A mechanical arm calibration method and system of a non-contact displacement sensor

Abstract

The application relates to the technical field of mechanical arm positioning, and provides a mechanical arm calibration method and system of a non-contact displacement sensor. The method is based on the 3-2-1 six-point positioning principle, six laser displacement sensors are arranged on three orthogonal reference surfaces, distance measuring data is collected through multi-pose rotation of a standard gauge block, an over-determined linear equation set is established to solve the spatial expression of the sensor beam axis, and initialization calibration is completed; further, the coefficient matrix condition number is taken as an optimization index, the optimal rotation angle scheme is determined through a control variable experiment and global angle optimization; finally, six nonlinear equation sets are established in combination with plane geometric constraints and homogeneous coordinate transformation, and the end position vector and the rotation matrix are solved by substituting the measured distance data. The application does not need external tracking equipment, can inhibit error amplification effect from the root, can significantly improve calibration accuracy and robustness, has low cost, easy operation and strong universality, and is suitable for high-precision field calibration scenes of various industrial robots.

Description

Technical Field

[0001] This invention relates to the field of robotic arm positioning technology, and in particular to a method and system for calibrating a robotic arm using a non-contact displacement sensor. Background Technology

[0002] Industrial robots, as core equipment in intelligent manufacturing, are a crucial engine for driving the transformation and upgrading of the manufacturing industry. With the continuous improvement of automation in manufacturing, industrial robots are increasingly widely used in welding, assembly, painting, and material handling, placing ever higher demands on the positioning accuracy of robot end effectors.

[0003] However, the generally low absolute positioning accuracy of industrial robots has become a key bottleneck restricting their widespread application in high-precision work scenarios. The absolute positioning accuracy of uncalibrated industrial robots is typically in the range of 2–5 mm, while typical applications such as precision assembly and aerospace component processing require end-effector positioning accuracy of 0.1 mm or even higher. Studies have shown that deviations in geometric parameters of the robot's kinematic model (such as link length, joint offset, and torsion angle) account for more than 80% of the total error in end-effector positioning accuracy. Therefore, it is essential to accurately identify and compensate for kinematic parameters through effective calibration methods.

[0004] Existing robot calibration methods are mainly divided into two categories: open-loop calibration and closed-loop calibration. Open-loop calibration uses external measuring devices such as laser trackers to obtain end-effector pose information. This method offers high measurement accuracy, but the equipment is expensive, the operation is complex, and the environmental requirements are stringent, making it difficult to deploy on a large scale in industrial settings.

[0005] Closed-loop calibration constructs pose constraints using displacement sensors mounted at the end effector, eliminating the need for external measuring equipment, resulting in relatively low cost and good field applicability. However, existing closed-loop calibration methods mostly employ three-point or four-point positioning schemes, limiting the number of sensors and providing insufficient spatial constraints. When sensor ranging errors exist, the calibration results under limited constraints are extremely sensitive to these errors, exhibiting poor robustness. Furthermore, existing methods rarely consider the impact of sensor spatial geometry on calibration accuracy, lacking systematic layout optimization strategies, making it difficult to guarantee the stability and repeatability of calibration results. Summary of the Invention

[0006] The present invention aims to at least improve one of the technical problems existing in the prior art. To this end, the present invention proposes a method and system for calibrating a robotic arm using a non-contact displacement sensor.

[0007] The technical solution of the present invention is as follows: A method for calibrating a robotic arm using a non-contact displacement sensor, comprising: S1: Construct a calibration scenario, which includes a calibration device and a standard gauge block located within the calibration device. The calibration device is assembled on three orthogonal reference planes by six laser displacement sensors in a 3-2-1 six-point positioning manner. The standard gauge block can rotate around the rotation reference axis of the reference plane. S2: Rotate the standard gauge block multiple times, collect the distance measurement data of each laser displacement sensor under each rotation posture, establish geometric constraint equations respectively, combine the measured distance data of each laser displacement sensor, obtain the overdetermined linear equation system of six unknown parameters of each laser displacement sensor, solve the overdetermined linear equation system to obtain the spatial expression of the laser beam axis of each laser displacement sensor in the measurement coordinate system, and complete the initial calibration of the calibration device. S3: Based on the initial calibration completed in S2, an overdetermined constraint calibration model with the condition number of the coefficient matrix as the optimization index is established. The control variable method is used to carry out comparative experiments with different angle intervals to determine the optimal range of angle intervals and eliminate abnormal angle combinations. Then, the rotation angle of the standard gauge block is globally optimized with the goal of minimizing the condition number. After iterative screening and experimental verification, the rotation angle scheme of the standard gauge block is determined and used for the multi-pose measurement of the standard gauge block in S4. S4: Based on the initial calibration results obtained in S2 and the rotation angle scheme obtained in S3, establish the measurement coordinate system and the workpiece coordinate system. Collect the distance measurement data of the intersection of the laser spot on the surface of the standard gauge block through six laser displacement sensors. Utilize the geometric constraint relationship of the equations of the laser beam central axis and the contact surface plane of the standard gauge block, and combine homogeneous coordinate transformation to establish a set of six nonlinear equations about the relative pose between the two coordinate systems. Substitute the measured distance data to solve for the position vector and rotation matrix, complete the accurate calculation of the end pose parameters, and output the final pose matrix.

[0008] In one possible technical solution, further, in S2, the overdetermined linear equation system is expressed as follows: , in, Let be the normal vector of the plane, and d be the plane position parameter. Here are the spatial coordinates of the laser displacement sensor's emission point in the measurement coordinate system. Let be the unit direction vector of the laser beam axis. This represents the measured distance from the emission point of the laser displacement sensor to the intersection of the laser spot on the surface of the standard gauge block. The number in the subscript is the serial number of the laser displacement sensor. Let the large number matrix on the left Coefficient matrix The column vector on the right is Matrix, using matrix inversion: , Once the calculation is complete, you will get and The six real solutions, when substituted into the equation of the spatial straight line, completely determine the spatial expression of the sensor's laser beam axis in the measurement coordinate system: .

[0009] In one possible technical solution, S3 further includes: S31, Establish the overdetermined constraint linear equation system and its matrix perturbation analysis model: Using a calibration device composed of three sets of orthogonal reference surfaces A, B, and C, the ranging data of each laser displacement sensor are collected under various rotational attitudes by rotating standard gauge blocks around different rotation axes, forming a multi-dimensional measurement constraint system, and constructing a system of the form... AX=D For overdetermined linear equation systems, the condition number of the coefficient matrix is ​​used as the core optimization index to measure the ill-conditionedness of the matrix; S32, Constructing a reference group calibration experiment and obtaining the condition number of the reference matrix: Based on the spatial expression obtained in S2, a preset small-angle concentrated distribution scheme is adopted, and multiple concentrated deflection angles are set around two reference axes parallel to the x-axis and z-axis of the global coordinate system to form several sets of reference measurement conditions; under each condition, the laser ranging value and the corresponding gauge block pose information are recorded, and the reference coefficient matrix is ​​constructed after importing them into the MATLAB solution model. The condition number of the reference coefficient matrix is ​​calculated, and the coordinates of the emission point and the direction vector obtained by the solution are compared with the design nominal values ​​of each laser displacement sensor in the measurement coordinate system to calculate the reference position error and angle deviation. S33, Investigate the influence of different angle intervals on the stability of the solution: Based on S32, keep other experimental conditions consistent, only change the rotation angle interval of the standard gauge block around the two reference axes, and carry out a single-factor comparison experiment: Set multiple different angle intervals in sequence, solve the coefficient matrix condition number, position error and angle deviation under each working condition, identify and eliminate abnormal angle combinations that lead to high linear correlation of column vectors, and determine the angle interval range in which the condition number and error are in the stable range. S34. Global angle distribution optimization and experimental verification based on condition number minimization: With minimizing the condition number of the coefficient matrix as the objective, and following the pattern obtained in S33, and using the baseline condition number obtained in S32 as the criterion for judging the optimization effect, the rotation angle sampling interval is widened and an alternating distribution of positive and negative angles is introduced. Candidate angle combination schemes are determined through iterative screening. Data is re-collected according to a standardized process, and the optimized coefficient matrix is ​​constructed. A The optimized coefficient matrix condition number is calculated and compared with the baseline coefficient matrix condition number obtained in S32 to verify the optimization effect. After verification, the current angle combination is determined as the rotation parameter scheme of the calibration device, which is used for end pose calculation in subsequent steps.

