Contact type measurement mechanical arm calibration method based on distance constraint

Abstract

The invention discloses a contact type measurement mechanical arm calibration method based on distance constraint, and relates to the technical field of mechanical arm calibration, and the method comprises the following steps: a plurality of non-collinear space reference points are fixedly installed in a mechanical arm working space, a contact type measuring head is installed on a flange at the tail end of a mechanical arm, and a measurement basis is established; the mechanical arm is controlled to move to different poses covering the working space, the measuring head is driven to make contact with the reference points in sequence, and the actual space distance is measured; according to the initial kinematics parameters of the mechanical arm, the theoretical position of the tail end is calculated through forward kinematics, and the theoretical geometric distance between the measuring head and the reference point is deduced; constructing a nonlinear optimization objective function based on a deviation value between an actual measurement distance and a theoretical calculation distance; the target function is converted into a matrix equation form, and a regularization iterative algorithm is adopted to calculate the correction amount of the kinematics parameters of the mechanical arm; and the obtained parameter correction amount is written into a mechanical arm controller, and parameter updating and calibration compensation are completed.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical arm calibration, and particularly relates to a contact type measurement mechanical arm calibration method based on distance constraint. BACKGROUND

[0002] In the application of a mechanical arm, accurate kinematic parameters are the key to guarantee the working precision and stability of the mechanical arm. However, due to errors in the manufacturing and assembly process of the mechanical arm and the wear of parts after long-term use, the actual kinematic parameters deviate from the theoretical values, which leads to the decrease of the positioning accuracy of the end effector of the mechanical arm, thereby affecting the performance of the mechanical arm in high-precision operations such as precision machining, measurement and assembly.

[0003] The existing mechanical arm calibration method has certain limitations in processing nonlinear geometric error compensation. Some methods are difficult to consider calibration accuracy and efficiency at the same time. Some calibration methods based on simple geometric relationships or single sensor measurement cannot fully consider the complex nonlinear characteristics of the mechanical arm, resulting in a large positioning error of the calibrated mechanical arm. Some high-precision calibration methods often require complex equipment and cumbersome operation processes, which are high in cost and long in calibration period, and are not conducive to wide application in actual production. Therefore, the application provides a contact type measurement mechanical arm calibration method based on distance constraint. SUMMARY

[0004] To solve the above technical problems, the application is realized by the following technical scheme: The application is a contact type measurement mechanical arm calibration method based on distance constraint, comprising the following steps: Step S1: fixing and installing a plurality of non-collinear space reference points in the working space of the mechanical arm, and installing a contact probe on the flange at the end of the mechanical arm to establish a measurement reference; Step S2: controlling the mechanical arm to move to different poses covering the working space, and driving the probe to contact the reference points in turn to measure the actual spatial distance; Step S3: calculating the theoretical position of the end according to the initial kinematic parameters of the mechanical arm, and deducing the theoretical geometric distance between the probe and the reference point through forward kinematics; Step S4: based on the deviation value between the actual measurement distance and the theoretical calculation distance, constructing a nonlinear optimization objective function containing the first and second derivative terms of the distance residual; Step S5: converting the objective function into a matrix equation form, and calculating the optimal correction amount of the kinematic parameters of the mechanical arm by using a regularization iterative algorithm; Step S6: writing the obtained parameter correction amount into the mechanical arm controller to complete the real-time updating and calibration compensation of the kinematic parameters.

[0005] Further, the step S1 comprises the following steps: Step S11, fix at least 3 non-collinear reference points in the workspace of the robot arm , the coordinate values of which are known in the global coordinate system, wherein is the coordinate of the reference point in the global coordinate system; Step S12, install a contact probe on the flange at the end of the robot arm, and use a coordinate measuring machine to measure the point at the tip of the probe in the coordinate system of the flange; Step S13, the reference points are distributed on three planes in the workspace that are not parallel to each other.

[0006] Further, the step S2 comprises the following steps: Step S21, control the robot arm to move to different poses to ensure that the main motion range of the workspace is covered; Step S22, at each pose : read the joint angle vector through the encoder , wherein is the angle value of the joint at the pose, is the number of joints of the robot arm; drive the probe to contact the fixed point , and use a laser interferometer to measure the actual distance ; repeat the measurement of each fixed point at least 10 times and take the arithmetic mean value; wherein is the actual distance.

