A method, system, device and medium for distance recognition-based loading arm kinematics calibration

Abstract

The application provides a kind of hose kinematics calibration method, system, equipment and medium based on distance identification, belongs to hose positioning technical field, constructs hose joint coordinate system and robot kinematics model, the differential motion error component generated by each joint coordinate system is sequentially transferred and synthesized, the mapping relationship of space error and each joint kinematics parameter error and pose deviation is obtained;Drive hose to execute multi-pose compound motion;The target features under different distances and inclination angles are extracted and positioned;The mapping relationship of image pixel coordinates and three-dimensional space coordinates is established, the depth and coordinates of target points in three-dimensional space are calculated;Fusion end pose error model and target measured space coordinates, realize the nonlinear optimization and stable convergence of parameter correction amount.The application effectively compensates the motion deviation of end effector and improves the positioning accuracy.The method bypasses the calculation of coordinate system conversion matrix, reduces the calibration complexity.

Description

Technical Field

[0001] This invention belongs to the field of loading arm positioning technology, specifically relating to a method, system, device, and medium for kinematic calibration of loading arms based on distance identification. Background Technology

[0002] In the chemical liquid transportation industry, tank trucks are the core transportation tool, and the accuracy and efficiency of their filling operations directly affect the safety and economy of chemical liquid logistics. However, the chemical liquid transportation sector utilizes loading arms to automate chemical liquid filling operations.

[0003] Among these technologies, the performance indicators of intelligent loading arms in chemical liquid loading systems, especially positioning accuracy, are key factors in evaluating the overall performance of such systems. In the kinematic calibration of intelligent loading arms, the joint coordinate system construction is not precise enough, resulting in multi-link kinematic models that cannot accurately describe the motion relationships between different parts of the loading arm. This leads to significant positioning errors in the end effector of the robotic arm, failing to meet the demands of high-precision industrial production. Furthermore, these technologies lack systematic analysis and effective compensation methods for the motion errors of each joint. Because an accurate mapping relationship has not been established between the spatial errors of the end effector and the kinematic parameter errors and pose deviations of each joint, targeted error correction is difficult. Moreover, the kinematic calibration optimization algorithms used in these technologies either have slow convergence speeds or are prone to getting trapped in local optima when dealing with nonlinear problems, failing to quickly and stably obtain the optimal kinematic parameters. This results in a lengthy calibration process and potentially inaccurate calibration results, affecting the practical application of intelligent loading arms. Summary of the Invention

[0004] This invention provides a kinematic calibration method for loading arms based on distance identification, which solves the problem of low absolute positioning accuracy of loading arms caused by multiple factors such as mechanical structure design, machining accuracy, assembly errors and wear and tear from long-term use.

[0005] The methods include: Step S101: Construct the coordinate system of the loading arm joint, define the direction of the Zi axis of each joint and determine the positive direction based on the characteristics of the rotational joint, define the direction of the Xi axis through the common perpendicular between adjacent links, take the intersection of the Zi axis and the Xi axis as the origin of the coordinate system, derive the direction of the Yi axis, and establish a multi-link kinematic model. Step S102: Construct a kinematic model of the robotic arm, and transfer and synthesize the differential motion error components generated by each joint coordinate system step by step to obtain the linear mapping relationship between the spatial error of the robotic arm end effector and the kinematic parameter errors and pose deviations of each joint. Step S103: Configure the preset baseline distance, synchronously acquire target images with preset resolution and frame rate, optimize imaging by combining uniform diffuse reflection light source and polarization filter, drive the loading arm to perform multi-posture compound motion, and record joint angle data; Step S104: Target recognition is achieved based on the improved target detection model. Pre-trained weights are loaded through transfer learning strategy, and the model is optimized by combining geometric enhancement, photometric adjustment and hard sample mining techniques to achieve target feature extraction and localization at different distances and tilt angles. Step S105: Using the principle of triangulation, the spatial position of the target object is calculated through the imaging geometric relationship of two cameras with different viewpoints. Based on the baseline distance of the optical axes of the two cameras and the principle of similar triangles, the mapping relationship between image pixel coordinates and three-dimensional spatial coordinates is established, and the depth and coordinates of the target point in three-dimensional space are calculated. Step S106: Apply the LM optimization algorithm to perform kinematic calibration of the loading arm, integrate the end pose 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.

[0006] It should be further explained that step S101 specifically includes: The rotation type of all joints is determined based on the motion characteristics of the loading arm, and is defined according to the straight line where the axis of rotation lies. Z i The spatial position of the axis; Constructing a link i With adjacent links i The common perpendicular between +1 and , the common perpendicular is X i Spatial positioning reference for the shaft; The method for determining the position of the origin of the joint coordinate system is to define the joint. Z i shaft and X i The spatial intersection of the axes serves as the reference origin of the coordinate system; when X i shaft and Z i After the axis is defined, Y i The direction of the axis is derived using the right-hand coordinate system rule.