[0010] In one possible technical solution, S4 further includes: S41: Establish the measurement coordinate system With workpiece coordinate system Measurement coordinate system Fixed to the calibration device body, workpiece coordinate system Fixed on the surface of the standard gauge block, workpiece coordinate system The origin is in the measurement coordinate system The spatial position is obtained through the position vector. This indicates that the spatial attitude transformation between two coordinate systems is achieved through a rotation matrix. describe; S42: Establish the equation of the central axis of the laser displacement sensor, and set the workpiece coordinate system. Transform the coordinates of the contact points and normal vectors of each contact surface of the standard gauge block to the measurement coordinate system. ; S43: Derivation of the contact plane of the standard gauge block in the measurement coordinate system Based on the geometric constraint relationship between the central axis of the laser beam of the laser displacement sensor and the spatial plane of the contact surface of the standard block, the theoretical ranging expressions from the emission point of the six laser displacement sensors to their respective corresponding spot intersection points are established. The actual output ranging values ​​of each laser displacement sensor are used as known quantities to construct six nonlinear equation sets. S44: Obtain the actual measurement values ​​of six sets of laser displacement sensors, substitute them into the six nonlinear equations established in S43, solve for the six unknown parameters in the position vector and rotation matrix, and calculate the relative pose matrix between the workpiece coordinate system and the measurement coordinate system to complete the accurate calculation of the end pose parameters.

[0011] S45: Output the final pose matrix.

[0012] In one possible technical solution, further, in step S41, the rotation matrix adopts Euler angles. Parameterization, respectively characterizing the workpiece coordinate system Around the measurement coordinate system The deflection attitude along the x-axis, y-axis, and z-axis, and their combined relationship is as follows: , Construct a homogeneous transformation matrix by combining the position vectors, i.e.: .

[0013] In one possible technical solution, further, in S42, in the measurement coordinate system... Below, the equation of the central axis of the i-th laser displacement sensor is given by its axial unit direction vector. and installation point coordinates Confirmed as: , , in, For the i-th laser displacement sensor in the measurement coordinate system The coordinate components of the unit direction vector along the axial direction below, in the x-axis direction. For the i-th laser displacement sensor in the measurement coordinate system The coordinate components of the unit direction vector along the y-axis. For the i-th laser displacement sensor in the measurement coordinate system The coordinate components of the unit direction vector along the axial direction below, with T being the matrix transpose symbol. For a fixed reference point on the central axis of the i-th laser displacement sensor in the measurement coordinate system The x-axis coordinate variable of the spatial coordinates below. For a fixed reference point on the central axis of the i-th laser displacement sensor in the measurement coordinate system The y-axis coordinate variable of the spatial coordinates below. For a fixed reference point on the central axis of the i-th laser displacement sensor in the measurement coordinate system The z-axis coordinate variable of the spatial coordinates below. For a fixed reference point on the central axis of the laser displacement sensor in the measurement coordinate system x-axis coordinate variable, For a fixed reference point on the central axis of the laser displacement sensor in the measurement coordinate system The y-axis coordinate variable, For a fixed reference point on the central axis of the laser displacement sensor in the measurement coordinate system The z-axis coordinate variable.

[0014] In one possible technical solution, further, in S43, the theoretical ranging expression is: , in, The direct output measurement value of the laser displacement sensor represents the straight-line distance from the laser displacement sensor's emission point, along the laser beam axis, to the intersection point of the laser spot on the surface of the standard gauge block. This indicates that the i-th sensor is in the measurement coordinate system. The coordinates of the contact point between the lower surface and the standard gauge block. Indicates the plane of the standard gauge block in the measurement coordinate system The normal vector below, This indicates that the sensor's central axis is in the measurement coordinate system. The actual installation point coordinates are determined below. This indicates that the i-th laser displacement sensor is in the measurement coordinate system. The axial unit direction vector below; The six nonlinear equations are: .

[0015] In one possible technical solution, the calibration device further includes: Measuring mounting plate; An adapter flange is installed on the surface of the measuring and fixing plate; A fixed flange is mounted on the surface of the measuring mounting plate, away from the adapter flange; Three mounting plates are assembled and connected in sequence to form three orthogonal reference planes. They are installed on the measuring and fixing plate to form an open cavity, wherein the fixing flange is located inside the cavity. Multiple laser displacement sensors are mounted on the three orthogonal reference planes of the mounting plate in a 3-2-1 six-point positioning configuration; The standard gauge block, which has a cube-shaped structure, is installed on the fixed flange.

[0016] In one possible technical solution, both the transition flange and the fixed flange are coaxial rotating structures. The three orthogonal reference planes are reference plane A, reference plane B, and reference plane C, which are used to install three, two, and one laser displacement sensor, respectively.

[0017] A non-contact displacement sensor robotic arm calibration system, calibrated using the aforementioned robotic arm calibration method, includes: The scene construction module is used to construct a calibration scene, which includes a calibration device and a standard block located in the calibration device. The calibration device is assembled by six laser displacement sensors in a 3-2-1 six-point positioning manner on three orthogonal reference planes. The standard block can rotate around the rotation reference axis of the base plane. The initialization calibration module is used to rotate the standard block multiple times, collect the distance measurement data of each laser displacement sensor under each rotation posture, establish geometric constraint equations, and solve the measured distance data of each laser displacement sensor to obtain the overdetermined linear equation system of six unknown parameters of each laser displacement sensor. Solving the overdetermined linear equation system yields the spatial expression of the laser beam axis of each laser displacement sensor in the measurement coordinate system, thus completing the initialization calibration of the calibration device. The angle optimization module, based on the initialization and calibration completed by the initialization and calibration module, establishes an overdetermined constraint calibration model with the condition number of the coefficient matrix as the optimization index. It conducts comparative experiments with different angle intervals using the control variable method to determine the optimal range of angle intervals and eliminate abnormal angle combinations. Then, it performs global optimization of the rotation angle of the standard gauge block with the goal of minimizing the condition number. After iterative screening and experimental verification, it determines the rotation angle scheme of the standard gauge block for multi-pose measurement of the standard gauge block. The solution output module is used to establish the measurement coordinate system and the workpiece coordinate system based on the initial calibration results and rotation angle scheme. It collects distance measurement data of the intersection point of the laser spot on the surface of the standard gauge block through six laser displacement sensors. It uses the geometric constraint relationship of the equations of the laser beam central axis and the plane of the contact surface of the standard gauge block to establish a set of six nonlinear equations about the relative pose between the two coordinate systems by combining homogeneous coordinate transformation. After substituting the measured distance data, it solves the position vector and rotation matrix to complete the accurate calculation of the end pose parameters and outputs the final pose matrix.

[0018] The robotic arm calibration method and system for the non-contact displacement sensor according to the present invention have the following advantages: 1. Significantly improves calibration accuracy and robustness: Based on the principle of six-point spatial positioning, this invention arranges 3, 2, and 1 laser displacement sensors in three mutually perpendicular spatial directions, respectively, for a total of six sets of sensors to form a complete constraint of six degrees of freedom in space. By simultaneously measuring the distance of the standard block with the six sets of sensors, an overdetermined measurement equation set is constructed, realizing the simultaneous solution of the six-dimensional pose parameters of the end effector. This effectively suppresses the measurement uncertainty caused by insufficient constraint in one direction. Compared with the traditional three-point or four-point positioning scheme, it significantly improves the stability and calibration accuracy of pose measurement.

[0019] 2. Suppressing the error amplification effect at the source: This invention uses the condition number of the coefficient matrix of the overdetermined equation system as the core evaluation index to globally optimize the spatial geometric layout of the six sets of sensors and the rotation angle sequence of the standard gauge blocks. This improves the orthogonality of the column vectors of the coefficient matrix and reduces the condition number, thereby effectively alleviating the matrix ill-conditioned problem. This suppresses the amplification effect of ranging error on the calibration results at the source and further improves the calibration accuracy and anti-interference capability.

