A painting robot calibration device and method

Abstract

The application discloses a kind of spraying robot calibration device and method, S100: calibration block is placed in the workspace that robot end can reach and is fixed;Establish coordinate system;S200: with teaching pendant, robot end contacts calibration block bevel vertex, and record the robot lifting joint length and the rest joint angle of this point;S300: with drag teaching mode, let robot end measuring tool respectively contact the mutually perpendicular three planes and bevel of calibration block, and respectively carry out multiple sets of point measurement, then record corresponding robot nominal theoretical pose, i.e. the robot lifting joint length and the rest joint angle;S400: compare the error of nominal position of robot end with actual position based on the mechanical structure of calibration block, calibrate robot kinematics parameter.The application obtains the purpose of robot actual parameter using calibration device low cost.

Description

Technical Field

[0001] This invention relates to the field of spray painting robot technology, and specifically to a spray painting robot calibration device and method. Background Technology

[0002] Robot calibration block calibration refers to the process of driving an end effector to reach a set of spatial positions that satisfy certain geometric constraints without using any external measuring equipment. Then, using the positional constraints between these points, a system of equations is established according to an error model, thereby improving the robot's positioning and motion control accuracy. Calibration block calibration relies solely on the robot's internal sensors to determine the model's kinematic parameters and the robot's own posture, and these parameters can be adjusted to ensure the robot's absolute positioning accuracy, simplifying the calibration workflow and improving production efficiency.

[0003] To improve coating quality and reduce the impact of differences in paint concentration and spraying equipment on the coating layer, thus meeting the high-precision coating requirements of spraying robots, calibration blocks are used to reduce the influence of manufacturing and installation factors on the accuracy of the spraying robot at the time of manufacture. This allows for convenient, quick, and low-cost acquisition of the actual geometric parameters of the spraying robot, improving its absolute positioning accuracy.

[0004] Existing technologies, such as Chinese invention patent with publication number CN112692833A, propose a method for self-calibrating a special calibration block using a camera; however, the drawback is that a 20° tilt angle is more likely to cause processing errors and increases the complexity of the objective function. The available plane is three planes, making it impossible to identify all parameters.

[0005] Chinese invention patent CN117283556A proposes a robot self-calibration device and method with a calibration plate having calibration holes; however, its drawback is that the calibration plate with calibration holes cannot fix the robot with lifting joints into the calibration holes, and the single calibration hole can identify few parameters and the effect after identification compensation is not good.

[0006] Problems exist with existing technology:

[0007] (1) Camera calibration requires a high level of operator skill; when a convex calibration block is calibrated using a planar calibration method, the 20° tilt angle causes some errors in the robot's objective function, increasing the amount of error.

[0008] (2) A single calibration plate can only calibrate some kinematic parameters of the spraying robot, resulting in low calibration accuracy. Summary of the Invention

[0009] To overcome the above technical problems, the present invention aims to provide a calibration device and method for a painting robot. This device and method are easy to manufacture, low in cost, and can identify the kinematic parameters of a robotic arm including lifting joints and a six-degree-of-freedom robot, so as to achieve the goal of obtaining the actual parameters of the robot at low cost using a calibration device.

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

[0011] A calibration device for a painting robot includes a main controller and a robot connected to the main controller. The main controller includes a robot control box and a computer system. A measuring device is installed at the end of the robot via a flange. The robot control box is used to control the movement of the robot and the measuring device, and the computer system is used to store the movement information of the robot and the measuring device.

[0012] The robot includes a base joint 1, a lifting joint 2, and a six-degree-of-freedom robotic arm 3;

[0013] The measuring device includes a metal probe 4 of the same size as the robot end effector and a calibration block 5 with an inclined surface. The metal probe 4 is mounted at the end effector of the six-degree-of-freedom robotic arm 3, and the calibration block 5 contacts the calibration plane through the robot end effector.

[0014] The measuring device obtains the pose transformation of the calibration block 5 relative to the robot's base coordinates by contacting the metal probe 4 with the vertex of the inclined side of the calibration block 5.

[0015] The robot performs contact measurement on one vertex of the hypotenuse of calibration block 5 to form a limiting position that restricts the movement of the robot's end effector and the movement of the lifting joint 2. The robot obtains a coordinate transformation matrix based on the robot's base coordinate system. That is, the robot's nominal pose is obtained based on the robot joint angles and the length of the lifting joint 2 based on the limiting position. The minimum error between the nominal pose and the actual pose is solved to achieve the calibration of the painting robot.