[0007] It should be further explained that step S102 specifically includes: After constructing the joint coordinate system of the robotic arm, the spatial transformation relationship between adjacent joint coordinate systems is decomposed into four ordered motion steps: Along the joint i -1 Xi-1 Translation along the axis a i-1 Distance; around the same X i-1 Axis rotation α i-1 Angle; along the joint i of Z i Translation along the axis d i Distance; around Z i Axis rotation θ i Angle, derived from the kinematic chain, establishes a coordinate system { i} to coordinate system { i The homogeneous transformation matrix of {-1} And, on the premise of establishing the coordinate system of each link and completing the definition of the corresponding parameters, construct the kinematic model of the robotic arm; .

[0008] It should be further explained that the coordinate system of the end effector is obtained by analytically calculating the homogeneous transformation matrix of each joint and performing matrix multiplication operations in the order of the kinematic chain. n} relative to the base coordinate system { 0 The pose transformation matrix of}:

[0009] In the formula, Let be the position vector of the robotic arm's end effector. This is the rotation matrix at the end of the robotic arm.

[0010] It should be further noted that in the method, the end coordinate system undergoes a small pose change, and the corresponding homogeneous transformation increment is denoted as... The transformation matrix of the robot's end effector 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 a weighted sum of the partial derivatives of each parameter:

[0013] In the formula, , , and To represent the parameter error, a linear mapping relationship between the parameter error and the pose deviation is constructed by analytically calculating each partial derivative term.

[0014] It should be further explained that step S105 specifically includes: Based on the baseline distance between the optical axes of the two cameras b Through parallax Calculate the target point P Depth in three-dimensional space ， Based on the principle of similar triangles, the target point coordinates satisfy the following condition, which serves as the mapping relationship between image pixel coordinates and three-dimensional spatial coordinates:

[0015] In the formula, f For the camera focal length, ( x , y , z ) represents the three-dimensional coordinates of the target in the camera coordinate system.

[0016] It should be further explained that step S106 specifically includes: in the kinematic calibration of the loading arm, optimizing the geometric parameters through the LM optimization algorithm to minimize the error between the actual distance value and the theoretical distance value predicted by the kinematic model.

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

[0018] In the formula, Let be the Jacobian matrix of the error function with respect to the parameters. This is the damping factor, used to adjust the direction of the algorithm. This is the parameter correction amount; The method incorporates parameter sensitivity analysis to eliminate redundant parameters and calculates the global sensitivity index for each parameter:

[0019] In the formula, For the first i Global sensitivity indicators of joints Let be the error of the k-th iteration.

[0020] This application also provides a distance-based kinematic calibration system for loading arms, the system comprising: The motion model building module is used to construct the coordinate system of the loading arm joint. Based on the characteristics of the rotational 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 between adjacent links. The intersection of the Zi axis and the Xi axis is taken as the origin of the coordinate system. The Yi axis direction is derived to establish a multi-link kinematic model. The robotic arm and joint mapping module is used to construct the kinematic model of the robotic arm, and to transfer and synthesize the differential motion error components generated by each joint coordinate system step by step to obtain the linear mapping relationship between the spatial error of the robotic arm end effector and the kinematic parameter error and pose deviation of each joint. The loading arm operation recording module is used to configure a preset baseline distance, synchronously acquire target images with a preset resolution and frame rate, optimize imaging by combining a uniform diffuse reflection light source and a polarizing filter, drive the loading arm to perform multi-posture compound motion, and record joint angle data. The feature extraction and localization module is used to achieve target recognition using an improved target detection model. It loads pre-trained weights through transfer learning strategy and optimizes the model by combining geometric enhancement, photometric adjustment and hard sample mining techniques to achieve target feature extraction and localization at different distances and tilt angles. The coordinate mapping module is used to calculate the spatial position of the target object by using the principle of triangulation and the imaging geometry of two cameras with different viewpoints. Based on the baseline distance of the optical axes of the two cameras and the principle of similar triangles, it establishes the mapping relationship between image pixel coordinates and three-dimensional spatial coordinates, and calculates the depth and coordinates of the target point in three-dimensional space. The parameter adjustment module is used to perform kinematic calibration of the loading arm by applying the LM optimization algorithm. It integrates the end pose error model with the measured spatial coordinates of the target and achieves 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 this application, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the distance-based kinematic calibration method for loading arms.

[0022] According to another embodiment of this application, a storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the distance-based kinematic calibration method for loading arms.

[0023] As can be seen from the above technical solutions, the present invention has the following advantages: The distance-based kinematic calibration method for the loading arm provided in this application accurately describes the motion relationships of the loading arm by constructing a joint coordinate system and a kinematic model of the robotic arm, defining the direction of each joint axis and the origin. Simultaneously, a linear mapping relationship between the spatial error of the end effector and the joint parameter error is established, effectively improving the motion accuracy of the intelligent loading arm. Configuring a preset baseline distance and combining a uniform diffuse light source with a polarizing filter to optimize imaging improves image acquisition quality. During image acquisition, the loading arm is driven to perform multi-pose composite motions, recording joint angle data and acquiring diverse image data, enhancing the system's adaptability to complex environments.