[0020] 3. Significantly reduces calibration costs and operational complexity: This invention requires only six sets of laser displacement sensors and standard gauge blocks to complete the complete end-effector pose calibration, without relying on expensive external measuring equipment such as laser trackers. This significantly reduces equipment investment costs and technical barriers, while simplifying the calibration operation process, and has good engineering economics and field applicability.

[0021] 4. High versatility and adaptability to different specifications of industrial robots: This invention does not depend on a specific robot model or end effector configuration. By replacing standard gauge blocks of different sizes or adjusting the sensor installation position, it can flexibly adapt to the end effector calibration requirements of industrial robots of different specifications. It has good versatility and personalized adaptability and can be widely used in on-site calibration scenarios of various robot models.

[0022] 5. Balancing high precision with practicality and economy to promote high-precision applications: While ensuring calibration accuracy, this invention also considers cost control and ease of operation, effectively solving the technical problems of insufficient accuracy, poor robustness, and complex operation of existing calibration methods. It has important engineering value for promoting the widespread application of industrial robots in high-precision operation scenarios such as precision assembly and aerospace manufacturing, and provides solid technical support for the development of intelligent manufacturing.

[0023] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0024] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart of a robotic arm calibration method for a non-contact displacement sensor according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of a robotic arm calibration device for a non-contact displacement sensor according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the robotic arm calibration device for a non-contact displacement sensor according to an embodiment of the present invention from another perspective. Figure 4 This is a schematic diagram of a simulation experiment for spatial linear calibration of a laser displacement sensor. Figure 5 This is a flowchart of coordinate transformation and end pose calculation under the six-point positioning constraint in S4 of the calibration method of this invention embodiment; Figure 6 This is a schematic diagram of the robot's end-effector pose spatial positioning.

[0026] Figure label: Measuring mounting plate 1, adapter flange 2, fixed flange 3, first sensor mounting plate 41, second sensor mounting plate 42, third sensor mounting plate 43, laser displacement sensor 5, standard gauge block 6. Detailed Implementation

[0027] The embodiments of the present invention are described in detail below. The embodiments described with reference to the accompanying drawings are exemplary. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit this application.

[0028] Example 1 like Figures 1 to 6 As shown, this embodiment provides a method for calibrating a robotic arm using a non-contact displacement sensor, which includes: S1: Construct a calibration scenario, which includes a calibration device and a standard gauge block located within the calibration device. The calibration device is assembled on three orthogonal reference planes by six laser displacement sensors in a 3-2-1 six-point positioning manner. The standard gauge block can rotate around the rotation reference axis of the reference plane. S2: Rotate the standard gauge block multiple times, collect the distance measurement data of each laser displacement sensor under each rotation posture, establish geometric constraint equations respectively, combine the measured distance data of each laser displacement sensor, obtain the overdetermined linear equation system of six unknown parameters of each laser displacement sensor, solve the overdetermined linear equation system to obtain the spatial expression of the laser beam axis of each laser displacement sensor in the measurement coordinate system, and complete the initial calibration of the calibration device. S3: Based on the initial calibration completed in S2, an overdetermined constraint calibration model with the condition number of the coefficient matrix as the optimization index is established. The control variable method is used to carry out comparative experiments with different angle intervals to determine the optimal range of angle intervals and eliminate abnormal angle combinations. Then, the rotation angle of the standard gauge block is globally optimized with the goal of minimizing the condition number. After iterative screening and experimental verification, the rotation angle scheme of the standard gauge block is determined and used for the multi-pose measurement of the standard gauge block in S4. S4: Based on the initial calibration results obtained in S2 and the rotation angle scheme obtained in S3, establish the measurement coordinate system and the workpiece coordinate system. Collect the distance measurement data of the intersection of the laser spot on the surface of the standard gauge block through six laser displacement sensors. Utilize the geometric constraint relationship of the equations of the laser beam central axis and the contact surface plane of the standard gauge block, and combine homogeneous coordinate transformation to establish a set of six nonlinear equations about the relative pose between the two coordinate systems. Substitute the measured distance data to solve for the position vector and rotation matrix, complete the accurate calculation of the end pose parameters, and output the final pose matrix.

[0029] It should be noted that, in this embodiment, the calibration device includes: Measuring fixing plate 1; The adapter flange 2 is installed on the surface of the measuring fixing plate 1; Fixed flange 3 is installed on the surface of the measuring fixed plate 1, which is away from the adapter flange 2; Three mutually perpendicular mounting plates are assembled and connected in sequence to form three orthogonal reference planes, which are installed on the measuring fixing plate 1 to form an open cavity, wherein the fixing flange 3 is located inside the cavity; Six laser displacement sensors 5 are installed in a 3-2-1 six-point positioning configuration on three orthogonal reference planes of the mounting plate, namely reference plane A, reference plane B, and reference plane C. These are used to install three, two, and one laser displacement sensor 5 respectively, forming 3, 2, and 1 measurement constraints in the three orthogonal directions, thus constituting a six-degree-of-freedom pose calculation reference. This layout makes the measurement errors in each direction more balanced, and the structure is simple and easy to process and assemble.

[0030] The standard gauge block 6 has a cube-shaped structure and is installed on the fixed flange 3. The standard gauge block 6 has multiple mounting thread holes and positioning pin holes for installation and corner fixing.

[0031] During calibration, the standard gauge block 6 is coaxially mounted on the rotary positioning mechanism of the robotic arm via the fixed flange 3 and the adapter flange 2. By controlling the standard gauge block 6 to rotate sequentially to six preset angles, it is positioned by a positioning pin and the locking bolt is tightened after each preset angle to ensure the stability of the standard gauge block 6's posture. After the posture is fixed, all laser displacement sensors 5 simultaneously measure their respective distances to the surface of the standard gauge block 6. Combining the known geometric dimensions and rotation parameters of the standard gauge block 6, the spatial coordinates and normal vectors of the emission points of each laser displacement sensor 5 can be calculated, thereby obtaining the precise pose of the robotic arm's end effector in the measurement coordinate system.

[0032] It should be noted that in this embodiment, the three mounting plates are the first sensor mounting plate 41, the second sensor mounting plate 42, and the third sensor mounting plate 43, all of which are rectangular plate structures with consistent material and surface roughness requirements.

[0033] Each mounting plate has three, two, and one rectangular mounting slots on its front side, corresponding to the number of laser displacement sensors 5 installed. The mounting slots are spaced apart along the plate surface and are used to accommodate and fix the sensor brackets of the laser displacement sensors 5. Threaded holes are symmetrically arranged on both sides of each mounting slot to lock the sensor brackets to the plate surface.

[0034] Each mounting plate has multiple bolt through holes evenly spaced along its length on its upper edge for interconnection. Each mounting plate also has a continuous positioning structure at its bottom. The first sensor mounting plate 41 and the second sensor mounting plate 42 are provided with positioning bosses, while the third sensor mounting plate 43 is provided with matching positioning grooves. During assembly, the bosses and grooves fit together to precisely define the relative positions between the plates. Flatness tolerances are specified on both the front and back sides of all mounting plates, and parallelism tolerances are set between the two sides. Furthermore, the mating surfaces of the positioning bosses and positioning grooves are required to have perpendicularity tolerances relative to the reference surface of the mounting plates to ensure good orthogonal accuracy between the assembled plates.

[0035] The three mounting plates fit together through positioning bosses and positioning grooves, and are fastened together by bolts passing through bolt holes on the upper edge of each plate, forming a stable three-dimensional orthogonal sensor bracket. This ensures that the emission direction of each laser displacement sensor 5 is strictly along the coordinate axis, providing an accurate geometric reference for subsequent pose calculation.

[0036] It should be noted that in this embodiment, the adapter flange 2 and the fixed flange 3 constitute a rotary positioning mechanism. The standard gauge block 6 is installed on the measuring fixed plate 1 through this mechanism and can rotate around the rotation axis of the adapter flange 2 and the fixed flange 3 to a preset angle. After reaching the preset angle, it is locked by the positioning pin, thereby realizing the switching and maintenance of multi-angle calibration posture.

