Loading arm kinematics calibration method, system and equipment based on distance identification and medium

Abstract

The invention provides a distance identification-based crane tube kinematics calibration method, system and equipment and a medium, and belongs to the technical field of crane tube positioning, a crane tube joint coordinate system and a mechanical arm kinematics model are constructed, differential motion error components generated by each joint coordinate system are transmitted and synthesized step by step, and a mechanical arm kinematics calibration model is constructed. Obtaining a mapping relation between the space error and the kinematics parameter error and the pose deviation of each joint; the loading arm is driven to execute multi-attitude composite motion; target features at different distances and inclination angles are extracted and positioned; establishing a mapping relation between image pixel coordinates and three-dimensional space coordinates, and calculating the depth and coordinates of the target point in the three-dimensional space; and fusing the tail end pose error model and a target actual measurement space coordinate to realize nonlinear optimization and stable convergence of parameter correction. The motion deviation of the end effector is effectively compensated, and the positioning precision is improved. According to the method, calculation of a coordinate system transformation matrix is bypassed, and calibration complexity is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of crane pipe positioning, and in particular relates to a crane pipe kinematic calibration method, system, equipment and medium based on distance identification. Background Art

[0002] In the chemical liquid transportation industry, tank trucks are the core transportation tool. The accuracy and efficiency of their filling operations are directly related to the safety and economic efficiency of chemical liquid logistics. However, the chemical liquid transportation industry uses crane filling to achieve automation of chemical liquid filling operations.

[0003] Among them, the performance indicators of the intelligent crane of the chemical liquid loading system, especially the positioning accuracy, have become the key factors in measuring the comprehensive performance of the chemical liquid loading system. In the related art of the kinematic calibration of the intelligent crane, the joint coordinate system is not constructed accurately, resulting in the multi-link kinematic model cannot accurately describe the motion relationship between the various parts of the crane. This results in a large positioning error of the end effector of the robot arm, which cannot meet the high-precision industrial production requirements. The related art lacks a systematic analysis and effective compensation method for the motion errors of each joint. Since the accurate mapping relationship between the spatial error of the end effector of the robot arm and the kinematic parameter errors and posture deviations of each joint has not been established, it is difficult to perform targeted error correction. Moreover, the kinematic calibration optimization algorithm used in the related art either has a slow convergence speed or is prone to falling into a local optimal solution when dealing with nonlinear problems, and it is impossible to quickly and stably obtain the optimal kinematic parameters. This results in a long calibration process and the calibration results may be inaccurate, affecting the practical application of the intelligent crane. Summary of the Invention

[0004] The present invention provides a crane tube kinematic calibration method based on distance identification, which solves the problem of low absolute positioning accuracy of the crane tube caused by multiple factors such as mechanical structure design, processing accuracy, assembly error and long-term wear.

[0005] Methods include: Step S101: Construct a crane-tube joint coordinate system. Define the Zi-axis direction of each joint based on the characteristics of the revolute joint and determine the positive direction. Define the Xi-axis direction through the common perpendicular line between adjacent links. Take the intersection of the Zi-axis and the Xi-axis as the origin of the coordinate system, derive the Yi-axis direction, and establish a multi-link kinematic model. Step S102: Constructing a kinematic model of the robotic arm, transferring and synthesizing the differential motion error components generated by each joint coordinate system step by step, and obtaining a linear mapping relationship between the spatial error of the robotic arm end effector and the kinematic parameter errors and posture deviations of each joint; Step S103: Configure a preset baseline distance, synchronously capture target images at a preset resolution and frame rate, optimize imaging by combining a uniform diffuse reflection light source with a polarization filter, and drive the crane to perform multi-posture compound motions, recording joint angle data; Step S104: Target recognition is achieved based on the improved target detection model. Pre-trained weights are loaded through a transfer learning strategy. The model is optimized by combining geometric enhancement, photometric adjustment, and difficult sample mining techniques to achieve target feature extraction and positioning at different distances and tilt angles. Step S105: Using the principle of triangulation, the spatial position of the target object is calculated based on the imaging geometric relationship of the two cameras with different viewpoints. Based on the baseline distance between the optical axes of the two cameras and the principle of similar triangles, a mapping relationship between the image pixel coordinates and the three-dimensional space coordinates is established to calculate the depth and coordinates of the target point in the three-dimensional space. Step S106: Apply the LM optimization algorithm to perform kinematic calibration on the crane tube, integrate the terminal posture error model with the measured target space coordinates, and achieve nonlinear optimization and stable convergence of parameter correction by dynamically adjusting the gradient descent and Gauss-Newton method weights.

[0006] It should be further explained that step S101 specifically includes: Determine the rotation type of all joints based on the motion characteristics of the crane, and define it based on the straight line where the rotation axis is located. Z i The spatial position of the axis; Building the connecting rod i With adjacent connecting rod i +1, the common perpendicular line is X i Spatial positioning reference of the axis; The origin of the joint coordinate system is determined by defining the joint Z i Axis and X i The spatial intersection point of the axes serves as the reference origin of the coordinate system; when X i Axis and Z i After the axis definition is completed, Y i The directions of the axes are derived using the right-hand coordinate rule.

[0007] It should be further explained that step S102 specifically includes: After the joint coordinate system of the robotic arm is constructed, the spatial transformation relationship between adjacent joint coordinate systems is decomposed into four orderly motion steps: Along the joints i -1 Xi-1 Axis translation a i-1 distance; around the same X i-1 Axis rotation α i-1 Angle; along the joint i of Z i Axis translation d i distance; around Z i Axis rotation θ i Angle, based on the kinematic chain derivation, establish the coordinate system { i} to coordinate system { i -1} homogeneous transformation matrix , and build the kinematic model of the robotic arm on the premise of establishing the coordinate system of each link and completing the corresponding parameter definition; .

[0008] It should be further explained that the end effector coordinate system { n}Relative to the base coordinate system{ 0}'s pose transformation matrix:

[0009] Where, is the position vector of the end of the robotic arm, is the rotation matrix of the end of the robotic arm.