[0024] Based on an improved target detection model, this study utilizes transfer learning to load pre-trained weights and combines various optimization techniques to enhance the model's accuracy in identifying and locating targets at different distances and tilt angles. It can accurately extract target features, providing accurate image information for triangulation and ensuring the accuracy of 3D coordinate calculations. The LM optimization algorithm is employed for kinematic calibration of the loading arm, dynamically adjusting the gradient descent and Gauss-Newton method weights to achieve nonlinear optimization and stable convergence of parameter corrections. Furthermore, the dynamic adjustment of kinematic parameters using the LM optimization algorithm minimizes 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 loading arm and shortening the calibration time. Attached Figure Description

[0025] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying 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.

[0026] Figure 1 This is a flowchart of the distance-based kinematic calibration method for loading arm. Figure 2 This is a schematic diagram of the link coordinate system; Figure 3 This is a schematic diagram of the image data; Figure 4 A schematic diagram of the target recognition results; Figure 5 This is a schematic diagram illustrating the principle of triangulation. Figure 6 This is a schematic diagram of an electronic device. Detailed Implementation

[0027] This invention addresses the problem of insufficient absolute positioning accuracy of loading arms (CA arms) in chemical liquid transportation due to machining errors, assembly deviations, and long-term wear. It proposes a kinematic calibration method for CA arms based on distance identification. This invention replaces traditional high-precision tools with vision-assisted measurement technology. It utilizes a stereo vision system to acquire images of the target at the end of the CA arm, combines this with a deep learning model to achieve rapid target identification, and employs kinematic calibration technology to accurately identify key parameters in the kinematic model. Based on this, it effectively corrects or compensates for motion deviations of the end effector, thereby achieving a higher level of absolute positioning accuracy. This method bypasses the calculation of coordinate system transformation matrices, reducing calibration complexity.

[0028] The following describes in detail the steps of the distance-based kinematic calibration method for loading arms involved in this application. Specific details, such as particular system structures and techniques, are presented for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can 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 feature, integral, step, operation, element, and / or component, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or collections thereof. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0030] The terms "one embodiment" or "some embodiments" used in this application mean that one or more embodiments of this application include the specific features, structures, or characteristics described in that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of 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 technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Please see Figure 1 The diagram shows a flowchart of a distance-based kinematic calibration method for loading arm in a specific embodiment. The method includes: Step S101: Construct the coordinate system of the loading arm joint, define the direction of the Zi axis of each joint and determine the positive direction based on the characteristics of the rotational joint, define the direction of the Xi axis through the common perpendicular between adjacent links, take the intersection of the Zi axis and the Xi axis as the origin of the coordinate system, derive the direction of the Yi axis, and establish a multi-link kinematic model.

[0033] In some embodiments, the loading arm is a device for loading and unloading liquids or gases, and can be of a conventional loading arm shape. The loading arm may typically include, but is not limited to, rotary joints, columns, inner arms, outer arms, drop arms, cylinders, sealing devices, flanges and other auxiliary components.

[0034] In this embodiment, within the field of kinematic calibration, constructing a kinematic model of the intelligent arm is the initial step in system calibration. A mathematical representation is established by analyzing the geometric structure and motion characteristic parameters of the mechanical system. The function of the kinematic model is to accurately describe the spatial transformation relationship between the end effector of the robotic arm and the base coordinate system.

[0035] The modeling methods for kinematic models take into account the significant variations in the number of parameters that need to be identified under different theoretical frameworks, and the positive correlation between the model's fitting accuracy to real motion and other factors.

[0036] It should be noted that while increasing the parameter dimension can improve the model's ability to capture the nonlinear characteristics of mechanical systems, it significantly increases the computational complexity of the parameter identification process. Specifically, this manifests as 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 link coordinate system is as follows: Figure 2 As shown, the main steps of kinematic modeling are: Step S1011: When setting the joint coordinate system, prioritize defining the coordinate system. Z i The orientation of the axis. Based on the motion characteristics of each joint, all joints are classified as rotational, defined according to the line containing their axis of rotation. Z i The spatial position of the axis.

[0038] In this embodiment, the positive direction of the coordinate axis is determined according to the right-hand screw rule, that is, when the direction of the four fingers is matched with the direction of rotation, the direction the thumb points is the positive direction. Z i The positive direction of the axis.

[0039] Step S1012: Construct the link i With adjacent links i The common perpendicular line between +1 and , the geometric characteristic line of the common perpendicular line is X iSpatial positioning reference for the axis.

[0040] The pointing rule in this embodiment is defined as: from the current link i Starting from the centroid or characteristic point, pointing along the common perpendicular towards the subsequent member i The position corresponding to +1 is used to determine 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 shaft and X i The spatial intersection of the axes serves as the reference origin of the coordinate system.

[0042] Step S1014: During the construction of the joint coordinate system, when X i shaft and Z i After the axis is defined, Y i The direction of the axis is derived using the right-hand coordinate system rule.

[0043] The specific method is as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error. Z i The axis can be considered as the direction axis of the right-hand screw's forward movement. X i The axis is considered as the common perpendicular pointing towards the axis, and is determined by the direction of the right four fingers bending from... Z i Axle Steering X i When the thumb is pointing vertically, that is... 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 consistency of mathematical calculations. The poses of each link are represented by four geometric parameters: (1) Link length a For along X i Axis, from Z i Move to Z i+1 The distance; (2) Linkage angle α To bypass X i Axis, from Z i Rotate to Z i+1 Angle; (3) Linkage offset d For alongZ i Axis, from X i-1 Move to X i The distance; (4) Joint angle θ To bypass Z i Axis, from X i-1 Rotate to X i The angle.