[0037] Specifically, the measuring fixing plate 1 is a rectangular plate structure, fixed to a mounting plate assembly formed by three mounting plates. The measuring fixing plate 1 has a through hole in its center for the adapter flange 2 to pass through. Around the central through hole, multiple bolt holes are evenly distributed on the inner circumference for locking the adapter flange 2 to the measuring fixing plate 1; multiple locating pin holes are evenly distributed on the outer circumference, arranged at a preset angle for inserting locating pins to achieve angular positioning. Bolt holes are also provided on the side edges of the measuring fixing plate 1 for connection to the mounting plate; a continuous locating groove is provided on the bottom of the plate, which cooperates with the locating boss of the adjacent mounting plate to achieve assembly positioning.

[0038] Both the fixed flange 3 and the transition flange 2 are coaxial rotating structures. One side of the fixed flange 3 has a cylindrical central boss with an assembly hole inside, and the other side has a flat connection end face with an assembly hole for mating with the standard gauge block 6. Multiple sets of connection holes with different radii are distributed on the end face for connecting the standard gauge block 6 and the transition flange 2.

[0039] The transition flange 2 has a stepped structure. The middle section is for fitting the shaft diameter, which passes through the central through hole of the measuring fixing plate 1 and mates with the assembly hole of the fixed flange 3 to form a rotating pair. One end face has threaded holes distributed around the circumference, which are bolted to the fixed flange 3. The other end is the flange connection end, and the end face has multiple sets of connection holes for locking the transition flange 2 onto the measuring fixing plate 1.

[0040] During assembly, the measuring fixing plate 1 is fixed to the mounting plate assembly, the adapter flange 2 is inserted into its central through hole and locked, the fixing flange 3 is aligned with the adapter flange 2 and bolted in place, and the standard gauge block 6 is installed on the connecting end face of the fixing flange 3. During calibration, the bolts are loosened, and the standard gauge block 6, together with the fixing flange 3, is rotated around the axis to the target angle. The locating pin is inserted into the corresponding pin hole to achieve angle positioning, and then the bolts are tightened to lock and fix it.

[0041] It should be noted that in this embodiment, all six outer surfaces of the standard gauge block 6 have undergone precision grinding and fine lapping. One end face is the mounting end face, used for mating and assembly with the fixed flange 3. On this mounting end face, a pair of threaded holes are symmetrically arranged along the vertical center line, and a pair of locating pin holes are symmetrically arranged along the horizontal center line. During installation, bolts pass through the corresponding through holes on the fixed flange 3 and are screwed into the threaded holes on the mounting end face of the standard gauge block 6. At the same time, locating pins are inserted into the locating pin holes to achieve limiting, thereby ensuring a secure connection between the standard gauge block 6 and the fixed flange 3 through a combination of bolt locking and pin positioning.

[0042] Specifically, the other five outer surfaces of standard gauge block 6 are all reference measurement surfaces. Each reference measurement surface has a parallelism tolerance requirement relative to the mounting end face, and each surface itself also has specified flatness tolerance and surface roughness requirements. During calibration, laser displacement sensors arranged in three orthogonal directions emit lasers towards the corresponding reference measurement surfaces and collect distance measurement data, which are used to solve for the spatial coordinates of each sensor emission point and the direction vector of its laser beam.

[0043] It should be noted that in this embodiment, S2 is based on the six-point positioning calibration device built in S1. By rotating the standard gauge block multiple times and collecting ranging data under various attitudes, the spatial linear equations of the six sets of laser displacement sensors are solved to complete the initial calibration of the device. Figure 4 As shown. Since the spatial installation position and orientation of the laser displacement sensor cannot be directly measured after the calibration device is assembled, it is necessary to use a standard gauge block with known geometric relationships as a calibration reference. By using the multiple sets of spatial constraints provided by the standard gauge block under different rotational attitudes, the spatial coordinates of the emission point of each laser displacement sensor and the normal vector of the laser beam axis are calculated in reverse, providing accurate sensor spatial geometric parameters for the end pose calculation in subsequent steps.

[0044] like Figures 2 to 4 As shown, when the standard gauge block rotates around the axis connecting the fixed flange and the transition flange, each measured surface rotates synchronously with the standard gauge block, and the spatial orientation of each measured surface can be uniquely determined by the rotation angle. Each laser displacement sensor is fixed to the mounting plate, and the axis of its emitted laser beam is a straight line in the measurement coordinate system. The equation of this straight line can be expressed in parametric form: .

[0045] in Here are the spatial coordinates of the laser displacement sensor's emission point in the measurement coordinate system. Let be the unit direction vector of the laser beam axis of the laser displacement sensor, and t be the measured distance from the emission point output by the laser displacement sensor to the intersection point of the laser spot on the surface of the standard block. The above linear equation is the objective to be solved for S2, which contains six unknown parameters.

[0046] The measured surfaces of the standard gauge block can be represented by the spatial plane equations in the measurement coordinate system: , in is the normal vector of the measured surface, whose direction is determined by the current rotational attitude of the standard gauge block and the known normal direction of the measured surface in the workpiece coordinate system through coordinate transformation; d is the planar position parameter, which is the normal vector of each measured surface when the standard gauge block rotates about the connecting axis. The laser beam changes synchronously with the rotation angle, and its variation is uniquely determined by the rotation angle and the known geometric dimensions of the gauge block. Substituting the laser beam parametric equation into the above spatial plane equation, the geometric constraint relationship between the sensor emission point, the laser beam direction, and the gauge block surface under a single ranging posture can be established: , After unfolding and organizing, we can obtain: , in t This represents the measured distance from the emission point of the laser displacement sensor to the intersection of the laser spot on the surface of the standard gauge block under this posture. The rotational attitude of the standard gauge block is determined by the current rotational attitude of the gauge block, and d is determined by the spatial position of the measured surface of the standard gauge block. In the above equation, and One is an unknown quantity, while the other parameters are known quantities.

[0047] By sequentially rotating the standard gauge block to six preset angles, six sets of laser displacement sensors simultaneously acquire the measured distance values ​​between themselves and the measured surface at each preset angle. Simultaneously, based on the spatial attitude of the standard gauge block at each preset angle, the normal vector and planar position parameters corresponding to each measured surface are calculated. For a single sensor, the six distance measurements correspond to six different standard gauge block attitudes. Each measurement establishes the geometric constraint relationship described above. Connecting the data from the six measurements together yields an overdetermined linear equation set regarding the six unknown parameters of the sensor: , Let the large number matrix on the left be the coefficient matrix. The column vector on the right is Matrix, using matrix inversion: , Once the calculation is complete, you will get and The six real solutions, when substituted into the spatial linear equation, completely determine the spatial expression of the sensor's laser beam axis in the measurement coordinate system. By performing the above calibration procedure on each of the six sets of laser displacement sensors, all six sets of spatial linear equations can be obtained, completing the initial calibration of the calibration device and providing the sensor's spatial geometric parameters for the accurate calculation of the S4 end-effector pose.

[0048] It should be noted that, in this embodiment, S3 specifically includes: S31, Establish the overdetermined constrained linear equation system and its matrix perturbation analysis model: Using a calibration device composed of three sets of orthogonal reference planes A, B, and C, the ranging data of each laser displacement sensor is collected under various rotational attitudes by rotating a standard block around different axes, forming a multidimensional measurement constraint system, and constructing an overdetermined linear equation system of the form AX=D, with the coefficient matrix condition number... As a core optimization index for measuring the ill-conditioning of a matrix, it provides a theoretical basis for the spatial linear calibration of laser displacement sensors.

[0049] Considering the continuous accumulation of various errors (such as optical path deviation, truncation and discretization errors) during the engineering calibration process, it will lead to the coefficient matrix... and its corresponding constant term vector Generate small perturbations According to matrix perturbation theory, the upper limit of error amplification is determined by the condition number of the coefficient matrix; this upper limit of amplification is the condition number of the matrix. In practical applications of robotic arm parameter identification, the coefficient matrix... A It is usually a non-square matrix, and its condition number needs to be calculated using the generalized inverse matrix, as shown in the formula: , In the formula, Represents the coefficient matrix The generalized inverse matrix. The closer the condition number is to 1, the more stable the solution to the equation. If the condition number is too large, it can lead to ill-conditioned problems, causing small errors to be significantly amplified. Therefore, this step aims to minimize the condition number of the coefficient matrix. The core optimization objective is to achieve this.