[0010] It should be further explained that in the method, the end coordinate system produces a slight posture change, and the corresponding homogeneous transformation increment is recorded as ; The transformation matrix of the robot end coordinate system relative to the base coordinate system is expressed as:

[0011] The homogeneous transformation increment is:

[0012] Differential error of the transformation matrix of adjacent joint coordinate systems Decomposed into the weighted sum of partial derivatives of each parameter:

[0013] Where, , , and is the parameter error, and the linear mapping relationship between the parameter error and the posture deviation is constructed by analytically calculating each partial derivative.

[0014] It should be further explained that step S105 specifically includes: The baseline distance between the optical axes of the two cameras is b , through parallax Calculate target point P Depth in three-dimensional space ， According to the principle of similar triangles, the target point coordinates satisfy the following formula as the mapping relationship between image pixel coordinates and three-dimensional space coordinates:

[0015] Where, f is the camera focal length, ( x , y , z ) is the three-dimensional coordinate of the target in the camera coordinate system.

[0016] It should be further explained that step S106 specifically includes: in the crane kinematic calibration, optimizing the geometric parameters by the LM optimization algorithm so that the error between the actual distance value and the theoretical distance value predicted by the kinematic model is minimized to:

[0017] The parameter update equation combines the advantages of gradient descent and Gauss-Newton method, and its form is:

[0018] Where, is the Jacobian matrix of the error function with respect to the parameters, is the damping factor, used to adjust the direction of the algorithm, is the parameter correction amount; In this method, parameter sensitivity analysis is introduced to eliminate redundant parameters and calculate the global sensitivity index of each parameter:

[0019] Where, For the i The global sensitivity index of the joint, is the error of the kth iteration.

[0020] The present application also provides a crane tube kinematic calibration system based on distance identification, the system comprising: The kinematic model building module is used to construct the crane-tube joint coordinate system. Based on the characteristics of the revolute joint, the Zi-axis direction of each joint is defined and the positive direction is determined. The Xi-axis direction is defined by the common perpendicular line between adjacent links. The intersection of the Zi-axis and the Xi-axis is used as the origin of the coordinate system. The Yi-axis direction is derived to establish a multi-link kinematic model. The robot arm and joint mapping module is used to build the robot arm kinematic model, transfer and synthesize the differential motion error components generated by each joint coordinate system step by step, and obtain the linear mapping relationship between the spatial error of the robot arm end effector and the kinematic parameter error and posture deviation of each joint; The crane operation recording module is used to configure a preset baseline distance, synchronously capture target images at a preset resolution and frame rate, optimize imaging by combining a uniform diffuse reflection light source with a polarizing filter, and drive the crane to perform multi-posture compound movements and record joint angle data. The feature extraction and positioning module is used to achieve target recognition using an improved target detection model. It loads pre-trained weights through a transfer learning strategy and optimizes the model by combining geometric enhancement, photometric adjustment, and difficult sample mining techniques to achieve target feature extraction and positioning at different distances and tilt angles. The coordinate mapping module is used to calculate the spatial position of the target object using the imaging geometric relationship of two cameras with different viewpoints using the principle of triangulation. Based on the baseline distance between the optical axes of the two cameras and the principle of similar triangles, it establishes a mapping relationship between the image pixel coordinates and the three-dimensional space coordinates, and calculates the depth and coordinates of the target point in three-dimensional space. The parameter adjustment module is used to apply the LM optimization algorithm to perform kinematic calibration on the crane tube, integrate the terminal posture error model with the measured spatial coordinates of the target, and achieve nonlinear optimization and stable convergence of the parameter correction by dynamically adjusting the gradient descent and Gauss-Newton method weights.

[0021] According to another embodiment of the present application, an electronic device is provided, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the crane kinematic calibration method based on distance identification when executing the program.

[0022] According to another embodiment of the present application, a storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the crane kinematic calibration method based on distance identification are implemented.

[0023] It can be seen from the above technical solutions that the present invention has the following advantages: The crane kinematic calibration method based on distance identification provided in this application defines the direction and origin of each joint axis by constructing an intelligent crane joint coordinate system and a robotic arm kinematic model, and accurately describes the motion relationship of the crane. At the same time, a linear mapping relationship between the end effector spatial error and the joint parameter error is established, which effectively improves the motion accuracy of the intelligent crane. The preset baseline distance is configured, and the imaging is optimized by combining a uniform diffuse reflection light source and a polarization filter, thereby improving the image acquisition quality. During the image acquisition process, the crane is driven to perform multi-posture compound motions, record joint angle data, and obtain a variety of image data, thereby enhancing the system's adaptability to complex environments.

[0024] Based on an improved target detection model, the model utilizes transfer learning to load pre-trained weights and combines multiple optimization techniques to improve the model's recognition and positioning accuracy for targets at different distances and tilt angles. It can accurately extract target features, provide accurate image information for triangulation, and ensure the accuracy of three-dimensional coordinate calculations. The LM optimization algorithm is used to perform kinematic calibration on the crane tube, dynamically adjusting the weights of the gradient descent and Gauss-Newton methods to achieve nonlinear optimization and stable convergence of parameter corrections. Furthermore, the LM optimization algorithm is used to dynamically adjust kinematic parameters to minimize the error between the actual distance value and the theoretical distance value predicted by the kinematic model, significantly improving the absolute positioning accuracy of the crane tube and shortening calibration time. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the technical solution of the present invention, the following is a brief introduction to the drawings required for the description. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0026] Figure 1 This is a flow chart of the crane tube kinematic calibration method based on distance identification; Figure 2 is a schematic diagram of the connecting rod coordinate system; Figure 3 Schematic diagram of image data; Figure 4 This is a schematic diagram of the target recognition results; Figure 5 This is the principle diagram of triangulation; Figure 6 Schematic diagram of an electronic device. DETAILED DESCRIPTION

[0027] The present invention addresses the problem of insufficient absolute positioning accuracy of crane pipes in chemical liquid transportation due to machining errors, assembly deviations, and long-term wear, and proposes a crane pipe kinematic calibration method based on distance identification. The present invention replaces traditional high-precision tools with visually assisted measurement technology, uses a stereo vision system to capture the target image at the end of the crane pipe, combines a deep learning model to achieve rapid target identification, and uses kinematic calibration technology to accurately identify key parameters in the kinematic model. Based on this, the motion deviation of the end effector is effectively corrected or compensated, thereby achieving a higher level of absolute positioning accuracy. This method bypasses the calculation of the coordinate system conversion matrix and reduces the calibration complexity.