[0016] The calibration block 5 is trapezoidal with an inclined angle of 45°. Among the other five planes, the top surface has a size of 200x200mm, and the inclined plane has the same size as the top surface. The lower base of the two adjacent trapezoids is 400mm, the upper base is 200mm, the height is 200mm, and the bottom surface size is 200mmx400mm. The five planes are perpendicular to each other except for the plane directly opposite each other.

[0017] A calibration method for a spraying robot calibration device includes the following steps:

[0018] S100: Place and fix calibration block 5 within the workspace accessible to the robot's end effector; establish a coordinate system;

[0019] S200: Use the teach pendant to make the robot end contact the apex of the inclined side of the calibration block 5, and record the length of the robot lifting joint 2 and the angles of the other joints at that point;

[0020] S300: Using the drag teaching method, the robot end-effector measuring tool is made to contact the three mutually perpendicular planes and the inclined plane of the calibration block 5 respectively, and multiple sets of point measurements are performed respectively. Then, the corresponding robot nominal theoretical pose, i.e. the length of the robot lifting joint 2 and the angles of the other joints, are recorded.

[0021] S400: Compare the nominal position of the robot end effector with the actual position based on the mechanical structure of calibration block 5 to calibrate the robot's kinematic parameters.

[0022] Step S100 includes establishing a base coordinate system {O0X0Y0Z0} at the center of the robot base and establishing a tool coordinate system {O0X0Y0Z0} on the robot's end effector. T X T Y T Z T}, establish a world coordinate system {O} at the hypotenuse vertex of calibration block 5. w X w Y w Z w};

[0023] The robot tool is calibrated by using the pose relationship between the robot's base coordinate system {O0X0Y0Z0} and the robot's end effector, and the robot tool coordinate system {O} is obtained. T X T Y T Z T This allows us to obtain the pose transformation and position of the robot tool end effector in the robot's base coordinate system.

[0024] Step S200 includes obtaining a coordinate system {O0X0Y0Z0} from the base coordinate system {O0X0Y0Z0} by having the robot end-effector contact the apex of the inclined surface of the calibration block 5. w X w Y w Z w The coordinate transformation is achieved by connecting the computer to the robot, obtaining and recording the length of the robot's lifting joint 2 and the angles of the other joints, establishing a kinematic model using the MDH method, and substituting the recorded data to obtain the coordinate transformation from base coordinates to world coordinates.

[0025] In S300, the specific operation measurement method of drag teaching is to let the robot end measuring tool contact the plane of the calibration block 5 to perform multiple sets of point measurements. After the robot end measuring tool contacts the plane of the calibration block 5, the corresponding robot lifting joint 2 length and other joint angles are recorded to obtain the robot's nominal theoretical pose on the calibration block 5.

[0026] Step S400 includes,

[0027] S401: Establish the coordinate system of the robot base, the coordinate system of the robot end effector, and the coordinate system of calibration block 5;

[0028] S402: Kinematic modeling of the robot is performed using the MDH method, at which point the robot's geometric parameters a are... i d i θ i α i And all simplified parameters are nominal parameters;

[0029] S403: Obtain the pose matrix of calibration block 5 in the base coordinate system through the contact of the robot end-effector measuring device. Obtain the actual pose of the contactor of the robot end-effector measuring device through the mechanical structure of calibration block 5. At the same time, solve the nominal pose of the robot corresponding to the robot joint angle. Substitute the above actual pose and nominal pose into the robot kinematic error model for mathematical solution to obtain the actual parameters of the robot.

[0030] Step S403 includes transforming the robot error from the original robot base coordinates to the coordinates of calibration block 5, and combining multiple sets of data measured by the robot on different planes with the original mechanical structure to establish a corresponding objective function, seeking an approximate solution that minimizes the difference between theoretical parameters and actual error, thereby obtaining the actual parameters of the robot.