[0045] In some specific embodiments, the intelligent loading arm employs a dual-rotation joint series design in its mechanical configuration, achieving planar spatial trajectory control through the coordinated motion of the two axes. Compared to multi-degree-of-freedom systems, this simplified architecture demonstrates greater economic and reliability advantages in scenarios such as fluid transport and docking.

[0046] The kinematic model of this embodiment is shown in Table 1. Based on the Denavit-Hartenberg (DH) modeling theory, the system's kinematic parameter set can be simplified to two sets of parameters, namely joint rotation angles. Link length The nominal size of the intelligent loading arm is The actual size is .

[0047] Table 1: Kinematic Models

[0048] As can be seen, this embodiment describes the relative position and attitude relationship between adjacent links by defining the axes and parameters of the joint coordinate system. Each joint coordinate system can be transformed with the adjacent coordinate system 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 movement of the loading arm, improving the accuracy and stability of the loading arm motion control.

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

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

[0051] This embodiment utilizes knowledge of differential geometry and kinematics to precisely 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 pose of the end effector will also change accordingly. By differentiating the kinematic equations, the relationship between the small changes in the motion parameters of each joint and the changes in the pose of the end effector is obtained.

[0052] This embodiment accumulates and synthesizes the relationship between minute changes in the motion parameters of each joint and changes in the pose of the end effector. This allows the establishment of a linear mapping model between the spatial error of the end effector and the kinematic parameter errors and pose deviations of each joint. This enables a quantitative analysis of the impact of joint errors on the accuracy of the end effector. Furthermore, by establishing this mapping relationship, joint parameters can be adjusted and optimized in a targeted manner, improving the motion accuracy and positioning precision of the robotic arm, reducing operational errors caused by joint errors, and enhancing the overall performance of the intelligent loading arm.

[0053] Step S103: Configure the preset baseline distance, synchronously acquire target images with preset resolution and frame rate, optimize imaging by combining uniform diffuse reflection light source and polarization filter, drive the loading arm to perform multi-posture compound motion, 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 reflection light source is arranged in the experimental area to eliminate the influence of specular highlights and shadows on image quality.

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

[0056] Before camera calibration, intrinsic parameter calibration is required. The Zhang Zhengyou 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, it is necessary to control the ambient light intensity and use polarizing filters to suppress reflective interference.

[0057] In this embodiment, the target is fixed to the end of the intelligent loading arm, which is then driven to move along a preset trajectory within the joint space, covering multiple typical poses within its workspace. Under each motion pose, the stereo vision system simultaneously acquires target images and records the corresponding joint angle data. To enhance data diversity, the translational and rotational movements of the intelligent loading arm can be combined to allow the target to exhibit different tilt angles and distance variations within the camera's field of view, fully exposing the impact of geometric parameter errors on stereo vision measurements. The joint angles are defined in Table 2, which defines six typical poses, each controlling the intelligent loading arm to move to a predetermined position.

[0058] Table 2: Definition of Joint Angles

[0059] This embodiment addresses the limitation of ordinary RGB cameras lacking depth information by employing a multi-frame fusion strategy: continuously acquiring 10-20 frames of images in each robotic arm's stationary pose, suppressing random noise through temporal averaging, and utilizing feature point tracking algorithms, such as LK optical flow, to verify the target's stationary state.

[0060] In this embodiment, a reference brightness board is placed in the scene to compensate for changes in ambient light, and the camera exposure parameters are dynamically adjusted. All image data must be accompanied by timestamps, joint angles, and robotic arm pose information to facilitate subsequent offline processing.

[0061] In this embodiment, the original image undergoes preprocessing to improve calibration reliability. First, an intrinsic parameter-based distortion correction model is applied; second, histogram equalization is used to enhance image contrast and highlight target feature edges. Image data is as follows: Figure 3 As shown, Figure 3 The images above are six images captured by the left camera. Figure 3 The images below are six images captured by the right camera.

[0062] As can be seen, configuring a suitable preset baseline distance, based on the target measurement range and system design requirements, is crucial. The baseline distance is a critical parameter between the two cameras in a stereo vision system, affecting the accuracy and range of 3D measurements. Setting the camera's preset resolution and frame rate ensures clear and rapid acquisition of target images. Regarding the acquisition environment, a uniform diffuse light source is used to avoid specular highlights and shadows, ensuring the target appears uniformly clear in the image. Simultaneously, polarizing filters are used when necessary to further suppress reflective interference and improve image quality. During acquisition, the loading arm is driven to perform multi-pose composite motions, causing the target to exhibit different tilt angles and distance variations within the camera's field of view, covering multiple typical poses within its workspace. The joint angle data for each pose are recorded, providing a more comprehensive reflection of the loading arm's characteristics under different working conditions.

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

[0064] In some embodiments, the target recognition method is based on an improved YOLOv5 deep learning model to efficiently detect preset targets from images in a stereo vision system. Considering the imaging characteristics of ordinary cameras, such as their sensitivity to lighting, a lightweight YOLOv5s model is selected as the baseline architecture, achieving a balance between speed and accuracy, and can be adapted to small-sample scenarios through transfer learning. The model input resolution is set to 640×640 pixels to ensure that target features can be effectively extracted at different distances while avoiding excessive consumption of computational resources.