[0028] The following describes in detail the steps of the crane kinematic calibration method based on distance identification involved in this application. Specific details such as specific system structures and technologies are provided for illustrative purposes rather than for limitation, to facilitate a thorough understanding of the embodiments of this application. However, it should be clear to those skilled in the art that this application may also be implemented in other embodiments without these specific details.

[0029] It should be understood that when used in this specification, the term "comprising" indicates the presence of the described features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their collections. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized.

[0030] The phrases "one embodiment" or "some embodiments" described in this application mean that the specific features, structures, or characteristics described in the embodiment are included in one or more embodiments of the application. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in other embodiments," etc. that appear in different places in this application do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized.

[0031] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0032] See also Figure 1 FIG. 1 is a flow chart of a crane kinematic calibration method based on distance identification in a specific embodiment, the method comprising: Step S101: Construct a crane-tube joint coordinate system. Define the Zi-axis direction of each joint based on the characteristics of the revolute joint and determine the positive direction. Define the Xi-axis direction through the common perpendicular line between adjacent links. Take the intersection of the Zi-axis and the Xi-axis as the origin of the coordinate system, derive the Yi-axis direction, and establish a multi-link kinematic model.

[0033] The crane pipe involved in some embodiments is a device used for loading and unloading liquids or gases. Conventional crane pipe shapes can be selected. The crane pipe can generally include but is not limited to a rotary joint, a column, an inner arm, an outer arm, a vertical arm, a cylinder, a sealing device, a flange and other auxiliary components.

[0034] In this embodiment, in the field of kinematic calibration, constructing a kinematic model for the intelligent crane is the initial step in system calibration. This mathematical representation is established by analyzing the geometric structure and kinematic parameters of the mechanical system. The kinematic model accurately describes the spatial transformation relationship between the robotic arm's end effector and the base coordinate system.

[0035] The modeling approach for the kinematic model takes into account the significant variation in the number of parameters required to be identified in different theoretical frameworks; and the positive correlation between the model's fitting accuracy to the real motion.

[0036] It should be noted that while increasing the parameter dimension can improve the model's ability to capture the nonlinear characteristics of the mechanical system, it also significantly increases the computational complexity of the parameter identification process. This is manifested in an exponential increase in the number of iterations due to the expansion of the Jacobian matrix dimension. Therefore, this embodiment seeks a Pareto optimal solution between model accuracy and calibration feasibility.

[0037] Specifically, the schematic diagram based on the connecting rod coordinate system is as follows Figure 2 As shown in Figure 2, the main steps of kinematic modeling are: Step S1011: When setting the joint coordinate system, first clarify Z i The orientation of the axis. According to the motion characteristics of each joint, all joints are determined to be rotational, and are defined by the straight line where their rotation axis lies. Z i The spatial position of the axis.

[0038] In this embodiment, the positive direction of the coordinate axis is determined by following the right-hand screw rule, that is, when the bending direction of the four fingers matches the rotation direction, the thumb points to the positive direction. Z i Positive direction of the axis.

[0039] Step S1012: Build the connecting rod i With adjacent connecting rod i +1, the geometric characteristic line of the common perpendicular line is X iThe spatial positioning reference of the axis.

[0040] The pointing rule of this embodiment is defined as: i Starting from the centroid or characteristic point, it points to the subsequent members along the common vertical line. i +1, thereby determining the direction of the coordinate system.

[0041] Step S1013: When constructing the joint coordinate system, the rule for determining the origin position is: take the joint Z i Axis and X i The spatial intersection point of the axes serves as the base origin of the coordinate system.

[0042] Step S1014: During the construction of the joint coordinate system, when X i Axis and Z i After the axis definition is completed, Y i The directions of the axes are derived using the right-hand coordinate rule.

[0043] The specific method is: Z i The axis is regarded as the direction axis of the right-handed screw. X i The axis is regarded as the common vertical line pointing to the axis, and the direction of the four fingers of the right hand is bent from Z i Axle steering X i When the thumb is pointing vertically, Y i The positive direction of the axis.

[0044] It should be noted that the construction of the orthogonal coordinate system ensures the standardization of joint kinematic modeling and the uniformity of mathematical calculations. The positions of the links are represented by four geometric parameters: (1) Connecting rod length a For the X i Axis, from Z i Move to Z i+1 distance; (2) Connecting rod angle α For around X i Axis, from Z i Rotate to Z i+1 Angle; (3) Connecting rod offset d For theZ i Axis, from X i-1 Move to X i distance; (4) Joint angle θ For around Z i Axis, from X i-1 Rotate to X i angle.

[0045] In some specific embodiments, the mechanical configuration of the intelligent crane utilizes a dual-rotational joint design in series, achieving planar spatial trajectory control through two-axis coordinated motion. Compared to multi-degree-of-freedom systems, this streamlined architecture offers greater economical efficiency and reliability in scenarios such as fluid transfer and docking.

[0046] The kinematic model of this embodiment is shown in Table 1. Based on the DH (Denavit-Hartenberg) modeling theory, the kinematic parameter set of the system can be simplified into two sets of parameters, namely the joint angle , connecting rod length , the nominal size of the intelligent crane pipe is , the actual size is .

[0047] Table 1: Kinematic model

[0048] As can be seen, this embodiment describes the relative position and posture relationships between adjacent links by defining the axes and parameters of the joint coordinate system. Each joint coordinate system can be transformed with adjacent coordinate systems through a series of translation and rotation operations. By connecting these transformation relationships in series, a complete kinematic model from the base coordinate system to the end-effector coordinate system can be established. This allows for a precise mathematical description and analysis of the crane's motion, improving the accuracy and stability of the crane's motion control.