[0031] In step S403, the coordinate system {O} of calibration block 5, which can be obtained by the end-effector contacting the hypotenuse of calibration block 5, is calculated through a series of coordinate transformations between the mechanical structure and the robot's coordinate system from the base to the robot tool coordinate system. w X w Y w Z w The nominal pose matrix of the base coordinate system {O0X0Y0Z0} is:

[0032]

[0033] in α, β, γ are the angles of clockwise rotation around the Z-axis, Y-axis and X-axis of the base coordinate system {O0X0Y0Z0}, respectively. The calibration block 5 corresponds to the position coordinates of the robot's base coordinate system;

[0034] The base coordinate system {O0X0Y0Z0} is equivalent to the calibration block 5 coordinate system {O w X w Y w Z w pose matrix of}

[0035] The position coordinates of the robot's end effector on the coordinate system of calibration block 5 are expressed as follows:

[0036] When the robot's end effector contacts a plane of calibration block 5, the end effector forms a planar constraint on calibration block 5 and obtains its theoretical position based on the special structure of calibration block 5 itself. With error position The corresponding data relationships;

[0037] Establish a corresponding objective function and seek an approximate solution that minimizes the difference between theoretical parameters and actual errors, thereby obtaining the actual parameters of the robot.

[0038] In step S403, the coordinate system {O} of calibration block 5 is calibrated. w X w Y w Z w The normal vector of the top surface is Z. w If the axis and the top surface are located at the origin of the coordinate system of calibration block 5, then the base coordinate system is equivalent to the coordinate system of calibration block 5 in the Z-axis. w If the actual position component on the axis is 0, then when the robot's end effector performs contact measurement on the top surface...

[0039] When the robot's end effector contacts the inclined edge of calibration block 5, the base coordinate system is equivalent to the coordinate system of calibration block 5 in the Z-axis. w The actual position components on the axis and in the Z-axis y If the actual position components on the axis are equal, then when the robot's end effector performs contact measurement on the inclined plane...

[0040] Similarly, the robot's end-effector measuring device has a contact normal vector of X. w When the axis and the surface are located at the origin of the coordinate system of calibration block 5, the robot end effector performs contact measurement on that surface.

[0041] The robot end effector has a contact normal vector of Y. w When the plane is not located at the origin of the coordinate system of calibration block 5, then the base coordinate system is equivalent to the coordinate system of calibration block 5 in the Y direction. w The actual position components on the axis are fixed values. When the robot's end effector performs contact measurement on this surface, the positional relationship between any two points i and j on this surface is as follows:

[0042] By conducting k sets of experiments on different planes of calibration block 5, the following relationship can be obtained:

[0043]

[0044] A nonlinear iterative least squares algorithm is used to make the error in the objective function approach zero:

[0045]

[0046] The beneficial effects of this invention are:

[0047] (1) This invention only requires a low-cost calibration block to complete the calibration of robot kinematic parameters. This provides an effective solution for robot manufacturers to calibrate robot parameters, and has a wide range of applications and prospects.

[0048] (2) The present invention provides a simple and effective calibration scheme for robots with lifting joints by using multi-plane constraints based on special calibration blocks. The operation process is simple and does not require a high level of professional expertise from the operator.

[0049] (3) The mechanical structure of the calibration block of the present invention, such as the inclined side with an inclination angle of 45°, simplifies the objective function. The nonlinear iterative least squares algorithm is used to make the error in the objective function tend to zero, thereby obtaining the actual parameters of the robot. After the error parameters are substituted into the kinematic model for compensation, the absolute positioning accuracy is improved from 2.887mm before calibration to 0.86mm, and the absolute positioning accuracy of the robot end is improved by 70.2%. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the overall process of robot calibration using the robot calibration device of the present invention.

[0051] Figure 2 This is a schematic diagram of the robot calibration device of the present invention.

[0052] Figure 3 A schematic diagram showing the contact between the robot's end effector and the calibration device.

[0053] Figure 4 A schematic diagram of robot kinematic errors. Detailed Implementation

[0054] The present invention will now be described in further detail with reference to the accompanying drawings.

[0055] Example 1

[0056] like Figure 2 and Figure 3 As shown, this example provides a calibration device for a painting robot, including a main controller and a robot connected to the main controller. The main controller includes a robot control box and a computer system. The robot control box is used to control the movement of the robot and the measuring device, and the computer system is used to store the movement information of the robot and the measuring device.

[0057] The measuring device at the end of the robot is mounted on the robot flange; the calibration block 5 is installed and fixed in the robot's workspace, and the measuring device at the end of the robot can reach any position of the calibration block 5 except for the bottom surface.