[0007] Further, the step S3 comprises the following steps: Step S31, calculate the end pose transformation matrix based on the initial DH parameters stored in the controller by forward kinematics chain: ; wherein is the homogeneous transformation matrix from the base to the end flange, is the transformation matrix of the joint; Step S32, calculate the theoretical coordinates of the probe in the global coordinate system based on the pose transformation matrix : ; Step S33, calculate the theoretical distance between the probe and the fixed point by the Euclidean distance formula , which is as follows: .

[0008] Furthermore, the step S4 includes the following steps: Step S41: define the actual measurement distance Distance from theoretical calculation The residual : ; Step S42: To accurately compensate for the nonlinear geometric error of the robotic arm, a residual optimization function including a second-order Taylor expansion is constructed. The formula is as follows: ; Where, is the first derivative of the distance with respect to the parameter, is the second-order derivative of the distance with respect to the parameter, is the parameter correction amount, is the regularization coefficient; Among them: The first-order derivative term is used to analyze the posture sensitivity through differential kinematics, and the formula is as follows: ; The second-order derivative term captures geometric nonlinearity through the Hessian matrix, which is as follows: .

[0009] Furthermore, step S5 includes the following steps: Step S51: convert the objective function into a matrix form by numerical solution. The matrix formula is as follows: ; Where, is the first-order derivative Jacobian matrix, is the second-order derivative Hessian term, is the residual vector; Step S52: Regularized Levenberg-Marquardt algorithm is used to iteratively solve the parameter correction amount. The formula is as follows: ; Set the convergence threshold ,when or number of iterations terminated when Where, is the identity matrix.

[0010] Furthermore, step S6 includes the following steps: Step S61: Output the optimal parameter correction amount ; Step S62, update the kinematics model of the mechanical arm, perform vector addition according to the DH parameter structure, and the formula is as follows: ; In the formula, is the initial DH parameter, is the updated kinematics parameter vector; write the parameter into the parameter storage area of the mechanical arm controller through the industrial bus; Step S63, disassemble the measuring head and clean the fixed point device, and control the mechanical arm to return to the zero point standby position.

[0011] The present application has the following beneficial effects: 1. The present application constructs a nonlinear optimization objective function containing the first and second order derivative terms of the distance residual, fully considers the complex nonlinear characteristics of the mechanical arm, can more accurately compensate the nonlinear geometric error of the mechanical arm compared with the existing methods that cannot compensate the nonlinear error, improves the positioning accuracy of the end effector of the mechanical arm, and effectively guarantees the performance of the mechanical arm in high-precision operations such as precision machining, measurement and assembly.

[0012] 2. The present application uses a regularization iterative algorithm to calculate the optimal correction amount of the kinematics parameters of the mechanical arm, simplifies the calculation process and operation steps compared with some high-precision but cumbersome methods, improves the calibration efficiency, shortens the calibration period, makes the mechanical arm can be put into production faster, and meets the efficient needs of actual production.

[0013] 3. The present application can be implemented relying on a conventional contact measuring head and a general measuring device, avoids purchasing high-cost special sensors, the measuring head is directly installed on the flange at the end of the mechanical arm, and after calibration, it can be quickly disassembled and restored to production without affecting the original functions of the device, the parameters are automatically written into the controller through the industrial bus, and periodic calibration is supported to compensate for the wear error of the device.

[0014] Of course, any product implementing the present application does not necessarily need to achieve all the advantages described above. BRIEF DESCRIPTION OF DRAWINGS

[0015] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0016] Figure 1 It is a flowchart of a contact measuring mechanical arm calibration method based on distance constraint. DETAILED DESCRIPTION ​

[0017] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the scope of protection of the present application.

[0018] Please refer to Figure 1 The present application is a kind of contact measurement mechanical arm calibration method based on distance constraint, comprising the following steps: Step S1: a plurality of non-collinear space reference points are fixedly installed in the workspace of the mechanical arm, and a contact probe is installed on the end flange of the mechanical arm, and a measurement reference is established; Step S2: control the mechanical arm to move to different poses covering the workspace, drive the probe to contact each reference point in turn, and measure the actual spatial distance; Step S3: according to the initial kinematic parameters of the mechanical arm, calculate the theoretical position of the end through forward kinematics, and deduce the theoretical geometric distance between the probe and the reference point; Step S4: based on the deviation value of the actual measured distance and the theoretically calculated distance, a nonlinear optimization objective function containing the first and second derivative terms of the distance residual is constructed; Step S5: convert the objective function into a matrix equation form, and use a regularization iterative algorithm to calculate the optimal correction amount of the kinematic parameters of the mechanical arm; Step S6: write the obtained parameter correction amount into the mechanical arm controller, complete the real-time update and calibration compensation of the kinematic parameters.