[0049] Step S102: Construct a kinematic model of the robotic arm, transfer and synthesize the differential motion error components generated by each joint coordinate system step by step, and obtain a linear mapping relationship between the spatial error of the robotic arm end effector and the kinematic parameter errors and posture deviations of each joint.

[0050] In some embodiments, when constructing the kinematic model of the robotic arm, it is considered that during the actual operation of the mechanical system, each joint will produce a certain amount of motion error. The differential motion error components generated by each joint coordinate system are transferred and synthesized step by step in the order from the base to the end effector. By differentiating the kinematic equations, the impact of small changes in each joint on the end effector posture is analyzed, and a linear mapping relationship between the spatial error of the robotic arm end effector and the kinematic parameter errors and posture deviations of each joint is obtained.

[0051] The implementation of this embodiment utilizes knowledge of differential geometry and kinematics to accurately analyze and calculate the motion parameters of each joint. Based on the differential theory of kinematics, when a joint undergoes a small change in motion, the position of the end effector will also change accordingly. By differentiating the kinematic equations, the relationship between small changes in the motion parameters of each joint and the change in the position of the end effector is determined.

[0052] This embodiment accumulates and synthesizes the relationship between small changes in the motion parameters of each joint and the change in the end effector's posture. This allows for the establishment of a linear mapping model between the spatial error of the end effector and the errors in the kinematic parameters and posture deviations of each joint. This allows for a quantitative analysis of the impact of joint errors on the accuracy of the end effector. Furthermore, by establishing this mapping relationship, it is possible to adjust and optimize the joint parameters in a targeted manner, improve the motion precision and positioning accuracy of the robotic arm, reduce the operating errors caused by joint errors, and enhance the overall performance of the intelligent crane.

[0053] Step S103: Configure a preset baseline distance, synchronously capture target images with a preset resolution and frame rate, optimize imaging by combining a uniform diffuse reflection light source with a polarizing filter, and drive the crane to perform multi-posture compound motions and record joint angle data.

[0054] In some embodiments, to ensure the measurement accuracy of the stereo vision system, the data acquisition environment and camera parameters are controlled. First, a stable optical experimental platform is built to avoid external vibration interference, and a uniform diffuse light source is arranged in the experimental area to eliminate the impact of specular highlights and shadows on image quality.

[0055] The stereo vision system in this embodiment uses a fixed installation with parallel optical axes. The baseline distance is determined to be 0.2m based on the target measurement range. The two cameras' optical axes are strictly parallel to simplify stereo matching calculations. The camera resolution is selected to be 3840×2160 pixels, and the camera frame rate is selected to be 30 FPS.

[0056] Before camera calibration, internal calibration is required. Zhang Zhengyou's calibration method is used to obtain parameters such as focal length, principal point coordinates, and distortion coefficients for subsequent image correction and depth calculation. During the experiment, ambient light intensity must be controlled, and a polarizing filter must be used to suppress reflections.

[0057] In this embodiment, the target is fixed to the end of the intelligent crane tube, and the intelligent crane tube is driven to move according to a preset trajectory in the joint space, covering multiple typical postures in its workspace. In each motion posture, the stereo vision system synchronously captures the target image and records the corresponding joint angle data. In order to improve data diversity, the translation and rotation compound motion of the intelligent crane tube can be combined to make the target present different tilt angles and distance changes in the camera field of view, fully exposing the impact of geometric parameter errors on stereo vision measurement. The definition of joint angles is shown in Table 2, which defines 6 groups of typical postures, which respectively control the intelligent crane tube to move to a predetermined position.

[0058] Table 2: Definition of joint angles

[0059] To address the limitation of ordinary RGB cameras in lacking depth information, this embodiment adopts a multi-frame fusion strategy: 10 to 20 frames of images are continuously collected at each static posture of the robotic arm, random noise is suppressed through temporal averaging, and feature point tracking algorithms such as LK optical flow are used to verify the static state of the target.

[0060] To compensate for ambient light variations, this embodiment places a reference brightness plate in the scene and dynamically adjusts the camera exposure parameters. All image data must be accompanied by a timestamp, joint angles, and robotic arm pose information to facilitate subsequent offline processing.

[0061] The original image of this embodiment is preprocessed to improve the calibration reliability. First, a distortion correction model based on internal parameters is applied; second, histogram equalization is used to enhance the image contrast and highlight the edge of the target feature. Image data is as follows Figure 3 As shown, Figure 3 The images above are 6 images captured by the left camera. Figure 3 The images below are 6 images captured by the right camera.

[0062] It can be seen that according to the target measurement range and system design requirements, a suitable preset baseline distance is configured. The baseline distance is an important parameter between the two cameras in the stereo vision system, which affects the accuracy and range of three-dimensional measurement. The preset resolution and frame rate of the camera are set to ensure that the target image can be acquired clearly and quickly. In terms of the acquisition environment, a uniform diffuse reflection light source is arranged. This light source can avoid the generation of specular highlights and shadows, so that the target appears uniform and clear in the image. At the same time, a polarizing filter is used when necessary to further suppress reflective interference and improve image quality. During the acquisition process, the crane is driven to perform multi-posture compound motion, so that the target presents different tilt angles and distance changes in the camera field of view, covering multiple typical postures in its workspace, and recording the joint angle data corresponding to each posture, which can more comprehensively reflect the characteristics of the crane in different working states.

[0063] Step S104: Target recognition is achieved based on the improved target detection model. Pre-trained weights are loaded through the transfer learning strategy. The model is optimized by combining geometric enhancement, photometric adjustment, and difficult sample mining techniques to achieve target feature extraction and positioning at different distances and tilt angles.