[0058] like Figure 1 As shown, the method for calibrating a robot using a calibration device includes:

[0059] Step S100: Install and fix calibration block 5 in the robot's workspace. For example... Figure 2 As shown, a base coordinate system {O0X0Y0Z0} is established at the center of the robot base, a coordinate system {O7X7Y7Z7} is established at the robot end effector, and a workpiece coordinate system {O7X7Y7Z7} is established at the center of the measuring device. T X T Y T Z T Ensure that the positive directions of the x-axis and y-axis of the workpiece coordinate system and the robot end effector coordinate system are the same. Establish a world coordinate system {O} at the vertex of the calibrated fast inclined plane. w X w Y w Z w This provides data support for the subsequent kinematic model of Robot 1.

[0060] Step S200: Using the drag-and-teach function of robot 1, make the robot end effector with a measuring device contact the vertex of calibration block 5, i.e., the origin of the world coordinate system; record the length of the lift joint 2 and the angles of the other joints at that point; drag the robot end effector with a measuring device to contact the points in the positive x-axis and positive y-axis directions of the world coordinate system, i.e., the vertices of calibration block 5, and record the joint angles and the length of the lift joint 2 at the two points; through the data connection between the robot and the computer, obtain and record the actual joint angles of the robot in real time, providing data support for the subsequent input of joint angles into the robot's kinematic model.

[0061] Step S300: As Figure 3 As shown, the robot end effector performs multi-point measurements on contact planes E1, E2, E3 and E4 respectively, and records the joint angles and lift joint 2 lengths corresponding to all points.

[0062] Step S400: Compare the nominal pose of the robot's end effector with its actual pose to calibrate the kinematic parameters of robot 1. Specifically, this includes:

[0063] Step S401. Establish the robot base coordinate system {O0X0Y0Z0} and the robot end effector coordinate system {O T X T Y T Z T} and the calibration block 5 coordinate system, i.e., the world coordinate system {O w X w Yw Z w};

[0064] S402 models the robot's kinematics, where all robot parameters are nominal.

[0065] S403 obtains the pose matrix of calibration block 5 in the base coordinate system through the contact of the robot end-effector measuring device. The actual pose of the contactor of the robot end-effector measuring device is obtained through the mechanical structure of calibration block 5. At the same time, the nominal pose of the robot corresponding to the robot joint angle is solved. The above actual pose and nominal pose are substituted into the robot kinematic error model for mathematical solution to obtain the actual parameters of the robot.

[0066] Through mechanical structure calculations, the coordinate system {O} of calibration block 5 can be obtained by contacting the hypotenuse of calibration block 5 (i.e., the base point of the world coordinate system) and the two vertices along the positive x and y axes of the world coordinate system via the end measuring device. w X w Y w Z w The nominal pose matrix of the base coordinate system {O0X0Y0Z0} is:

[0067]

[0068] in α, β, γ are the angles of clockwise rotation around the Z-axis, Y-axis and X-axis of the base coordinate system {O0X0Y0Z0}, respectively. The calibration block 5 corresponds to the position coordinates of the robot's base coordinate system;

[0069] The base coordinate system {O0X0Y0Z0} is equivalent to the calibration block 5 coordinate system {O w X w Y w Z w pose matrix of}

[0070] The position coordinates of the robot's end effector on the coordinate system of calibration block 5 are expressed as follows:

[0071]

[0072] When the robot's end effector contacts a plane of calibration block 5, the end effector forms a planar constraint on calibration block 5 and obtains its theoretical position based on the special structure of calibration block 5 itself. With error position The corresponding data relationships;

[0073] Establish a corresponding objective function and seek an approximate solution that minimizes the difference between theoretical parameters and actual errors, thereby obtaining the actual parameters of the robot.

[0074] Calibration block 5 coordinate system {O w X w Y w Z w The normal vector of the top surface is Z. w If the axis and the top surface are located at the origin of the coordinate system of calibration block 5, then the base coordinate system is equivalent to the coordinate system of calibration block 5 in the Z-axis. w If the actual position component on the axis is 0, then when the robot's end effector performs contact measurement on the top surface:

[0075]

[0076] When the robot's end effector contacts the inclined edge of calibration block 5, the base coordinate system is equivalent to the coordinate system of calibration block 5 in the Z-axis. w The actual position components on the axis and in the Z-axis y If the actual position components on the axis are equal, then when the robot's end effector performs contact measurement on the inclined plane:

[0077]

[0078] Similarly, the robot's end-effector measuring device has a contact normal vector of X. w When the axis and the surface are located at the origin of the coordinate system of calibration block 5, the robot end effector performs contact measurement on that surface.