[0019] Step S1 includes the following steps: Step S11, at least 3 non-collinear reference points are fixedly installed in the workspace of the mechanical arm , the coordinate values of which are known in the global coordinate system, wherein is the coordinate of the reference point in the global coordinate system; Step S12, a contact probe is installed on the end flange of the mechanical arm, and a coordinate measuring machine is used to measure the coordinate value of the tip point of the probe in the flange coordinate system; Step S13, the reference points are distributed on three planes in the workspace which are not parallel to each other.

[0020] Step S2 includes the following steps: Step S21, control the mechanical arm to move to different poses , to ensure that the main motion range of the workspace is covered; Step S22, in each pose : Reading joint angle vector by encoder wherein is the angle value of the jth joint at the ith pose, is the number of joints of the robot arm; Driving the probe to contact the fixed point Measuring the actual distance with a laser interferometer ; Each fixed point is measured at least 10 times and the arithmetic mean is taken; wherein is the actual distance.

[0021] Step S3 includes the following steps: Step S31, calculating the end pose transformation matrix through forward kinematics chain according to the DH parameter initial value stored by the controller: ; wherein, is the homogeneous transformation matrix from the base to the end flange, is the transformation matrix of the kth joint; Step S32, calculating the theoretical coordinates of the probe in the global coordinate system based on the pose transformation matrix: ; ; Step S33, calculating the theoretical distance between the probe and the fixed point through the Euclidean distance formula, as follows: ; Step S4 includes the following steps: Step S41, defining the residual error between the actual measured distance and the theoretically calculated distance : ; Step S42, to accurately compensate for the nonlinear geometric error of the robot arm, constructing a residual error optimization function containing a second-order Taylor expansion, as follows: ; wherein, is the first-order derivative of the distance with respect to the parameter, is the second-order derivative of the distance with respect to the parameter, is the parameter correction amount, is the regularization coefficient; wherein: the first-order derivative term is obtained by differentiating the kinematic analysis pose sensitivity, as follows: ​​​​​ ; The second derivative term captures the geometric nonlinearity through the Hessian matrix, which is as follows: .

[0022] The step S5 includes the following steps: Step S51, by implementing numerical solution, the objective function is converted into a matrix form, and the matrix formula is as follows: ; In the formula, is a first derivative Jacobian matrix, is a second derivative Hessian term, is a residual vector; Step S52, a regularized Levenberg-Marquardt algorithm is used to iteratively solve the parameter correction amount, and the formula is as follows: ; The convergence threshold is set , when or the iteration number is terminated; In the formula, is a unit matrix.

[0023] The step S6 includes the following steps: Step S61, the optimal parameter correction amount ; Step S62, the kinematics model of the robot arm is updated, and the vector addition is performed according to the DH parameter structure, and the formula is as follows: ; In the formula, is an initial DH parameter, is an updated kinematics parameter vector; The is written into the parameter storage area of the robot arm controller through the industrial bus; Step S63, the probe is disassembled and the fixed point device is cleaned, and the robot arm is controlled to return to the zero point standby position.

[0024] One specific application of the embodiment is: A 6-axis industrial robot arm (model: KUKA KR500) is taken as an implementation object, and the calibration process and effect verification are described in detail; 1. Reference point arrangement: Five non-collinear ceramic reference balls (accuracy ±1 μm) are arranged in the workspace, and the global coordinates are: ; Reference points are distributed in XY, XZ and YZ planes (non-coplanar constraint is satisfied); Measuring equipment: Contact probe (Renishaw RMP60, repeatability 2μm); Laser interferometer (API Radian, resolution 0.1μm); Coordinate measuring machine (ZEISS Prismo, calibrated probe tip flange coordinates: ; 2. Pose planning: Control the robot to move to 25 poses (m=25>20), covering 80% of the workspace volume (joint motion range: ±170°); At each pose j: ; Drive the probe to sequentially contact 5 reference points, and the laser interferometer records the actual distance ; Each point is measured 12 times (>10 times), and the mean value is taken after removing gross errors ; 3. Initial : ; Calculate the theoretical distance residual (maximum residual example): ; 4. Objective function parameters: ; where, ; Iterative solution: Regularized Levenberg-Marquardt algorithm is used : ; Convergence process: 1, 5, 10, 12; ; Residual norm ; At k=12, the convergence condition is met ; 5. DH parameter update: ; Write to the controller through the EtherCAT bus Calibration effect: End positioning error: ; Distance residual RMS: ; 6. Production resumption: Remove the probe (takes less than 2 minutes) and return the robotic arm to the zero standby position.