[0050] S32, Constructing a reference group calibration experiment and obtaining the condition number of the reference matrix: Based on the spatial expression obtained in S2, a preset angle concentration distribution scheme is adopted, and multiple concentrated deflection angles are set around two reference axes parallel to the x-axis and z-axis of the global coordinate system to form several sets of reference measurement conditions; under each condition, the laser ranging value and the corresponding gauge block pose information are recorded, and the reference coefficient matrix is ​​constructed after importing them into the MATLAB solution model. The condition number of the reference coefficient matrix is ​​calculated, and the coordinates of the emission point and the direction vector obtained by the solution are compared with the design nominal values ​​of each laser displacement sensor in the measurement coordinate system to calculate the reference position error and angle deviation.

[0051] Specifically, the original reference calibration experiment is carried out using a traditional small-angle concentrated distribution scheme to calculate the condition number of the reference matrix and the initial error. Preset small angle distribution: Select a small angle concentration range (e.g., positive rotation of 10° to 35°), and set 3 concentrated deflection angles for each of the two reference axes parallel to the global coordinate system x-axis and z-axis (e.g., 20°, 25°, and 35° around the x-axis; and 10°, 15°, and 20° around the z-axis), forming a total of 6 sets of reference measurement conditions; Collect measured data: Under each working condition, record the following key measured data using geometric measurement tools (such as CATIA or 3D measurement software): Three-dimensional coordinates of the spatial intersection point of the laser line and the gauge block plane The normal direction vector of the plane at the intersection point Measurement distance from laser emission point to spatial intersection point .

[0052] Solving for the baseline condition number and error: Import the above 6 sets of measured data into the MATLAB solution model and construct a 6×6 coefficient matrix. and constant term vector The condition number of the baseline coefficient matrix of the reference group was calculated. The coordinates and normal vector of the launch point are solved and compared with the theoretical true value to obtain the Euclidean distance comprehensive error and angle deviation of the launch point coordinates.

[0053] S33, Investigating the influence of different angle intervals on the stability of the solution: Based on S32, in order to avoid blind adjustment, while keeping the theoretical coordinates of the laser emission point consistent with the inherent error of the system, only the rotation angle interval of the standard block around the two reference axes was changed, and a single-factor comparison experiment was carried out: Multiple different angle intervals were set in sequence, and the condition number of the coefficient matrix, position error and angle deviation under each working condition were solved respectively. Abnormal angle combinations that lead to high linear correlation of column vectors were identified and eliminated, and the angle interval range in which the condition number and error are in the stable range was determined.

[0054] Specifically, it includes: Set up multiple sets of equally spaced working conditions: rotate the standard gauge block around the reference axis parallel to the x-axis and z-axis, and set the interval between adjacent angles to 10°, 20°, 30°, 40° and 50° in sequence; Identifying and eliminating anomalous distribution features: The solution results show that the angle combinations (30°, 60°, 90°) corresponding to 30° intervals have obvious problems: the complementarity of 30° and 60° leads to high coupling of the normal vector, while the orthogonal flip of 90° significantly compresses the distance parameter. The range of variation causes the coefficient matrix to change. A The column vectors exhibit severe linear dependence. Therefore, it is essential to strictly avoid consecutive equally spaced configurations containing complementary angles, supplementary angles, or 90° right-angle flips. Determine a reasonable interval range: Comparing the working conditions of 10°, 20°, 40° and 50°, it can be seen that when the angle interval is within the range of 20° to 40°, the condition number of the coefficient matrix and the solution error of each item are maintained at a low and stable level.

[0055] S34. Perform global angle distribution optimization and experimental verification based on condition number minimization: With minimizing the condition number of the coefficient matrix as the objective, based on the pattern obtained in S33 and using the baseline condition number obtained in S32 as the criterion for judging the optimization effect, widen the rotation angle sampling interval and introduce alternating positive and negative angle distributions. Determine the candidate angle combination scheme through iterative screening; re-collect data according to the standardized process and construct the optimized coefficient matrix A, calculate the optimized coefficient matrix condition number, and compare it with the baseline coefficient matrix condition number obtained in S32 to verify the optimization effect; after verification, determine the current angle combination as the rotation parameter scheme of the calibration device for use in the end pose calculation of subsequent steps.

[0056] Specifically, based on the influence patterns derived from S33, with To achieve the goal, a global optimization is performed on the spatial distribution of the rotation angles of the standard gauge blocks: Expanding the angle range and introducing positive and negative symmetrical distribution: The sampling range of rotation angle is expanded from the concentrated area (10°~35°) to (-59°~59°), and the alternating distribution of positive and negative angles is introduced to significantly improve the spatial coverage uniformity of the plane normal vector on the three-dimensional unit sphere. Determine the optimal angle combination: After multiple rounds of iterative screening, 6 sets of mutually non-interfering optimal angle conditions were determined (e.g., 59°, 32°, and -42° around the x-axis; 46°, -15°, and -59° around the z-axis). Data collection and optimization: Strictly following the standardized S32 process, six sets of core measured data (plane intersection coordinates, distance, and normal vector) under optimized angle combinations were re-collected, imported into the solution model, and the optimized coefficient matrix was constructed. .

[0057] Effect comparison and verification: Calculate the condition number of the optimized matrix The original calibration scheme was compared with the optimized scheme.

[0058] It should be noted that, in this embodiment, based on the optimal rotation angle scheme of the calibration device determined in S3 and the initial calibration results, in S4, distance data of six intersection points on the surface of the standard gauge block are collected by six sets of displacement sensors (where the intersection point is the intersection point of the laser emission line and the surface of the standard gauge block). Combined with coordinate transformation theory, the accurate calculation of the end pose parameters is completed. The specific process is as follows: Figure 5 As shown. Includes: S41: Establish the measurement coordinate system With workpiece coordinate system Measurement coordinate system Fixed to the calibration device body, workpiece coordinate system Fixed on the surface of the standard gauge block, workpiece coordinate system The origin is in the measurement coordinate system The spatial position is obtained through the position vector. This indicates that the spatial attitude transformation between two coordinate systems is achieved through a rotation matrix. Description. Reference Figure 6 As shown, the rotation matrix Euler angles The parameters represent the deflection attitude of the workpiece coordinate system about the x-axis, y-axis, and z-axis of the measurement coordinate system, respectively, and their composite relationship is as follows: .

[0059] Construct a homogeneous transformation matrix by combining the position vectors, i.e.: .

[0060] S42: Establish the equation of the central axis of the laser displacement sensor, and set the workpiece coordinate system. Transform the coordinates of the contact points and normal vectors of each contact surface of the standard gauge block to the measurement coordinate system. ; Specifically, in the measurement coordinate system Below, the equation of the central axis of the i-th laser displacement sensor is given by its axial unit direction vector. and installation point coordinates Confirmed as: , , in, For the i-th laser displacement sensor in the measurement coordinate system The coordinate components of the unit direction vector along the axial direction below, in the x-axis direction. For the i-th laser displacement sensor in the measurement coordinate system The coordinate components of the unit direction vector along the y-axis. For the i-th laser displacement sensor in the measurement coordinate system The coordinate components of the unit direction vector along the axial direction below, with T being the matrix transpose symbol. For a fixed reference point (such as the laser emission point) on the central axis of the i-th laser displacement sensor in the measurement coordinate system The x-axis coordinate variable of the spatial coordinates below. For a fixed reference point (such as the laser emission point) on the central axis of the i-th laser displacement sensor in the measurement coordinate system The y-axis coordinate variable of the spatial coordinates below. For a fixed reference point on the central axis of the i-th laser displacement sensor in the measurement coordinate system The z-axis coordinate variable of the spatial coordinates below. For a fixed reference point (such as the laser emission point) on the central axis of the laser displacement sensor in the measurement coordinate system x-axis coordinate variable, For a fixed reference point (such as the laser emission point) on the central axis of the laser displacement sensor in the measurement coordinate system The y-axis coordinate variable, For a fixed reference point (such as the laser emission point) on the central axis of the laser displacement sensor in the measurement coordinate system The z-axis coordinate variable.