[0065] In this embodiment, the image data is divided into training, validation, and test sets in an 8:1:1 ratio to ensure the model's generalization ability. The LabelImg tool is used for annotation, precisely annotating target bounding boxes in PASCALVOC format with an error controlled within 2 pixels. To improve model robustness, multi-dimensional data augmentation is implemented: geometric transformation, photometric adjustment, random occlusion, and Gaussian noise injection to simulate the impact of complex industrial environments on imaging.

[0066] This embodiment employs a transfer learning strategy for model training, loading COCO data to train weights and accelerate convergence. Hyperparameters include a batch size of 16, an initial learning rate of 0.01 (adjusted by cosine annealing), and a weighted loss function CIoULoss (weight 0.8) to optimize boundary regression accuracy. For target characteristics, K-means clustering analysis is used to analyze actual target sizes and generate customized anchor boxes to improve small target detection capabilities. A hard sample mining mechanism is introduced during training, specifically enhancing missed samples in the validation set before retraining.

[0067] The model achieved 98.2% precision and 96.7% recall on the independent test set, with an mAP of 97.5% at 0.5 and a single-frame inference time of 8.3 milliseconds (NVIDIA RTX 3080 GPU). In actual deployment, the model is seamlessly integrated with the intelligent loading arm 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 loading arms, providing a reliable visual perception foundation for industrial automation scenarios. The target recognition results are as follows: Figure 4 As shown.

[0068] It can be seen that target recognition is achieved based on an improved target detection model. Choosing the lightweight YOLOv5s as the baseline architecture achieves a good balance between detection speed and accuracy. Through transfer learning, weights pre-trained on a large-scale dataset are loaded, utilizing the general image features learned in these pre-trained weights to accelerate the model's convergence speed on the target recognition task. In terms of data processing, geometric enhancements such as rotation, scaling, and translation, as well as photometric adjustments such as brightness, contrast, and saturation, are performed on the image data. Geometric enhancement and photometric adjustments can simulate complex environmental conditions in industrial settings, increasing data diversity. Hard sample mining targets and enhances samples that are easily missed in the validation set, then retrains the model to improve its ability to detect targets under various complex conditions. Through these operations, target feature extraction and localization are achieved at different distances and tilt angles.

[0069] Step S105: Using the principle of triangulation, the spatial position of the target object is calculated by the imaging geometry of two cameras with different viewpoints. Based on the baseline distance of the optical axes of the two cameras and the principle of similar triangles, the mapping relationship between image pixel coordinates and three-dimensional spatial coordinates is established, and the depth and coordinates of the target point in three-dimensional space are calculated.

[0070] In some embodiments, the principle of triangulation is used for target stereo localization. The stereo vision system includes two cameras with different viewpoints. When a target point is observed simultaneously by these two cameras in space, projection points are formed in the left and right images respectively. Due to the baseline distance between the optical axes of the two cameras, based on the principle of similar triangles, by measuring the parallax of the target point in the left and right images—that is, the positional difference of the projection points—and combining this with known parameters such as the camera focal length, the depth Z of the target point in three-dimensional space can be calculated. Furthermore, based on other relationships of similar triangles, the three-dimensional coordinates (x, y, z) of the target point in the camera coordinate system are calculated, thereby establishing a mapping relationship between image pixel coordinates and three-dimensional spatial coordinates. This enables stereo localization of the target, achieving the conversion from two-dimensional image information to three-dimensional spatial information, and improving the accuracy and reliability of loading arm kinematic calibration.

[0071] Step S106: Apply the LM optimization algorithm to perform kinematic calibration of the loading arm, integrate the end pose 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.

[0072] In some embodiments, the LM optimization algorithm is applied to perform kinematic calibration of the loading arm. The end-effector pose error model established in step S102 is combined with the measured target spatial coordinates obtained in step S105. During operation, the LM optimization algorithm dynamically adjusts the weights of gradient descent and the Gauss-Newton method, continuously attempting to find the optimal parameter correction during iteration. In each iteration, a suitable parameter correction is calculated based on the current parameter values ​​and error conditions, and the model parameters are then updated until the parameter correction converges to a stable value. This achieves nonlinear optimization and stable convergence of the loading arm's kinematic parameters, completing the kinematic calibration process.

[0073] The LM optimization algorithm in this embodiment combines the advantages of gradient descent and the Gauss-Newton method. Gradient descent is a simple and effective optimization method that searches for the optimal solution along the negative gradient of the objective function, but its convergence speed is slow when approaching the optimal solution. The Gauss-Newton method is an optimization method for nonlinear least squares problems, which converges quickly under certain conditions, but it is sensitive to the choice of initial values ​​and may become unstable. The LM optimization algorithm introduces a damping factor to dynamically adjust the weights of gradient descent and the Gauss-Newton method. In the early stages of the algorithm, gradient descent is used to ensure stability, while the weight of the Gauss-Newton method is gradually increased as the optimal solution approaches, accelerating the convergence speed. This achieves efficient solution to nonlinear problems, finds the optimal kinematic parameters, reduces working errors caused by kinematic parameter errors, and improves the reliability and stability of loading arms in industrial applications.