[0064] In some embodiments, the target recognition method is based on a modified YOLOv5 deep learning model, efficiently detecting pre-set targets from stereo vision system images. To address the imaging characteristics of common cameras, such as light sensitivity, a lightweight YOLOv5s model was selected as the baseline architecture. This model strikes a balance between speed and accuracy and can adapt to small sample scenarios through transfer learning. The model input resolution is set to 640×640 pixels to ensure effective target feature extraction at various distances while avoiding excessive consumption of computing resources.

[0065] The image data in this example was divided into training, validation, and test sets in an 8:1:1 ratio to ensure model generalization. Labeling was performed using the LabelImg tool, accurately annotating target bounding boxes in the PASCAL VOC format with an error of less than 2 pixels. To improve model robustness, multi-dimensional data augmentation was implemented: geometric transformation, photometric adjustment, random occlusion, and Gaussian noise injection to simulate the effects of complex industrial environments on imaging.

[0066] This example uses a transfer learning strategy for model training, loading COCO data training weights to accelerate convergence. Hyperparameters include a batch size of 16, an initial learning rate of 0.01 (cosine annealing adjustment), and a weighted loss function (CIoULoss) with a weight of 0.8 to optimize boundary regression accuracy. K-means clustering is used to analyze the actual target size based on target characteristics, generating customized anchor boxes to improve small object detection. A difficult sample mining mechanism is introduced during training, and missed samples in the validation set are targeted for enhancement and retraining.

[0067] The model achieved 98.2% precision and 96.7% recall on an independent test set, with an mAP@0.5 of 97.5%. Single-frame inference took 8.3 milliseconds (NVIDIA RTX3080 GPU). In actual deployment, the model is seamlessly integrated with the intelligent crane control system, and the output target bounding box information is directly used for subsequent calibration equation construction, improving the overall system efficiency by 40%. This method has been successfully applied to high-precision equipment such as intelligent cranes, providing a reliable visual perception foundation for industrial automation scenarios. The target recognition results are shown in Figure 2. Figure 4 shown.

[0068] As can be seen, target recognition is achieved based on the improved object detection model. The lightweight YOLOv5s was chosen as the baseline architecture, achieving a good balance between detection speed and accuracy. A transfer learning strategy was implemented, loading weights pre-trained on a large-scale dataset and leveraging the common image features learned from these pre-trained weights to accelerate the model's convergence on target recognition tasks. In terms of data processing, the image data was subjected to geometric enhancement, such as rotation, scaling, and translation, as well as photometric adjustments, such as brightness, contrast, and saturation. Geometric enhancement and photometric adjustments can simulate the complex environmental conditions of industrial sites and increase data diversity. Difficult sample mining targets samples in the validation set that are easily missed, and then retrains the model to improve its detection capabilities in various complex situations. These operations enable target feature extraction and localization at varying distances and tilt angles.

[0069] Step S105: Using the principle of triangulation, the spatial position of the target object is solved through the imaging geometric relationship of two cameras with different viewpoints. According to the baseline distance of the optical axes of the two cameras and the principle of similar triangles, a mapping relationship between the image pixel coordinates and the three-dimensional space coordinates is established to calculate the depth and coordinates of the target point in three-dimensional space.

[0070] In some embodiments, the principle of triangulation is used to perform stereo positioning of the target. The stereo vision system includes two cameras with different viewpoints. When the target point is observed by the two cameras simultaneously in space, projection points are formed in the left and right images respectively. Since there is a baseline distance between the optical axes of the two cameras, according to the principle of similar triangles, by measuring the parallax of the target point in the left and right images, that is, the position difference of the projection point, combined with known parameters such as the focal length of the camera, the depth Z of the target point in three-dimensional space can be calculated. Based on other relationships of similar triangles, the three-dimensional coordinates (x, y, z) of the target point in the camera coordinate system are further calculated, thereby establishing a mapping relationship between the image pixel coordinates and the three-dimensional space coordinates, realizing the stereo positioning of the target, realizing the conversion from two-dimensional image information to three-dimensional space information, and improving the accuracy and reliability of the crane tube kinematic calibration.

[0071] Step S106: Apply the LM optimization algorithm to perform kinematic calibration on the crane tube, integrate the terminal posture error model with the measured target space coordinates, and achieve nonlinear optimization and stable convergence of parameter correction by dynamically adjusting the gradient descent and Gauss-Newton method weights.

[0072] In some embodiments, the LM optimization algorithm is applied to perform kinematic calibration on the crane tube. The end position error model established in step S102 is combined with the measured spatial coordinates of the target obtained in step S105. During operation, the LM optimization algorithm continuously attempts to find the optimal parameter correction amount in the iterative process by dynamically adjusting the weights of the gradient descent and Gauss-Newton method. In each iteration, a suitable parameter correction amount is calculated based on the current parameter value and error situation, and then the model parameters are updated until the parameter correction amount converges to a stable value, thereby achieving nonlinear optimization and stable convergence of the crane tube kinematic parameters and completing the kinematic calibration process.

[0073] The LM optimization algorithm of this embodiment combines the advantages of the gradient descent method and the Gauss-Newton method. The gradient descent method is a simple and effective optimization method that searches for the optimal solution along the negative gradient direction of the objective function, but the convergence speed is slow when approaching the optimal solution. The Gauss-Newton method is an optimization method for nonlinear least squares problems. It converges quickly under certain conditions, but it is sensitive to the choice of initial values ​​and may be unstable. The LM optimization algorithm dynamically adjusts the weights of the gradient descent and Gauss-Newton methods by introducing a damping factor. The gradient descent method is used in the early stage of the algorithm to ensure the stability of the algorithm. When approaching the optimal solution, the weight of the Gauss-Newton method is gradually increased to speed up the convergence speed, thereby achieving efficient solution to nonlinear problems, finding the optimal kinematic parameters, reducing the working error caused by kinematic parameter errors, and improving the reliability and stability of the crane pipe in industrial applications.

[0074] In an embodiment of the present invention, based on step S102, a possible embodiment will be given below to illustrate its specific implementation scheme in a non-limiting manner.