[0079] The robot end effector has a contact normal vector of Y. w When the plane is not located at the origin of the coordinate system of calibration block 5, then the base coordinate system is equivalent to the coordinate system of calibration block 5 in the Y direction. w The actual position components on the axis are fixed values. When the robot's end effector performs contact measurement on this surface, the positional relationship between any two points i and j on this surface is as follows:

[0080]

[0081] By conducting k sets of experiments on different planes of calibration block 5, the following relationship can be obtained:

[0082]

[0083] A nonlinear iterative least squares algorithm is used to make the error in the objective function approach zero:

[0084]

[0085] The final absolute positioning accuracy decreased from 2.887mm to 0.848mm, with the error improved by 70.2%.

Claims

1. A calibration method for a spraying robot calibration device, characterized in that, The calibration device includes a main controller and a robot. The main controller includes a robot control box and a computer system. The robot control box and computer system are connected to the robot. A measuring device is installed at the robot's end via a flange. The robot control box is used to control the movement of the robot and the measuring device, and the computer system is used to store the movement information of the robot and the measuring device. The robot includes a base joint (1), a lifting joint (2), and a six-degree-of-freedom robotic arm (3). The base joint (1) is connected to the six-degree-of-freedom robotic arm (3) through the lifting joint (2). The measuring device includes a metal probe (4) of the same size as the robot end effector and a calibration block (5) with an inclined plane. The metal probe (4) is mounted at the end of the six-degree-of-freedom robotic arm (3), and the calibration block (5) contacts the calibration plane through the robot end effector. The calibration method includes the following steps: S100: Place and fix the calibration block (5) within the workspace accessible to the robot end effector; establish a coordinate system; S200: Use the teach pendant to make the robot end contact the apex of the calibration block (5) and record the length of the robot lifting joint (2) and the angles of the other joints at the apex of the calibration block (5); S300: Using the drag teaching method, let the robot end measuring device contact the three mutually perpendicular planes and the inclined plane of the calibration block (5) respectively, and perform multiple sets of point measurements respectively, and then record the corresponding robot nominal theoretical pose, i.e. the length of the robot lifting joint (2) and the angles of the other joints. S400: Compare the nominal position of the robot end effector with the actual position based on the mechanical structure of the calibration block (5) to calibrate the robot's kinematic parameters; The measuring device obtains the pose transformation of the calibration block (5) relative to the robot base coordinates by contacting the apex of the inclined side of the calibration block (5) with the metal probe (4); Step S400 includes: S401: Establish the coordinate system of the robot base, the coordinate system of the robot end-effector measuring device, and the coordinate system of the calibration block (5); S402: Kinematic modeling of the robot using the MDH method, including the robot's geometric parameters. , , , And all simplified parameters are nominal parameters; S403: Obtain the pose matrix of the calibration block (5) in the base coordinate system through the contact of the robot end measuring device, obtain the actual pose of the robot end measuring device contactor through the mechanical structure of the calibration block (5), and solve the robot nominal pose corresponding to the robot joint angle at the same time. Substitute the above actual pose and nominal pose into the robot kinematic error model for mathematical solution to obtain the actual parameters of the robot. The step S403 includes transforming the robot error from the original robot base coordinates to the coordinates of the calibration block (5), and combining multiple sets of data measured by the robot on different planes with the original mechanical structure to establish a corresponding objective function, seeking an approximate solution with the smallest difference between a set of theoretical parameters and actual error, thereby obtaining the actual parameters of the robot. In step S403, the coordinate system of the calibration block (5) that can be obtained by contacting the hypotenuse of the calibration block (5) through the end-effector measuring device is calculated through a series of coordinate transformations between the mechanical structure and the robot from the base to the robot tool coordinate system. } is equivalent to the base coordinate system { The nominal pose matrix of} is: in , These are the coordinates around the base coordinate system { The Z-axis, Y-axis, and X-axis rotate clockwise by the following angles; The calibration block (5) is equivalent to the position coordinates of the robot's base coordinate system; Then the base coordinate system { } Equivalent to the calibration block (5) coordinate system { pose matrix of} ; The position coordinates of the robot end effector on the calibration block (5) coordinate system are expressed as follows: ; When the robot's end-effector touches a plane of the calibration block (5), the end-effector forms a planar constraint on the calibration block (5) and obtains the theoretical position. With error position The corresponding data relationships; Establish a corresponding objective function and seek an approximate solution that minimizes the difference between theoretical parameters and actual errors, thereby obtaining the actual parameters of the robot.