[0061] S43: Derivation of the contact plane of the standard gauge block in the measurement coordinate system Based on the geometric constraint relationship between the central axis of the laser beam of the laser displacement sensor and the spatial plane of the contact surface of the standard block, the theoretical ranging expressions from the emission point of the six laser displacement sensors to their respective corresponding spot intersection points are established. The actual output ranging values ​​of each laser displacement sensor are used as known quantities to construct six nonlinear equation sets. Specifically, the workpiece coordinate system The coordinates of the contact points and their normal vectors on each contact surface of the standard gauge block are transformed to the measurement coordinate system using a homogeneous transformation matrix. Thus, the contact plane of the standard gauge block is constructed in the measurement coordinate system. The equation of the space plane in the equation is: i = 1, 2, ..., 6 This formula shows that any plane The vector formed by a point and the contact point is orthogonal to the normal vector. Subsequently, based on the geometric characteristics of a non-contact laser displacement sensor emitting a laser beam along its central axis and forming a spot intersection on the surface of a standard gauge block, it can be seen that the spatial coordinates of the actual contact point simultaneously satisfy both the plane equation and the sensor's central axis equation. Based on this key geometric constraint, the expression for calculating the distance from the sensor's emission point to the spot intersection can be derived, and after simplification, the following formula is obtained: , in, The direct output measurement value of the laser displacement sensor represents the straight-line distance from the laser displacement sensor's emission point, along the laser beam axis, to the intersection point of the laser spot on the surface of the standard gauge block. This indicates that the i-th sensor is in the measurement coordinate system. The coordinates of the contact point between the lower surface and the standard gauge block. Indicates the plane of the standard gauge block in the measurement coordinate system The normal vector below, This indicates that the sensor's central axis is in the measurement coordinate system. The actual installation point coordinates are determined below. This indicates that the i-th laser displacement sensor is in the measurement coordinate system. The axial unit direction vector below.

[0062] The measurement coordinate system is described by the established homogeneous transformation matrix. With workpiece coordinate system The spatial pose relationship between them, the workpiece coordinate system Transform the coordinates of the contact points and normal vectors of each contact surface of the standard gauge block to the measurement coordinate system. Furthermore, combining this with the distance from the laser beam emission point along its axial direction to the surface of the gauge block, the distances from the six emission points to their corresponding intersection points can be expressed as six nonlinear equations: .

[0063] S44: Obtain the actual measurement values ​​from six sets of laser displacement sensors, substitute them into the six nonlinear equations established in S43, and solve for the six unknown parameters in the position vector and rotation matrix. Based on this, the relative pose matrix between the workpiece coordinate system and the measurement coordinate system can be calculated. This completes the accurate calculation of the end-effector pose parameters.

[0064] S45: Output the final pose matrix.

[0065] A non-contact displacement sensor robotic arm calibration system, calibrated using the aforementioned robotic arm calibration method, includes: The scene construction module is used to construct a calibration scene, which includes a calibration device and a standard block located in the calibration device. The calibration device is assembled by six laser displacement sensors in a 3-2-1 six-point positioning manner on three orthogonal reference planes. The standard block can rotate around the rotation reference axis of the base plane. The initialization calibration module is used to rotate the standard block multiple times, collect the distance measurement data of each laser displacement sensor under each rotation posture, establish geometric constraint equations, and solve the measured distance data of each laser displacement sensor to obtain the overdetermined linear equation system of six unknown parameters of each laser displacement sensor. Solving the overdetermined linear equation system yields the spatial expression of the laser beam axis of each laser displacement sensor in the measurement coordinate system, thus completing the initialization calibration of the calibration device. The angle optimization module, based on the initialization and calibration completed by the initialization and calibration module, establishes an overdetermined constraint calibration model with the condition number of the coefficient matrix as the optimization index. It conducts comparative experiments with different angle intervals using the control variable method to determine the optimal range of angle intervals and eliminate abnormal angle combinations. Then, it performs global optimization of the rotation angle of the standard gauge block with the goal of minimizing the condition number. After iterative screening and experimental verification, it determines the rotation angle scheme of the standard gauge block for multi-pose measurement of the standard gauge block. The solution output module is used to establish the measurement coordinate system and the workpiece coordinate system based on the initial calibration results and rotation angle scheme. It collects distance measurement data of the intersection point of the laser spot on the surface of the standard gauge block through six laser displacement sensors. It uses the geometric constraint relationship of the equations of the laser beam central axis and the plane of the contact surface of the standard gauge block to establish a set of six nonlinear equations about the relative pose between the two coordinate systems by combining homogeneous coordinate transformation. After substituting the measured distance data, it solves the position vector and rotation matrix to complete the accurate calculation of the end pose parameters and outputs the final pose matrix.

[0066] To verify the beneficial effects of the present invention, the following specific implementation examples are provided in this embodiment: A set of laser displacement sensors was selected for calibration experiments: Initial calibration of the spatial linear equation of the laser displacement sensor. Before calibration, a simplified experimental model of the calibration device is pre-built in 3D modeling software, consisting of three parts: standard gauge blocks, laser emission point, spatial linear equation of the laser sensor, and rotation reference axis.

[0067] Standard gauge blocks are positioned parallel to the global coordinate system. Rotate the reference axis of the surface sequentially by 0°, 5°, and 10°, then around... The reference axis of the surface is rotated sequentially by 5°, 10°, and 15°, resulting in six orientations. In each orientation, the intersection coordinates of the spatial line between the standard gauge block surface and the laser sensor are obtained using the intersection function of the 3D modeling software. The measured distance t from the emission point to the intersection point of the laser spot on the standard gauge block surface is measured, and the normal vector of the standard gauge block surface at the intersection point is read. The calibration measurement data collected under the six attitudes are shown in Tables 1 and 2.

[0068] Table 1 Standard Gauge Block Wrapping Calibration measurement data of surface rotation Table 2 Standard Gauge Blocks Around Calibration measurement data of surface rotation Substitute the six sets of measured data from Tables 1 and 2 into the overdetermined linear equations and perform matrix inversion operations. Six real solutions were obtained. Comparing the results with the preset theoretical coordinates of the laser emission point and the theoretical direction vector of the laser sensor's spatial straight line in the 3D modeling software revealed that the deviations of the emission point along the three coordinate axes and the angular deviations of the direction vectors were all within reasonable ranges. The solved spatial straight line equation basically matched the theoretical axis. This result demonstrates that the spatial geometric parameters of the sensor's laser beam axis can be accurately derived using ranging data from six preset attitudes, thus verifying the effectiveness of the above calibration process.

[0069] Traditional small-angle concentrated distribution scheme calibration experiment: To verify the actual impact of the calibration point distribution on the solution accuracy of the calibration model, a calibration experiment was first conducted using a traditional small-angle concentrated distribution scheme. To more closely approximate the error characteristics of actual equipment, an initial systematic error of 3° was assumed in the spatial straight line of the laser displacement sensor. The theoretical coordinates of the laser displacement sensor emission point were set to (0, 300, 85) mm, and the theoretical initial straight line direction vector was (0.052, 0.999, 0). In the experiment, the standard gauge block was deflected around two reference axes parallel to the x-axis and z-axis of the global coordinate system. Three angles of 20°, 25°, and 35° were set around the x-axis, and three angles of 10°, 15°, and 20° were set around the z-axis, forming a total of six calibration conditions. Standardized measurements were performed after each attitude adjustment, and the coordinates of the spatial intersection points were collected. Normal vector and measured distance value t The measured data are shown in Table 3.

[0070] Table 3 Measurement data of the original calibration scheme Substituting the six sets of measured data from Table 3 into the overdetermined linear equation system, the coordinates of the laser emission point are obtained as (0.4299, 300.7060, 85.7462) mm, and the normalized direction vector of the laser line is (-0.0535, -0.9986, -0.0021). The condition number of the coefficient matrix is... The above results indicate that the matrix exhibits severe ill-conditioning under the original small-angle concentrated distribution scheme, with significant defects in calibration accuracy, and cannot meet the sub-millimeter-level high-precision positioning requirements of the robotic arm end effector.

[0071] Comparison experiment at different angle intervals: To reveal the inherent relationship between angular interval and solution accuracy, five sets of comparative experiments were conducted with adjacent angular intervals set to 10°, 20°, 30°, 40°, and 50°, while keeping other experimental conditions consistent. Data acquisition and solution were completed for each set according to the same standardized procedure. The coefficient matrix condition number, launch point distance error, and direction vector angle error were recorded for each set of conditions. The optimal range of angular interval was determined accordingly. The experimental results are shown in Table 4.

