.
[0022] In this embodiment of the invention, the pose matrix T n The transformation matrix is a 4×4 homogeneous matrix, consisting of a 3×3 rotation matrix and a 3×1 position vector. Given a set of joint angle vectors q=[θ1,θ2,...,θ...] n ] T The rotation matrix and position vector of the end flange coordinate system relative to the base coordinate system can be uniquely determined using the above forward kinematic equations. These forward kinematic equations provide the basis for constructing the vector identity required for geometric TCP calibration in subsequent step S2—that is, the rotation matrix R of the end flange during the j-th measurement in the vector identity. j and position vector P base,j All are determined by the joint angle vector q corresponding to the j-th measurement. j The above forward kinematics equations are substituted into the calculation.
[0023] In this embodiment of the invention, a base coordinate system and an end flange coordinate system of the robot are defined, and a link coordinate system of the six-axis serial robot is established based on the DH parameter method. Specifically, the DH parameter method describes the geometric relationship between two adjacent link coordinate systems in the robot using four parameters, namely, the link length 'a' of the i-th link in the robot. i α, connecting rod torsion angle i Linkage offset d i and joint rotation angle θ i Based on the above four parameters, the transformation matrix A between two adjacent link coordinate systems is... i By circling Z (i-1) Axis rotation θ i Along Z (i-1) Axis translation d i Along X i Axis translation a i , around X i Axis rotation α i These four basic transformations are combined sequentially to obtain the result. Following the above method, six link coordinate systems are established sequentially, and the forward kinematic equations from the base coordinate system to the end flange coordinate system, as shown in the above equation, are derived.
[0024] S2: Based on the motion observed in step S1, the geometric TCP of the flexible ball head tool is calibrated. To eliminate robot geometric parameter errors and installation errors, this invention employs a multi-point relocation method based on least squares optimization to calibrate the geometric TCP of the flexible ball head tool.
[0025] Specifically, in some embodiments, step S2 includes: S21: Based on the position and orientation of the robot's end flange, determine the vector identity between the geometric TCP and the fixed reference point. The vector identity is as follows: R j ×P tcp +P base,j =P ref ; Among them, P ref R represents the position vector of a fixed reference point. j P represents the rotation matrix of the end flange when the j-th geometric vertex of the flexible ball end tool contacts the fixed reference point. tcp Represents geometric TCP, P base,j This represents the position vector of the end flange at the j-th contact.
[0026] S22: Solve the vector identity using the least squares method to obtain the geometric TCP.
[0027] ; Among them, J(P tcp ) indicates geometric TCP (i.e., P) tcp Let be the least-squares objective function constructed with N measurements as independent variables, where ∑ represents the summation over N measurements, and ||·|| represents the Euclidean norm of the vector. Specifically, the robot is controlled to change its joint configuration so that the geometric vertex of the flexible ball-head tool contacts the same fixed reference point multiple times (N≥3 times), and the above vector identity is established for each measurement; by subtracting the vector identities corresponding to any two measurements, the unknown fixed reference point P can be eliminated. ref We obtain TCP (i.e., P) only with respect to the geometry to be determined. tcp The linear equation of P can be constructed from multiple measurements. tcp The overdetermined linear equation system is solved by least squares, i.e., by solving the corresponding normal equations, the optimal estimate of the geometric TCP is obtained.
[0028] S3: Based on the characteristics of the flexible ball end tool pressing into the workpiece surface in step S1, determine the mapping relationship between the normal load and the compression amount of the flexible ball end tool.
[0029] In some embodiments, considering the characteristics of a flexible ball end tool pressing into the workpiece surface, a mapping relationship is established between the normal load F and the compression amount δ when the flexible ball end tool presses into the workpiece, based on Hertz contact theory. Specifically: ; Where R represents the geometric radius of the flexible ball end tool, and E represents the equivalent elastic modulus of the contact system formed by the flexible ball end tool and the workpiece. This mapping relationship is used to calculate the theoretical compression of the flexible ball end tool when the robot drives it to perform polishing with a target constant polishing pressure. For workpieces with varying curvature surfaces, the robot is controlled to move the polishing TCP along the theoretical contour of the workpiece surface, while keeping the axis of the flexible ball end tool coincident with the normal of the workpiece surface. At this time, the flexible ball end tool naturally presses into the workpiece, thereby generating a constant polishing pressure.
[0030] S4: Using the compression amount determined in step S3 as a compensation value, the geometric TCP calibrated in step S2 is corrected to generate the polishing TCP for the robot during the polishing operation.
[0031] In some embodiments, a polished TCP is obtained by modifying the geometric TCP using the following formula: Ptcp' = Ptcp - δ × n; Among them, P tcp ' represents the polishing TCP, and n represents the axial direction vector of the flexible ball end tool. This formula can be understood as the polishing TCP during the actual polishing process of the flexible ball end tool being the position of the geometric vertex of the flexible ball end tool along the axial compression amount δ.
[0032] In some embodiments, the method further includes: S5: Based on the polishing TCP obtained in step S4, perform polishing trajectory planning, and avoid the robot's wrist singularity, elbow singularity and shoulder singularity areas during the polishing trajectory planning process.