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

[0075] Step S102 specifically includes the following: The modeling method for the pose error of the robotic arm end effector 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 robotic arm end effector and the kinematic parameter deviation of each joint.

[0076] After constructing the joint coordinate system of the robotic arm, the spatial transformation relationship between adjacent joint coordinate systems can be decomposed into four ordered motion steps: First, along the joint... i -1 Xi-1 Translation along the axis a i-1 Distance; then, around the same X i-1 Axis rotation α i-1 Angle; then, along the joint i of Z i Translation along the axis d i Distance; finally, around Z i Axis rotation θ i Angle. Based on the above kinematic chain derivation, an angle can be established from the coordinate system { i} to coordinate system { i The homogeneous transformation matrix of {-1} :

[0077] This embodiment, assuming the coordinate systems of each link are clearly established and the corresponding parameters are defined, allows for the direct construction of the robotic arm's kinematic model. By analytically calculating the homogeneous transformation matrix of each joint, the coordinate system of the end effector can be solved by performing matrix multiplication operations in the kinematic chain order. n} relative to the base coordinate system { 0 The pose transformation matrix of}:

[0078] In the formula, Let be the position vector of the robotic arm's end effector. This represents the rotation matrix of the robotic arm's end effector. After acquiring real-time measurement data from the robotic arm's joint position sensors, the pose transformation matrix of the end effector in the Cartesian coordinate system can be determined through forward kinematics calculations. .

[0079] The pose transformation matrix of the robotic arm's end effector 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 a deviation in the end effector's pose. Assume that the end effector coordinate system undergoes a small pose change at this time, and the corresponding homogeneous transformation increment is denoted as... According to the principle of differential motion, this minute motion can be decomposed into translational and rotational components. Therefore, considering the differential motion between links, the transformation matrix of the robot's end effector coordinate system relative to the base coordinate system can be expressed as:

[0080] Expanding the above equation completely and then omitting higher-order differential terms, we obtain the homogeneous transformation increment:

[0081] Differential error of the transformation matrix of adjacent joint coordinate systems It can be decomposed into a weighted sum of the partial derivatives of each parameter: In the formula, , , and To account for parameter errors, the partial derivative terms are calculated analytically as follows: It is possible to construct a linear mapping relationship between parameter error and pose deviation.

[0082] The robotic arm end-effector distance error modeling method in this embodiment focuses on constructing geometric distance constraints between feature points. The method establishes an error compensation model by comparing the actual distance values ​​of the robot's end effector in multiple poses with the theoretical distance values ​​predicted by the kinematic model. In the formula, and These represent the distances between corresponding points on the actual trajectory and the predicted trajectory of the robotic arm, respectively.

[0083] To improve the accuracy of the system's evaluation of the intelligent loading arm's kinematic model, this embodiment uses Monte Carlo sampling to generate 100 sets of random joint angle combinations that uniformly cover the joint space. Each set of angle values ​​is randomly generated within a uniform distribution across the physical limits of each joint, ensuring full coverage of the intelligent loading arm's working space. Table 3 shows the model errors before calibration, illustrating the distribution of the 100 sets of model errors.

[0084] Table 3: Model Error Before Calibration

[0085] Based on the above embodiments, in order to further improve the reliability of the distance-based kinematic calibration method for loading arms provided in the above embodiments, the following is an implementable method for steps S105 and S106. In the following embodiment, the target stereo positioning is based on triangulation. Through the three-dimensional positioning principle in a stereo vision system, the spatial position of the target object is calculated 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 observed simultaneously by left and right cameras in space, its projection point in the left image is: In the image on the right, it is .

[0086] Due to the 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 The calculations show that, based on the principle of similar triangles, the target point coordinates satisfy:

[0087] In the formula, f For the camera focal length, ( x , y , z Let be the three-dimensional coordinates of the target in the camera coordinate system. This formula establishes a direct mapping relationship between image pixel coordinates and three-dimensional spatial coordinates.

[0088] To adapt to industrial environments, this embodiment introduces a dynamic calibration mechanism: when the movement of the intelligent loading arm causes a slight change in camera pose, the extrinsic parameters are updated in real time by acquiring images from the calibration board online, ensuring long-term stability. The results of the stereo positioning are shown in Table 4, which expresses the coordinates of six typical poses in the left camera coordinate system.

[0089] Table 4: Results of stereo positioning

[0090] In step S106, during the kinematic calibration of the loading arm, the LMLevenberg-Marquardt optimization algorithm is used. 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 the Gauss-Newton method. In the kinematic calibration of the intelligent loading arm, the algorithm optimizes geometric parameters to minimize the error between the actual distance value and the theoretical distance value predicted by the kinematic model.

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

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

[0093] To improve the robustness of the algorithm, damping factor Dynamic adjustment is required: 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 increased to enhance stability. Simultaneously, parameter sensitivity analysis is introduced to eliminate redundant parameters, and the global sensitivity index of each parameter is calculated.