2. The calibration method for a spraying robot calibration device according to claim 1, characterized in that, The robot performs contact measurement on one vertex of the hypotenuse of the calibration block (5) to form a limiting position that restricts the movement of the robot end and the movement of the lifting joint (2). The coordinate transformation matrix based on the robot base coordinate system is obtained. That is, the robot joint angle and the length of the lifting joint (2) based on the limiting position are used to obtain the robot's nominal pose. The minimum error between the nominal pose and the actual pose is solved to achieve the calibration of the spraying robot.

3. The calibration method for a spraying robot calibration device according to claim 2, characterized in that, The calibration block (5) is trapezoidal with an inclination angle of 45°. The top surface of the other five planes is 200x200mm. The opposite plane of the inclination is the same as the top surface. The lower base of the two adjacent trapezoids is 400mm, the upper base is 200mm, the height is 200mm, and the bottom surface is 200mmx400mm. The above five planes are perpendicular to each other except for the plane directly opposite.

4. The calibration method for a spraying robot calibration device according to claim 3, characterized in that, Step S100 includes establishing a base coordinate system at the center of the robot base. }, Establish a tool coordinate system on the robot's end effector. }, establish a world coordinate system at the hypotenuse vertex of calibration block (5) { }; Using the robot's base coordinate system { The pose relationship from the robot's end effector to the robot tool is used to calibrate the robot tool coordinate system. This allows us to obtain the pose transformation and position of the robot tool end effector in the robot's base coordinate system.

5. The calibration method for a spraying robot calibration device according to claim 3, characterized in that, Step S200 includes obtaining a base coordinate system by having the robot end-effector contact the apex of the inclined plane of the calibration block (5). } to world coordinate system { The coordinate transformation of the robot is obtained by connecting the computer to the robot, acquiring and recording the length of the robot's lifting joint (2) and the angles of the other joints, establishing a kinematic model using the MDH method, and substituting the recorded data to obtain the coordinate transformation from base coordinates to world coordinates.

6. The calibration method for a spraying robot calibration device according to claim 3, characterized in that, In the S300, the specific operation measurement method of drag teaching is to let the robot end measuring device contact the calibration block (5) plane to perform multiple sets of point measurements. After seeing the robot end measuring device contact the calibration block (5) plane, record the corresponding robot lifting joint (2) length and other joint angles to obtain the robot's nominal theoretical pose on the calibration block (5).

7. The calibration method for a spraying robot calibration device according to claim 6, characterized in that, In step S403, the coordinate system of the calibration block (5) is { The normal vector of the top surface is If the axis and the top surface are located at the origin of the coordinate system of the calibration block (5), then the base coordinate system is equivalent to the coordinate system of the calibration block (5) at this time. If the actual position component on the axis is 0, then when the robot's end effector performs contact measurement on the top surface... ; When the robot's end-effector touches the hypotenuse of the calibration block (5), the base coordinate system is equivalent to the coordinate system of the calibration block (5). The actual position components on the axis and in If the actual position components on the axis are equal, then when the robot's end effector performs contact measurement on the inclined plane... ; Similarly, the robot's end-effector measuring device has a contact normal vector of... When the inclined plane is located at the origin of the coordinate system of the calibration block (5), the robot end-effector measuring device performs contact measurement on the inclined plane. ; The robot end effector's contact normal vector is When the axis and the inclined plane are not located at the origin of the coordinate system of the calibration block (5), then the base coordinate system is equivalent to the coordinate system of the calibration block (5) at this time. The actual position components on the axis are fixed values. When the robot's end effector performs contact measurement on the inclined plane, the positional relationship between any two points i and j on the inclined plane is as follows: ； The following relationship is obtained by conducting k sets of experiments on different planes of the calibration block (5): A nonlinear iterative least squares algorithm is used to make the error in the objective function approach zero: 。

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