[0025] Throughout this specification, references to terms such as "one embodiment," "example," or "specific example" indicate that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0026] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A contact measurement manipulator calibration method based on distance constraints, characterized by: The following steps are involved: Step S1: multiple non-collinear spatial reference points are fixedly installed in the working space of the robot arm, and a contact probe is installed on the end flange of the robot arm to establish a measurement benchmark; Step S2: Control the robotic arm to move to different positions covering the workspace, drive the probe to contact each reference point in turn, and measure the actual space distance; Step S3: Based on the initial kinematic parameters of the manipulator, the theoretical end position is calculated by forward kinematics, and the theoretical geometric distance between the probe and the reference point is derived; Step S4: Based on the deviation between the actual measured distance and the theoretical calculated distance, a nonlinear optimization objective function including the first-order and second-order derivative terms of the distance residual is constructed; Step S5: converting the objective function into a matrix equation form and using a regularized iterative algorithm to calculate the optimal correction amount of the robot arm kinematic parameters; Step S6: Writing the obtained parameter correction amount into the robot arm controller to complete the real-time update and calibration compensation of the kinematic parameters.

2. The contact measurement manipulator calibration method based on distance constraint according to claim 1, characterized in that: The step S1 includes the following steps: Step S11: Fix at least three non-collinear reference points in the robot arm workspace , whose coordinate values ​​are known in the global coordinate system, where is the coordinate of the reference point in the global coordinate system; Step S12: Install a contact probe on the end flange of the robotic arm and use a three-dimensional coordinate measuring machine to measure the probe tip point. Coordinate values ​​in the flange coordinate system; Step S13: The reference points are distributed on three non-parallel planes in the workspace.

3. The contact measurement manipulator calibration method based on distance constraint according to claim 1, characterized in that: The step S2 includes the following steps: Step S21: Control the robot arm to move to Different postures , ensuring that the main range of motion of the workspace is covered; Step S22: At each pose : Read the joint angle vector through the encoder ,in For the The joint in The angle value of each pose, is the number of joints of the robotic arm; Drive the probe into contact with a fixed point , using laser interferometer to measure the actual distance ; Each fixed point was measured at least 10 times and the arithmetic mean was taken; Where, is the actual distance.

4. The contact measurement manipulator calibration method based on distance constraint according to claim 1, characterized in that: The step S3 includes the following steps: Step S31: Initial DH parameter values ​​stored in the controller , calculate the end pose transformation matrix through the forward kinematics chain: ； Where, is the homogeneous transformation matrix from the base to the end flange, is the transformation matrix of the kth joint; Step S32: Calculate the theoretical coordinates of the probe in the global coordinate system based on the posture transformation matrix : ； Step S33: Calculate the theoretical distance between the probe and the fixed point using the Euclidean distance formula , the formula is as follows: 。 5. The contact measurement manipulator calibration method based on distance constraint according to claim 1, characterized in that: The step S4 includes the following steps: Step S41: define the actual measurement distance Distance from theoretical calculation The residual : ； Step S42: To accurately compensate for the nonlinear geometric error of the robotic arm, a residual optimization function including a second-order Taylor expansion is constructed. The formula is as follows: ； Where, is the first derivative of the distance with respect to the parameter, is the second-order derivative of the distance with respect to the parameter, is the parameter correction amount, is the regularization coefficient; Among them: The first-order derivative term is used to analyze the posture sensitivity through differential kinematics, and the formula is as follows: ； The second-order derivative term captures geometric nonlinearity through the Hessian matrix, which is as follows: 。 6. The contact measurement manipulator calibration method based on distance constraint according to claim 1, characterized in that: The step S5 includes the following steps: Step S51: convert the objective function into a matrix form by implementing a numerical solution. The matrix formula is as follows: ； Where, is the first-order derivative Jacobian matrix, is the second-order derivative Hessian term, is the residual vector; Step S52: Regularized Levenberg-Marquardt algorithm is used to iteratively solve the parameter correction amount. The formula is as follows: ； Set the convergence threshold ,when or number of iterations terminated when Where, is the identity matrix.

7. The contact measurement manipulator calibration method based on distance constraint according to claim 1, characterized in that: The step S6 includes the following steps: Step S61: Output the optimal parameter correction amount ; Step S62: Update the kinematic model of the robot arm and perform vector addition according to the DH parameter structure. The formula is as follows: ； Where, is the initial DH parameter, is the updated kinematic parameter vector; Through the industrial bus Write into the parameter storage area of ​​the robot controller; Step S63: disassemble the probe and clean the fixed point device, and control the robotic arm to return to the zero standby position.

Images