[0094] In the formula, For the first i Global sensitivity indicators of joints Let be the error of the k-th iteration. If If the kinematic calibration results are not found, they will be removed from the optimization variables to reduce the computational dimensionality. The kinematic calibration results are shown in Table 5. The calibration dimensions of the intelligent loading arm are... The actual size is The model errors after calibration are shown in Table 6, which describes the distribution of 100 sets of model errors. The errors are significantly reduced compared to those before calibration.

[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 observation data, and the model parameters are continuously updated until the convergence condition is met. Moreover, by using nonlinear optimization methods, the kinematic parameters of the intelligent loading arm can be accurately estimated, improving the accuracy and reliability of the model.

[0098] It should be understood that the sequence number of each step in the above embodiments does not imply 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 are embodiments of the distance identification-based loading arm kinematics calibration system provided in this disclosure. This system and the distance identification-based loading arm kinematics calibration methods in the above embodiments belong to the same inventive concept. For details not described in detail in the embodiments of the distance identification-based loading arm kinematics calibration system, please refer to the embodiments of the distance identification-based loading arm kinematics calibration methods described above.

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

[0101] The robotic arm and joint mapping module is used to construct the kinematic model of the robotic arm. It transfers and synthesizes the differential motion error components generated by each joint coordinate system step by step to obtain the linear mapping relationship between the spatial error of the robotic arm end effector and the kinematic parameter errors and pose deviations of each joint.

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

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

[0104] The coordinate mapping module is used to calculate the spatial position of the target object by using the principle of triangulation and the imaging geometry of two cameras with different viewpoints. Based on the baseline distance between the optical axes of the two cameras and the principle of similar triangles, it establishes the mapping relationship between image pixel coordinates and three-dimensional spatial coordinates, and calculates the depth and coordinates of the target point in three-dimensional space.

[0105] The parameter adjustment module is used to perform kinematic calibration of the loading arm by applying the LM optimization algorithm. It integrates the end pose error model with the measured spatial coordinates of the target and achieves nonlinear optimization and stable convergence of the parameter correction by dynamically adjusting the gradient descent and Gauss-Newton method weights.

[0106] This invention employs kinematic calibration technology to accurately identify key parameters in the kinematic model, and accordingly implements effective correction or compensation for motion deviations of the end effector, thereby achieving a higher level of absolute positioning accuracy.

[0107] like Figure 6 As shown, this 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. When the processor 101 executes the program, it implements the steps of a distance-based kinematic calibration method for loading arm.

[0108] In 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 processors, cellular phones, smartphones, 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 described and / or claimed herein.

[0109] In this embodiment, processor 101 may be implemented using at least one of an application-specific integrated circuit, a programmable logic device, a field-programmable gate array, a processor, a controller, a microcontroller, a microprocessor, or an electronic unit designed to perform the functions described herein. In some cases, such an implementation may be implemented within a controller. For software implementation, implementations such as processes or functions may be implemented with separate software modules that allow the performance of at least one function or operation. The software code may be implemented by a software application written in any suitable programming language, and the software code may be stored in memory and executed by the 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, or the like.

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

[0112] This application also provides a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the distance-based kinematic calibration method for loading arms.

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

[0114] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those 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 invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for kinematic calibration of a loading arm based on distance identification, characterized in that, The methods include: Step S101: Construct the coordinate system of the loading arm joint, define the direction of the Zi axis of each joint and determine the positive direction based on the characteristics of the rotational joint, define the direction of the Xi axis through the common perpendicular between adjacent links, take the intersection of the Zi axis and the Xi axis as the origin of the coordinate system, derive the direction of the Yi axis, and establish a multi-link kinematic model. Step S102: Construct a kinematic model of the robotic arm, and transfer and synthesize the differential motion error components generated by each joint coordinate system step by step to obtain the linear mapping relationship between the spatial error of the robotic arm end effector and the kinematic parameter errors and pose deviations of each joint. Step S103: Configure the preset baseline distance, synchronously acquire target images with preset resolution and frame rate, optimize imaging by combining uniform diffuse reflection light source and polarization filter, drive the loading arm to perform multi-posture compound motion, and record joint angle data; Step S104: Target recognition is achieved based on the improved target detection model. Pre-trained weights are loaded through transfer learning strategy, and the model is optimized by combining geometric enhancement, photometric adjustment and hard sample mining techniques to achieve target feature extraction and localization at different distances and tilt angles. Step S105: Using the principle of triangulation, the spatial position of the target object is calculated through the imaging geometric relationship of two cameras with different viewpoints. Based on the baseline distance of the optical axes of the two cameras and the principle of similar triangles, the mapping relationship between image pixel coordinates and three-dimensional spatial coordinates is established, and the depth and coordinates of the target point in three-dimensional space are calculated. Step S106: Apply the LM optimization algorithm to perform kinematic calibration of the loading arm, integrate the end pose 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.

2. The kinematic calibration method for the loading arm based on distance identification according to claim 1, characterized in that, Step S101 specifically includes: The rotation type of all joints is determined based on the motion characteristics of the loading arm, and is defined according to the straight line where the rotation axis lies. Z i The spatial position of the axis; Constructing a link i With adjacent links i The common perpendicular between +1 and , the common perpendicular is X i Spatial positioning reference for the shaft; The method for determining the position of the origin of the joint coordinate system is to define the joint. Z i shaft and X i The spatial intersection of the axes serves as the reference origin of the coordinate system; when X i shaft and Z i After the axis is defined, Y i The direction of the axis is derived using the right-hand coordinate system rule.