[0072] Table 4 Comparison of calibration experimental results at different angle intervals Verification experiment of the optimized calibration angle distribution scheme: Based on the patterns revealed by the comparative experiments above, the rotation angle combinations of the gauge blocks were optimized using minimizing the condition number as the core criterion. This involved expanding the range of angle values ​​to make the normal vector more evenly distributed on the unit sphere; employing alternating positive and negative angles to ensure full coverage of the normal vectors along each coordinate axis; and ensuring uniform and reasonable angle intervals between different working conditions. After multiple rounds of iterative selection, six optimal rotation angles were finally determined. The measured data collected after optimization are shown in Table 5.

[0073] Table 5 Measurement data of the optimized calibration scheme Substituting the six sets of measured data from Table 5 into the linear equation system, we obtain the coordinates of the laser emission point as (-0.0307, ​​299.9990, 84.9814) mm, the direction vector as (-0.0523, -0.9986, 0.0000), and the condition number of the coefficient matrix. Comparing the original calibration scheme with the optimized scheme, the condition number of the coefficient matrix is ​​reduced by approximately 51.7 times, the launch point distance error is reduced by approximately 30.8 times, and the direction vector angle error is reduced by approximately 50.7 times. This demonstrates that the symmetrical distribution of positive and negative angles based on minimizing the condition number effectively solves the matrix ill-conditioned problem, and the calibration accuracy meets the engineering application requirements for high-precision positioning of the robotic arm's end effector. The optimized rotation angle scheme described above is the optimal measurement parameter used for accurate pose calculation of the S4 end effector.

[0074] The robotic arm calibration method and system for the non-contact displacement sensor according to the present invention have the following advantages: 1. Significantly improves calibration accuracy and robustness: Based on the principle of six-point spatial positioning, this invention arranges 3, 2, and 1 laser displacement sensors in three mutually perpendicular spatial directions, respectively, for a total of six sets of sensors to form a complete constraint of six degrees of freedom in space. By simultaneously measuring the distance of the standard block with the six sets of sensors, an overdetermined measurement equation set is constructed, realizing the simultaneous solution of the six-dimensional pose parameters of the end effector. This effectively suppresses the measurement uncertainty caused by insufficient constraint in one direction. Compared with the traditional three-point or four-point positioning scheme, it significantly improves the stability and calibration accuracy of pose measurement.

[0075] 2. Suppressing the error amplification effect at the source: This invention uses the condition number of the coefficient matrix of the overdetermined equation system as the core evaluation index to globally optimize the spatial geometric layout of the six sets of sensors and the rotation angle sequence of the standard gauge blocks. This improves the orthogonality of the column vectors of the coefficient matrix and reduces the condition number, thereby effectively alleviating the matrix ill-conditioned problem. This suppresses the amplification effect of ranging error on the calibration results at the source and further improves the calibration accuracy and anti-interference capability.

[0076] 3. Significantly reduces calibration costs and operational complexity: This invention requires only six sets of laser displacement sensors and standard gauge blocks to complete the complete end-effector pose calibration, without relying on expensive external measuring equipment such as laser trackers. This significantly reduces equipment investment costs and technical barriers, while simplifying the calibration operation process, and has good engineering economics and field applicability.

[0077] 4. High versatility and adaptability to different specifications of industrial robots: This invention does not depend on a specific robot model or end effector configuration. By replacing standard gauge blocks of different sizes or adjusting the sensor installation position, it can flexibly adapt to the end effector calibration requirements of industrial robots of different specifications. It has good versatility and personalized adaptability and can be widely used in on-site calibration scenarios of various robot models.

[0078] 5. Balancing high precision with practicality and economy to promote high-precision applications: While ensuring calibration accuracy, this invention also considers cost control and ease of operation, effectively solving the technical problems of insufficient accuracy, poor robustness, and complex operation of existing calibration methods. It has important engineering value for promoting the widespread application of industrial robots in high-precision operation scenarios such as precision assembly and aerospace manufacturing, and provides solid technical support for the development of intelligent manufacturing.

[0079] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for calibrating a robotic arm using a non-contact displacement sensor, characterized in that, include: S1: Construct a calibration scenario, which includes a calibration device and a standard gauge block located within the calibration device. The calibration device is assembled on three orthogonal reference planes by six laser displacement sensors in a 3-2-1 six-point positioning manner. The standard gauge block can rotate around the rotation reference axis of the reference plane. S2: Rotate the standard gauge block multiple times, collect the distance measurement data of each laser displacement sensor under each rotation posture, establish geometric constraint equations respectively, combine the measured distance data of each laser displacement sensor, obtain the overdetermined linear equation system of six unknown parameters of each laser displacement sensor, solve the overdetermined linear equation system to obtain the spatial expression of the laser beam axis of each laser displacement sensor in the measurement coordinate system, and complete the initial calibration of the calibration device. S3: Based on the initial calibration completed in S2, an overdetermined constraint calibration model with the condition number of the coefficient matrix as the optimization index is established. The control variable method is used to carry out comparative experiments with different angle intervals to determine the optimal range of angle intervals and eliminate abnormal angle combinations. Then, the rotation angle of the standard gauge block is globally optimized with the goal of minimizing the condition number. After iterative screening and experimental verification, the rotation angle scheme of the standard gauge block is determined and used for the multi-pose measurement of the standard gauge block in S4. S4: Based on the initial calibration results obtained in S2 and the rotation angle scheme obtained in S3, establish the measurement coordinate system and the workpiece coordinate system. Collect the distance measurement data of the intersection of the laser spot on the surface of the standard gauge block through six laser displacement sensors. Utilize the geometric constraint relationship of the equations of the laser beam central axis and the contact surface plane of the standard gauge block, and combine homogeneous coordinate transformation to establish a set of six nonlinear equations about the relative pose between the two coordinate systems. Substitute the measured distance data to solve for the position vector and rotation matrix, complete the accurate calculation of the end pose parameters, and output the final pose matrix.

2. The robotic arm calibration method for the non-contact displacement sensor according to claim 1, characterized in that, In S2, the overdetermined linear equation system is expressed as follows: ， in, Let be the normal vector of the plane, and d be the plane position parameter. Here are the spatial coordinates of the laser displacement sensor's emission point in the measurement coordinate system. Let be the unit direction vector of the laser beam axis. This represents the measured distance from the emission point of the laser displacement sensor to the intersection of the laser spot on the surface of the standard gauge block. The number in the subscript is the serial number of the laser displacement sensor. Let matrix Coefficient matrix The column vector on the right is Matrix, using matrix inversion: ， Once the calculation is complete, you will get and The six real solutions, when substituted into the equation of the spatial straight line, completely determine the spatial expression of the sensor's laser beam axis in the measurement coordinate system: 。 3. The robotic arm calibration method for a non-contact displacement sensor according to claim 1, characterized in that, S3 specifically includes: S31, Establish the overdetermined constraint linear equation system and its matrix perturbation analysis model: Using a calibration device composed of three sets of orthogonal reference surfaces A, B, and C, the ranging data of each laser displacement sensor are collected under various rotational attitudes by rotating standard gauge blocks around different rotation axes, forming a multi-dimensional measurement constraint system, and constructing a system of the form... AX=D For overdetermined linear equation systems, the condition number of the coefficient matrix is ​​used as the core optimization index to measure the ill-conditionedness of the matrix; S32, Constructing a reference group calibration experiment and obtaining the condition number of the reference matrix: Based on the spatial expression obtained in S2, a preset angle concentration distribution scheme is adopted, and multiple concentrated deflection angles are set around two reference axes parallel to the x-axis and z-axis of the global coordinate system to form several sets of reference measurement conditions; under each condition, the laser ranging value and the corresponding gauge block pose information are recorded, and the reference coefficient matrix is ​​constructed after importing them into the MATLAB solution model. The condition number of the reference coefficient matrix is ​​calculated, and the coordinates of the emission point and the direction vector obtained by the solution are compared with the design nominal values ​​of each laser displacement sensor in the measurement coordinate system to calculate the reference position error and angle deviation. S33, Investigate the influence of different angle intervals on the stability of the solution: Based on S32, keep other experimental conditions consistent, only change the rotation angle interval of the standard gauge block around the two reference axes, and carry out a single-factor comparison experiment: Set multiple different angle intervals in sequence, solve the coefficient matrix condition number, position error and angle deviation under each working condition, identify and eliminate abnormal angle combinations that lead to high linear correlation of column vectors, and determine the angle interval range in which the condition number and error are in the stable range. S34. Global angle distribution optimization and experimental verification based on condition number minimization: With minimizing the condition number of the coefficient matrix as the objective, and following the pattern obtained in S33, and using the baseline condition number obtained in S32 as the criterion for judging the optimization effect, the rotation angle sampling interval is widened and an alternating distribution of positive and negative angles is introduced. Candidate angle combination schemes are determined through iterative screening. Data is re-collected according to a standardized process, and the optimized coefficient matrix is ​​constructed. A The optimized coefficient matrix condition number is calculated and compared with the baseline coefficient matrix condition number obtained in S32 to verify the optimization effect. After verification, the current angle combination is determined as the rotation parameter scheme of the calibration device, which is used for end pose calculation in subsequent steps.