[0075] Step S102 specifically includes the following methods: the robot arm end posture error modeling method is constructed based on its kinematic model. The kinematic model uses the chain accumulation principle to transfer and synthesize the differential motion error components generated by each joint coordinate system step by step, and finally derives the mapping relationship between the spatial error of the robot arm end effector and the kinematic parameter deviation of each joint.

[0076] After the joint coordinate system of the robotic arm is constructed, the spatial transformation relationship between adjacent joint coordinate systems can be decomposed into four orderly motion steps: First, along the joint i -1 Xi-1 Axis translation a i-1 distance; then, around the same X i-1 Axis rotation α i-1 angle; subsequently, along the joint i of Z i Axis translation d i distance; finally, around Z i Axis rotation θ i Angle. Based on the above kinematic chain derivation, we can establish the coordinate system { i} to coordinate system { i -1} homogeneous transformation matrix :

[0077] In this embodiment, the kinematic model of the robot arm can be directly constructed on the premise of clearly establishing the coordinate system of each link and completing the corresponding parameter definition. By analytically calculating the homogeneous transformation matrix of each joint, the matrix multiplication operation can be performed in the order of the kinematic chain to solve the end effector coordinate system { n}Relative to the base coordinate system{ 0}'s pose transformation matrix:

[0078] Where, is the position vector of the end of the robotic arm, is the rotation matrix of the end of the robotic arm. After obtaining the real-time measurement data of the robotic arm joint position sensor, the position transformation matrix of the end effector in the Cartesian coordinate system can be determined by forward kinematics calculation. .

[0079] The pose transformation matrix of the robot arm end coordinate system relative to the base coordinate system in this embodiment is: , when there is a small relative motion between the links, it will cause deviation in the end position. Assuming that the end coordinate system has a small position change at this time, the corresponding homogeneous transformation increment is recorded as According to the principle of differential motion, this small motion can be decomposed into translational components and rotational components. Therefore, after considering the differential motion between the links, the transformation matrix of the robot end coordinate system relative to the base coordinate system can be expressed as:

[0080] Expand the above formula completely and omit the high-order differential terms to obtain the homogeneous transformation increment:

[0081] Differential error of the transformation matrix of adjacent joint coordinate systems It can be decomposed into the weighted sum of partial derivatives of each parameter: Where, , , and is the parameter error, and the partial derivatives are calculated analytically as , a linear mapping relationship between parameter error and posture deviation can be constructed.

[0082] The method for modeling distance errors at the end of a robotic arm in this embodiment is to establish a geometric distance constraint relationship between feature points. The method measures the actual distance values ​​of the robot end effector at multiple positions and compares them with the theoretical distance values ​​predicted by the kinematic model to establish an error compensation model: Where, and are the distances between the corresponding two points on the actual trajectory and the predicted trajectory of the robotic arm, respectively.

[0083] To improve the accuracy of the system's kinematic model evaluation for intelligent cranes, this example uses a Monte Carlo sampling method to generate 100 random joint angle combinations that evenly cover the joint space. Each angle combination is randomly generated within the physical limits of each joint, ensuring full coverage of the intelligent crane workspace. Table 3 shows the distribution of the model errors before calibration for the 100 combinations.

[0084] Table 3: Model error before calibration

[0085] On the basis of the above embodiment, in order to further improve the reliability of the crane kinematic calibration method based on distance identification provided by the above embodiment, the following is an implementable method of step S105 and step S106. In the following embodiment, the target stereo positioning is based on triangulation. Through the three-dimensional positioning principle in the stereo vision system, the spatial position of the target object is solved based on the geometric relationship of camera imaging from two different viewpoints. The principle of triangulation is as follows: Figure 5 As shown, when the target point When it is observed by the left and right cameras simultaneously in space, its projection point in the left image is , in the right image it is .

[0086] Since there is a baseline distance between the optical axes of the two cameras b , that is, the distance between the centers of the two cameras, the target point P Depth in three-dimensional space Z Parallax Calculated. According to the principle of similar triangles, the target point coordinates satisfy:

[0087] Where, f is the camera focal length, ( x , y , z ) is the three-dimensional coordinate of the target in the camera coordinate system. This formula establishes a direct mapping relationship between image pixel coordinates and three-dimensional space coordinates.

[0088] To adapt to industrial environments, this embodiment introduces a dynamic calibration mechanism. When the movement of the intelligent crane causes slight changes in the camera's pose, the extrinsic parameters are updated in real time by online acquisition of calibration plate images, ensuring long-term stability. The results of stereo positioning are shown in Table 4, which shows the coordinates of six typical poses in the left camera coordinate system.

[0089] Table 4: Stereotaxic results

[0090] In step S106, the LMLevenberg-Marquardt optimization algorithm is used during crane kinematic calibration. The LMLevenberg-Marquardt optimization algorithm is an efficient optimization method for nonlinear least squares problems. The algorithm achieves stable convergence of parameter corrections by dynamically balancing the characteristics of gradient descent and Gauss-Newton method. In intelligent crane kinematic calibration, the algorithm minimizes the error between the actual distance value and the theoretical distance value predicted by the kinematic model by optimizing geometric parameters:

[0091] The parameter update equation combines the advantages of gradient descent and Gauss-Newton method, and its form is:

[0092] Where, is the Jacobian matrix of the error function with respect to the parameters, is the damping factor, used to adjust the direction of the algorithm, is the parameter correction amount.

[0093] To improve the robustness of the algorithm, the damping factor Need to be adjusted dynamically: the initial value is set to If the current iteration reduces the error, it is reduced to accelerate convergence; if the error increases, it is expanded to enhance stability. At the same time, parameter sensitivity analysis is introduced to eliminate redundant parameters and calculate the global sensitivity index of each parameter:

[0094] Where, For the i The global sensitivity index of the joint, is the error of the kth iteration. , then it is removed from the optimization variables to reduce the calculation dimension. The results of kinematic calibration are shown in Table 5. The calibration size of the intelligent crane is , the actual size is The model errors after calibration are shown in Table 6, which describes the distribution of the 100 sets of model errors. Compared with the errors before calibration, the errors are significantly reduced.