3. The kinematic calibration method for the loading arm based on distance identification according to claim 1, characterized in that, Step S102 specifically includes: After constructing the joint coordinate system of the robotic arm, the spatial transformation relationship between adjacent joint coordinate systems is decomposed into four ordered motion steps: Along the joint i -1 X i-1 Translation along the axis a i-1 Distance; around the same X i-1 Axis rotation α i-1 Angle; along the joint i of Z i Translation along the axis d i Distance; around Z i Axis rotation θ i Angle, derived from the kinematic chain, establishes a coordinate system { i } to coordinate system { i The homogeneous transformation matrix of {-1} And, on the premise of establishing the coordinate system of each link and completing the corresponding parameter definition, construct the kinematic model of the robotic arm; 。 4. The kinematic calibration method for the loading arm based on distance identification according to claim 3, characterized in that, The coordinate system of the end effector is obtained by analytically calculating the homogeneous transformation matrix of each joint and performing matrix multiplication operations in the order of the kinematic chain. n } relative to the base coordinate system { 0 The pose transformation matrix of}: In the formula, Let be the position vector of the robotic arm's end effector. This is the rotation matrix at the end of the robotic arm.

5. The kinematic calibration method for the loading arm based on distance identification according to claim 4, characterized in that, In the method, the end coordinate system undergoes a small pose change, and the corresponding homogeneous transformation increment is denoted as... The transformation matrix of the robot's end effector 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 a weighted sum of the partial derivatives of each parameter: In the formula, To represent the parameter error, a linear mapping relationship between the parameter error and the pose deviation is constructed by analytically calculating each partial derivative term.

6. The kinematic calibration method for the loading arm based on distance identification according to claim 1, characterized in that, Step S105 specifically includes: Based on the baseline distance between the optical axes of the two cameras b Through parallax Calculate the target point P Depth in three-dimensional space ， Based on the principle of similar triangles, the target point coordinates satisfy the following condition, which serves as the mapping relationship between image pixel coordinates and three-dimensional spatial coordinates: In the formula, f For the camera focal length, ( x , y , z ) represents the three-dimensional coordinates of the target in the camera coordinate system.

7. The method for kinematic calibration of the loading arm based on distance identification according to claim 1, characterized in that, Step S106 specifically includes: In the kinematic calibration of the loading arm, the geometric parameters are optimized using the LM optimization algorithm to minimize the error between the actual distance value and the theoretical distance value predicted by the kinematic model. The parameter update equation combines the advantages of gradient descent and the Gauss-Newton method, and its form is as follows: In the formula, Let be the Jacobian matrix of the error function with respect to the parameters. This is the damping factor, used to adjust the direction of the algorithm. This is the parameter correction amount; The method incorporates parameter sensitivity analysis to eliminate redundant parameters and calculates the global sensitivity index for each parameter: In the formula, For the first i Global sensitivity indicators of joints Let be the error of the k-th iteration.

8. A kinematic calibration system for a loading arm based on distance recognition, characterized in that, The system is used to implement the distance identification-based kinematic calibration method for loading arms as described in any one of claims 1 to 7; The system includes: The motion model building module is used to construct the coordinate system of the loading arm joint. Based on the characteristics of the rotational 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 between adjacent links. The intersection of the Zi axis and the Xi axis is taken as the origin of the coordinate system. The Yi axis direction is derived to establish a multi-link kinematic model. The robotic arm and joint mapping module is used to construct the kinematic model of the robotic arm, and to transfer and synthesize the differential motion error components generated by each joint coordinate system step by step to obtain the linear mapping relationship between the spatial error of the robotic arm end effector and the kinematic parameter error and pose deviation of each joint. The loading arm operation recording module is used to configure a preset baseline distance, synchronously acquire target images with a preset resolution and frame rate, optimize imaging by combining a uniform diffuse reflection light source and a polarizing filter, drive the loading arm to perform multi-posture compound motion, and record joint angle data. The feature extraction and localization module is used to achieve target recognition using an improved target detection model. It loads pre-trained weights through transfer learning strategy and optimizes the model by combining geometric enhancement, photometric adjustment and hard sample mining techniques to achieve target feature extraction and localization at different distances and tilt angles. The coordinate mapping module is used to calculate the spatial position of the target object by using the principle of triangulation and the imaging geometry of two cameras with different viewpoints. Based on the baseline distance of the optical axes of the two cameras and the principle of similar triangles, it establishes the mapping relationship between image pixel coordinates and three-dimensional spatial coordinates, and calculates the depth and coordinates of the target point in three-dimensional space. The parameter adjustment module is used to perform kinematic calibration of the loading arm by applying the LM optimization algorithm. It integrates the end pose error model with the measured spatial coordinates of the target and achieves 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, characterized in that, When the processor executes the program, it implements the steps of the distance-based kinematic calibration method for loading arm as described in any one of claims 1 to 7.

10. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the distance-based kinematic calibration method for loading arm as described in any one of claims 1 to 7.

Images