4. The robotic arm calibration method for the non-contact displacement sensor according to claim 1, characterized in that, S4 includes: S41: Establish the measurement coordinate system With workpiece coordinate system Measurement coordinate system Fixed to the calibration device body, workpiece coordinate system Fixed on the surface of the standard gauge block, workpiece coordinate system The origin is in the measurement coordinate system The spatial position below is obtained through the position vector. This indicates that the spatial attitude transformation between two coordinate systems is achieved through a rotation matrix. describe; S42: Establish the equation of the central axis of the laser displacement sensor, and set the workpiece coordinate system. Transform the coordinates of the contact points and normal vectors of each contact surface of the standard gauge block to the measurement coordinate system. ; S43: Derivation of the contact plane of the standard gauge block in the measurement coordinate system Based on the geometric constraint relationship between the central axis of the laser beam of the laser displacement sensor and the spatial plane of the contact surface of the standard block, the theoretical ranging expressions from the emission point of the six laser displacement sensors to their respective corresponding spot intersection points are established. The actual output ranging values ​​of each laser displacement sensor are used as known quantities to construct six nonlinear equation sets. S44: Obtain the actual measurement values ​​of six sets of laser displacement sensors, substitute them into the six nonlinear equations established in S43, solve for the six unknown parameters in the position vector and rotation matrix, and calculate the relative pose matrix between the workpiece coordinate system and the measurement coordinate system to complete the accurate calculation of the end pose parameters. S45: Output the final pose matrix.

5. The robotic arm calibration method for the non-contact displacement sensor according to claim 4, characterized in that, In step S41, the rotation matrix uses Euler angles. Parameterization, respectively characterizing the workpiece coordinate system Around the measurement coordinate system The deflection attitude along the x-axis, y-axis, and z-axis, and their combined relationship is as follows: ， Construct a homogeneous transformation matrix by combining the position vectors, i.e.: 。 6. The robotic arm calibration method for a non-contact displacement sensor according to claim 4, characterized in that, In S42, in the measurement coordinate system Below, the equation of the central axis of the i-th laser displacement sensor is given by its axial unit direction vector. and installation point coordinates Confirmed as: ， ， in, For the i-th laser displacement sensor in the measurement coordinate system The coordinate components of the unit direction vector along the axial direction below, in the x-axis direction. For the i-th laser displacement sensor in the measurement coordinate system The coordinate components of the unit direction vector along the y-axis. For the i-th laser displacement sensor in the measurement coordinate system The coordinate components of the unit direction vector along the axial direction below, with T being the matrix transpose. For a fixed reference point on the central axis of the i-th laser displacement sensor in the measurement coordinate system The x-axis coordinate variable of the spatial coordinates below. For a fixed reference point on the central axis of the i-th laser displacement sensor in the measurement coordinate system The y-axis coordinate variable of the spatial coordinates below. For a fixed reference point on the central axis of the i-th laser displacement sensor in the measurement coordinate system The z-axis coordinate variable of the spatial coordinates below. For a fixed reference point on the central axis of the laser displacement sensor in the measurement coordinate system x-axis coordinate variable, For a fixed reference point on the central axis of the laser displacement sensor in the measurement coordinate system The y-axis coordinate variable, For a fixed reference point on the central axis of the laser displacement sensor in the measurement coordinate system The z-axis coordinate variable.

7. The robotic arm calibration method for a non-contact displacement sensor according to claim 4, characterized in that, In S43, the theoretical ranging expression is: ， in, The direct output measurement value of the laser displacement sensor represents the straight-line distance from the laser displacement sensor's emission point, along the laser beam axis, to the intersection point of the laser spot on the surface of the standard gauge block. This indicates that the i-th sensor is in the measurement coordinate system. The coordinates of the contact point between the lower surface and the standard gauge block. Indicates the plane of the standard gauge block in the measurement coordinate system The normal vector below, This indicates that the sensor's central axis is in the measurement coordinate system. The actual installation point coordinates are determined below. This indicates that the i-th laser displacement sensor is in the measurement coordinate system. The axial unit direction vector below; The six nonlinear equations are: 。 8. The robotic arm calibration method for a non-contact displacement sensor according to claim 1, characterized in that, The calibration device includes: Measurement fixing plate (1); The adapter flange (2) is installed on the surface of the measuring fixing plate (1); A fixed flange (3) is mounted on the surface of the measuring fixed plate (1) away from the transition flange (2); Three mounting plates are assembled and connected in sequence to form three orthogonal reference planes, which are installed on the measuring fixing plate (1) to form an open cavity, wherein the fixing flange (3) is located inside the cavity; Multiple laser displacement sensors (5) are installed on the three orthogonal reference planes of the mounting plate in a 3-2-1 six-point positioning manner; The standard gauge block (6) has a cube-shaped structure and is installed on the fixed flange (3).

9. The robotic arm calibration method for a non-contact displacement sensor according to claim 8, characterized in that, Both the transition flange (2) and the fixed flange (3) are coaxial rotating structures; The three orthogonal reference planes are reference plane A, reference plane B and reference plane C, which are used to install three, two and one laser displacement sensors respectively (5).

10. A robotic arm calibration system for a non-contact displacement sensor, characterized in that, The calibration is performed using the robotic arm calibration method as described in any one of claims 1 to 9, including: The scene construction module is used to construct a calibration scene, which includes a calibration device and a standard block located in the calibration device. The calibration device is assembled by six laser displacement sensors in a 3-2-1 six-point positioning manner on three orthogonal reference planes. The standard block can rotate around the rotation reference axis of the base plane. The initialization calibration module is used to rotate the standard block multiple times, collect the distance measurement data of each laser displacement sensor under each rotation posture, establish geometric constraint equations, and solve the measured distance data of each laser displacement sensor to obtain the overdetermined linear equation system of six unknown parameters of each laser displacement sensor. Solving the overdetermined linear equation system yields the spatial expression of the laser beam axis of each laser displacement sensor in the measurement coordinate system, thus completing the initialization calibration of the calibration device. The angle optimization module, based on the initialization and calibration completed by the initialization and calibration module, establishes an overdetermined constraint calibration model with the condition number of the coefficient matrix as the optimization index. It conducts comparative experiments with different angle intervals using the control variable method to determine the optimal range of angle intervals and eliminate abnormal angle combinations. Then, it performs global optimization of the rotation angle of the standard gauge block with the goal of minimizing the condition number. After iterative screening and experimental verification, it determines the rotation angle scheme of the standard gauge block for multi-pose measurement of the standard gauge block. The solution output module is used to establish the measurement coordinate system and the workpiece coordinate system based on the initial calibration results and rotation angle scheme. It collects distance measurement data of the intersection point of the laser spot on the surface of the standard gauge block through six laser displacement sensors. It uses the geometric constraint relationship of the equations of the laser beam central axis and the plane of the contact surface of the standard gauge block to establish a set of six nonlinear equations about the relative pose between the two coordinate systems by combining homogeneous coordinate transformation. After substituting the measured distance data, it solves the position vector and rotation matrix to complete the accurate calculation of the end pose parameters and outputs the final pose matrix.

Images