[0033] In some embodiments, the geometric symmetry of the rotation of the flexible ball-head tool around its own axis is utilized to monitor the condition number of the robot's kinematic Jacobian matrix, and the angles of the robot's joints are actively adjusted to avoid the robot's wrist singularity, elbow singularity, and shoulder singularity regions.
[0034] Further, the robot's kinematic Jacobian matrix describes the linear mapping between the robot's joint velocity vectors and the linear and angular velocities of the end flange. During the robot's motion, near singular configurations at the wrist, elbow, or shoulder, the Jacobian matrix exhibits rank deficiency, significantly increasing its condition number. This leads to ill-conditioned joint velocity solutions and decreased trajectory tracking accuracy. Considering the geometric symmetry of the flexible ball-end tool's rotation around its own axis (i.e., the line containing the axial direction vector n of the flexible ball-end tool), meaning the shape of the removal function between the flexible ball-end tool and the workpiece remains unchanged regardless of the angle of rotation around this axis, the robot's joint angles constitute redundant degrees of freedom, allowing them to vary freely within a certain range without affecting the polishing results, provided the axial direction of the flexible ball-end tool coincides with the workpiece surface normal. Based on this, this invention, during the polishing trajectory planning process, actively adjusts the robot's joint angles by real-time monitoring of the condition number of the robot's Jacobian matrix, keeping the condition number below a preset threshold to avoid singular regions at the wrist, elbow, and shoulder.
[0035] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.
[0036] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.
Claims
1. A method for polishing TCP calibration compensation of a robot flexible ball head, characterized in that, include: S1: Install the flexible ball head tool at the end flange of the robot and control the robot's movement so that the geometric vertex of the flexible ball head tool contacts the fixed reference point in the activity space multiple times. S2: Based on the motion in step S1, calibrate the geometric TCP of the flexible ball head tool; S3: Based on the characteristics of the flexible ball end tool pressing into the workpiece surface in step S1, determine the mapping relationship between the normal load and the compression amount of the flexible ball end tool; S4: Using the compression amount determined in step S3 as a compensation value, the geometric TCP calibrated in step S2 is corrected to generate the polishing TCP for the robot during the polishing operation.
2. The polishing TCP calibration compensation method for a robot flexible ball head according to claim 1, characterized in that, Before step S1, the system also includes constructing the forward kinematic equations from the robot's base coordinate system to the robot's end flange coordinate system.
3. The polishing TCP calibration compensation method for a robot flexible ball head according to claim 2, characterized in that, The forward kinematic equations are: ； Among them, T n Let A represent the pose matrix of the robot with respect to the nth axis and the robot's base. i This represents the transformation matrix between the coordinate systems of two adjacent links in a robot.
4. The polishing TCP calibration compensation method for a robot flexible ball head according to claim 1, characterized in that, Step S2 includes: Based on the position and orientation of the robot's end flange, determine the vector identity between the geometric TCP and the fixed reference point; The geometric TCP is obtained by solving the vector identity using least squares.
5. The polishing TCP calibration compensation method for a robot flexible ball head according to claim 4, characterized in that, The vector identity is: R j ×P tcp +P base,j =P ref ; Among them, P ref R represents the position vector of a fixed reference point. j P represents the rotation matrix of the end flange when the j-th geometric vertex of the flexible ball end tool contacts the fixed reference point. tcp Represents geometric TCP, P base,j This represents the position vector of the end flange at the j-th contact. The least squares solution is obtained using the following formula: ； Among them, J(P tcp ) denotes the least squares objective function constructed with geometric TCP as the independent variable, ∑ denotes the summation over N measurements, and ‖·‖ denotes the Euclidean norm of the vector.
6. The polishing TCP calibration compensation method for a robot flexible ball head according to claim 1, characterized in that, The mapping relationship in step S3 is as follows: ； Where δ represents the compression amount when the flexible ball end tool is pressed into the workpiece, F represents the normal load, R represents the geometric radius of the flexible ball end tool, and E represents the equivalent elastic modulus of the contact system formed by the flexible ball end tool and the workpiece.
7. The polishing TCP calibration compensation method for a robot flexible ball head according to claim 1, characterized in that, In step S4, the geometric TCP is corrected using the following formula to obtain the polished TCP: Ptcp' = Ptcp - δ × n; Among them, P tcp Represents geometric TCP, P tcp ' represents polishing TCP, δ represents the compression amount when the flexible ball end tool is pressed into the workpiece, and n represents the axial direction vector of the flexible ball end tool.
8. The polishing TCP calibration compensation method for a robot flexible ball head according to claim 1, characterized in that, The method also includes: S5: Based on the polishing TCP obtained in step S4, perform polishing trajectory planning, and avoid the robot's wrist singularity, elbow singularity and shoulder singularity areas during the polishing trajectory planning process.
9. The polishing TCP calibration compensation method for a robot flexible ball head according to claim 8, characterized in that, In step S5, the geometric symmetry of the flexible ball-head tool rotating around its own axis is used to monitor the condition number of the robot's kinematic Jacobian matrix, and the angles of the robot's joints are actively adjusted to avoid the robot's wrist singularity, elbow singularity and shoulder singularity regions.