[0095] Table 5: Results of kinematic calibration

[0096] Table 6: Model error after calibration

[0097] The above steps ensure the stability of the optimization process and accelerate convergence. During the iteration process, parameter corrections are calculated based on the current parameter estimates and observed data, and the model parameters are continuously updated until convergence conditions are met. Furthermore, through nonlinear optimization methods, the kinematic parameters of the intelligent crane can be accurately estimated, improving the accuracy and reliability of the model.

[0098] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0099] The following is an embodiment of the crane pipe kinematic calibration system based on distance identification provided by the embodiments of the present disclosure. This system and the crane pipe kinematic calibration methods based on distance identification of the above-mentioned embodiments belong to the same inventive concept. For details not fully described in the embodiment of the crane pipe kinematic calibration system based on distance identification, please refer to the embodiment of the above-mentioned crane pipe kinematic calibration method based on distance identification.

[0100] The system includes: a motion model establishment module, which is used to construct the crane-tube joint coordinate system, define the Zi-axis direction of each joint and determine the positive direction based on the characteristics of the rotational joint, define the Xi-axis direction through the common perpendicular line between adjacent links, take the intersection of the Zi-axis and the Xi-axis as the origin of the coordinate system, and derive the Yi-axis direction to establish a multi-link kinematic model.

[0101] The robot arm and joint mapping module is used to build the kinematic model of the robot arm, transfer and synthesize the differential motion error components generated by each joint coordinate system step by step, and obtain the linear mapping relationship between the spatial error of the robot arm end effector and the kinematic parameter error and posture deviation of each joint.

[0102] The crane operation recording module is used to configure a preset baseline distance, synchronously collect target images at a preset resolution and frame rate, optimize imaging by combining a uniform diffuse reflection light source with a polarizing filter, and drive the crane to perform multi-posture compound movements and record joint angle data.

[0103] The feature extraction and positioning module is used to achieve target recognition using an improved target detection model. It loads pre-trained weights through a transfer learning strategy, and optimizes the model by combining geometric enhancement, photometric adjustment, and difficult sample mining techniques to achieve target feature extraction and positioning at different distances and tilt angles.

[0104] The coordinate mapping module is used to use the principle of triangulation to solve the spatial position of the target object through the imaging geometric relationship of two cameras with different viewpoints. According to the baseline distance of the optical axes of the two cameras and the principle of similar triangles, the mapping relationship between the image pixel coordinates and the three-dimensional space coordinates is established to calculate the depth and coordinates of the target point in three-dimensional space.

[0105] The parameter adjustment module is used to apply the LM optimization algorithm to perform kinematic calibration on the crane tube, integrate the terminal posture error model with the measured spatial coordinates of the target, and achieve nonlinear optimization and stable convergence of the parameter correction by dynamically adjusting the gradient descent and Gauss-Newton method weights.

[0106] The present invention uses kinematic calibration technology to accurately identify key parameters in the kinematic model, and accordingly effectively corrects or compensates the motion deviation of the end effector, thereby achieving a higher level of absolute positioning accuracy.

[0107] like Figure 6 As shown, the present application also provides an electronic device, including a display module 103, a memory 102, a processor 101, and a computer program stored in the memory and executable on the processor 101, wherein the processor 101 implements the steps of a crane kinematic calibration method based on distance identification when executing the program.

[0108] In the embodiments of the present invention, electronic devices include, but are not limited to, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices may also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the embodiments of the present application described and / or claimed herein.

[0109] In the embodiment of the present application, the processor 101 can be implemented by using at least one of a special purpose integrated circuit, a programmable logic device, a field programmable gate array, a processor, a controller, a microcontroller, a microprocessor, and an electronic unit designed to perform the functions described herein. In some cases, such an embodiment can be implemented in a controller. For software implementation, an embodiment such as a process or function can be implemented with a separate software module that allows the execution of at least one function or operation. The software code can be implemented by a software application written in any appropriate programming language, and the software code can be stored in a memory and executed by a controller.

[0110] The display module 103 is used to display information input by the user or information provided to the user. The display module 103 may include a display panel, which may be configured in the form of a liquid crystal display, an organic light emitting diode, etc.

[0111] The memory 102 can be used to store software programs and various data. The memory 102 can include high-speed random access memory and non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0112] The present application also provides a storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the crane kinematic calibration method based on distance identification.

[0113] The storage medium can be any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or component, or any combination thereof. More specific examples (non-exhaustive list) of readable storage media include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof.

[0114] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A crane kinematic calibration method based on distance identification, characterized in that: Methods include: Step S101: Construct a crane-tube joint coordinate system. Define the Zi-axis direction of each joint based on the characteristics of the revolute joint and determine the positive direction. Define the Xi-axis direction through the common perpendicular line between adjacent links. Take the intersection of the Zi-axis and the Xi-axis as the origin of the coordinate system, derive the Yi-axis direction, and establish a multi-link kinematic model. Step S102: Constructing a kinematic model of the robotic arm, transferring and synthesizing the differential motion error components generated by each joint coordinate system step by step, and obtaining a linear mapping relationship between the spatial error of the robotic arm end effector and the kinematic parameter errors and posture deviations of each joint; Step S103: Configure a preset baseline distance, synchronously capture target images at a preset resolution and frame rate, optimize imaging by combining a uniform diffuse reflection light source with a polarization filter, and drive the crane to perform multi-posture compound motions, recording joint angle data; Step S104: Target recognition is achieved based on the improved target detection model. Pre-trained weights are loaded through a transfer learning strategy. The model is optimized by combining geometric enhancement, photometric adjustment, and difficult sample mining techniques to achieve target feature extraction and positioning at different distances and tilt angles. Step S105: Using the principle of triangulation, the spatial position of the target object is calculated based on the imaging geometric relationship of the two cameras with different viewpoints. Based on the baseline distance between the optical axes of the two cameras and the principle of similar triangles, a mapping relationship between the image pixel coordinates and the three-dimensional space coordinates is established to calculate the depth and coordinates of the target point in the three-dimensional space. Step S106: Apply the LM optimization algorithm to perform kinematic calibration on the crane tube, integrate the terminal posture error model with the measured target space coordinates, and achieve nonlinear optimization and stable convergence of parameter correction by dynamically adjusting the gradient descent and Gauss-Newton method weights.

2. The crane kinematic calibration method based on distance identification according to claim 1 is characterized in that: Step S101 specifically includes: Determine the rotation type of all joints based on the motion characteristics of the crane, and define it based on the straight line where the rotation axis is located. Z i The spatial position of the axis; Building the connecting rod i With adjacent connecting rod i +1, the common perpendicular line is X i Spatial positioning reference of the axis; The origin of the joint coordinate system is determined by defining the joint Z i Axis and X i The spatial intersection point of the axes serves as the reference origin of the coordinate system; when X i Axis and Z i After the axis definition is completed, Y i The directions of the axes are derived using the right-hand coordinate rule.

3. The crane kinematic calibration method based on distance identification according to claim 1 is characterized in that: Step S102 specifically includes: After the joint coordinate system of the robotic arm is constructed, the spatial transformation relationship between adjacent joint coordinate systems is decomposed into four orderly motion steps: Along the joints i -1 X i-1 Axis translation a i-1 distance; around the same X i-1 Axis rotation α i-1 Angle; along the joint i of Z i Axis translation d i distance; around Z i Axis rotation θ i Angle, based on the kinematic chain derivation, establish the coordinate system { i } to coordinate system { i -1} homogeneous transformation matrix , and build the kinematic model of the robotic arm on the premise of establishing the coordinate system of each link and completing the corresponding parameter definition; 。 4. The crane kinematic calibration method based on distance identification according to claim 3 is characterized in that: By analytically calculating the homogeneous transformation matrix of each joint, the matrix multiplication operation is performed in the order of the kinematic chain to solve the end effector coordinate system { n }Relative to the base coordinate system{ 0 }'s pose transformation matrix: Where, is the position vector of the end of the robotic arm, is the rotation matrix of the end of the robotic arm.

5. The crane kinematic calibration method based on distance identification according to claim 4 is characterized in that: In this method, the end coordinate system produces a slight change in posture, and the corresponding homogeneous transformation increment is recorded as ; The transformation matrix of the robot end coordinate system relative to the base coordinate system is expressed as: The homogeneous transformation increment is: Differential error of the transformation matrix of adjacent joint coordinate systems Decomposed into the weighted sum of partial derivatives of each parameter: Where, is the parameter error, and the linear mapping relationship between the parameter error and the posture deviation is constructed by analytically calculating each partial derivative.

6. The crane kinematic calibration method based on distance identification according to claim 1 is characterized in that: Step S105 specifically includes: The optical axis baseline distance between the two cameras is b , through parallax Calculate target point P Depth in three-dimensional space ， According to the principle of similar triangles, the target point coordinates satisfy the following formula as the mapping relationship between image pixel coordinates and three-dimensional space coordinates: Where, f is the camera focal length, ( x , y , z ) is the three-dimensional coordinate of the target in the camera coordinate system.

7. The crane kinematic calibration method based on distance identification according to claim 1 is characterized in that: Step S106 specifically includes: in the crane kinematic calibration, optimizing the geometric parameters by the LM optimization algorithm so that the error between the actual distance value and the theoretical distance value predicted by the kinematic model is minimized to: The parameter update equation combines the advantages of gradient descent and Gauss-Newton method, and its form is: Where, is the Jacobian matrix of the error function with respect to the parameters, is the damping factor, used to adjust the direction of the algorithm, is the parameter correction amount; In this method, parameter sensitivity analysis is introduced to eliminate redundant parameters and calculate the global sensitivity index of each parameter: Where, For the i The global sensitivity index of the joint, is the error of the kth iteration.

8. A crane kinematic calibration system based on distance identification, characterized in that: The system is used to implement the crane tube kinematic calibration method based on distance identification as described in any one of claims 1 to 7; The system includes: The kinematic model building module is used to construct the crane-tube joint coordinate system. Based on the characteristics of the revolute joint, the Zi-axis direction of each joint is defined and the positive direction is determined. The Xi-axis direction is defined by the common perpendicular line between adjacent links. The intersection of the Zi-axis and the Xi-axis is used as the origin of the coordinate system. The Yi-axis direction is derived to establish a multi-link kinematic model. The robot arm and joint mapping module is used to build the robot arm kinematic model, transfer and synthesize the differential motion error components generated by each joint coordinate system step by step, and obtain the linear mapping relationship between the spatial error of the robot arm end effector and the kinematic parameter error and posture deviation of each joint; The crane operation recording module is used to configure a preset baseline distance, synchronously capture target images at a preset resolution and frame rate, optimize imaging by combining a uniform diffuse reflection light source with a polarizing filter, and drive the crane to perform multi-posture compound movements and record joint angle data. The feature extraction and positioning module is used to achieve target recognition using an improved target detection model. It loads pre-trained weights through a transfer learning strategy and optimizes the model by combining geometric enhancement, photometric adjustment, and difficult sample mining techniques to achieve target feature extraction and positioning at different distances and tilt angles. The coordinate mapping module is used to calculate the spatial position of the target object using the imaging geometric relationship of two cameras with different viewpoints using the principle of triangulation. Based on the baseline distance between the optical axes of the two cameras and the principle of similar triangles, it establishes a mapping relationship between the image pixel coordinates and the three-dimensional space coordinates, and calculates the depth and coordinates of the target point in three-dimensional space. The parameter adjustment module is used to apply the LM optimization algorithm to perform kinematic calibration on the crane tube, integrate the terminal posture error model with the measured spatial coordinates of the target, and achieve nonlinear optimization and stable convergence of the parameter correction by dynamically adjusting the gradient descent and Gauss-Newton method weights.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the crane kinematic calibration method based on distance identification as described in any one of claims 1 to 7 are implemented.

10. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the crane kinematic calibration method based on distance identification as described in any one of claims 1 to 7 are implemented.

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