Non-geometric Errors Research Articles

A deep learning approach for pose error prediction in parallel robots

Parallel robots are increasingly favored in industrial automation due to their high precision, stability, and rigidity in high-speed and heavy-load tasks. However, factors such as manufacturing tolerances, assembly deviations, loads, and environmental conditions can lead to pose inaccuracies, manifesting as both geometric and non-geometric errors. Traditional model-driven approaches effectively predict geometric errors but often neglect non-geometric factors, potentially impacting the overall accuracy. This paper presents a deep learning-based method for comprehensive pose error prediction in parallel robots, addressing both geometric and non-geometric errors. The proposed approach employs an encoder-decoder network that takes target pose inputs and outputs predicted pose errors. The encoder integrates multi-layer convolutional sparse coding (CSC) blocks and efficient channel attention (ECA) modules to extract features from the network inputs. Monte Carlo dropout is utilized to estimate prediction uncertainties, enhancing the reliability of the network predictions. Experimental validation on a Stewart platform demonstrates the high accuracy and robustness of the method under various loading conditions. Comparative analyses with several typical models affirm the superior performance of the proposed network, indicating its potential to improve the operational accuracy and reliability of parallel robots in high-precision applications.

Deep learning-based predicting and compensating method for the pose deviations of parallel robots

The static pose accuracy is regarded as a crucial performance indicator for parallel robots, which is inevitably affected by the geometric and nongeometric errors. However, an accurate error model for parallel robots is highly complex, especially for mathematical modeling and identifying non-geometric errors. This limitation hampers the application of parallel robots in high-precision processing and manufacturing fields. To enhance the performance of parallel robots and address the complexities in establishing their error models, a deep learning-based predicting and compensating method is investigated, which can accurately predict their pose deviations. This method ingeniously integrates the spatial feature extraction capabilities of convolutional neural networks, the bidirectional dependency capturing prowess of bilateral long short-term memory networks, and the feature significance discernment offered by squeeze-and-excitation networks. Subsequently, the pose deviations are definitely predicted by this method and are pre-compensated into nominal pose so as to improve the performance. A pose-deviation pairs dataset is established to accomplish the comparison of the investigated method with the two commonly used artificial neural network and long short-term memory on the 6-UPS parallel robot. Experiment on the 6-UPS parallel robot against traditional kinematic calibration methods demonstrate the investigated method achieves satisfactory pose accuracies, with the ability to reduce pose deviations by 88.60 %. Meanwhile, the effectiveness and general applicability of this method have also been validated by successful implementation on a 6-UCU parallel robot.

Uncertainty-aware error modeling and hierarchical redundancy optimization for robotic surface machining

Industrial robots are commonly utilized in in-situ machining, but their inherent limitations in stiffness and positioning accuracy can pose challenges in achieving precise freeform surface milling. Previous research primarily focused on robot stiffness optimization and positioning error prediction separately, neglecting the uncertainty of robot errors and the modeling of surface profile errors. To address these issues, this work introduces a novel evaluation method for surface profile errors in robotic milling. It combines geometric error prediction models, based on kinematic and stiffness models, with non-geometric errors using Gaussian process regression. Moreover, collaborative optimization of multiple redundancies in robotic surface milling systems is crucial for reducing machining errors effectively. To achieve this, this work proposes a collaborative optimization method for optimizing the robot’s posture change sequence and the workpiece’s orientation, considering the motion constraints and error requirements of the robot. Among them, this work introduces the improved Whale Optimization Star Algorithm (WOA*) method to address the optimization problem of coupling robot posture and workpiece’s orientation. The proposed method’s effectiveness is confirmed through simulations and experiments, which clearly demonstrate its capability in improving error prediction and machining accuracy in robotic milling.

Hierarchical Error Compensation Method for Two-Degree-of-Freedom Manipulator Positioning Error in Hybrid Robots

In this paper, taking a two-degree-of-freedom parallelogram serial manipulator of a hybrid robot as an example, a hierarchical error compensation method that combines geometric and non-geometric error compensation is proposed. First, we establish the geometric kinematic modeling and error model and use the Levenberg-Marquardt (L-M) method to identify the geometric error parameters. Then, we use the grid interpolation method to compensate for non-geometric errors, thereby improving the overall positioning accuracy of the manipulator. Finally, a simulation is presented to verify the correctness and effectiveness of the proposed method. The results show that the positioning accuracy is improved from 4.8568 mm to 0.0036 mm, and the attitude error is improved from 0.9437° to 0.0105°.

Adaptive hierarchical positioning error compensation for long-term service of industrial robots based on incremental learning with fixed-length memory window and incremental model reconstruction

Industrial robots have been extensively used in industry, however, geometric errors mainly caused by connecting rod parameter error and non-geometric errors caused by deflection and friction, etc., limit its application in high-accuracy machining. Aiming at addressing these two types of errors, parametric methods for error compensation based on the kinematic model and non-parametric methods of directly establishing the mapping relationship between the actual and target poses of the robot end-effector are investigated and proposed. Currently both types of methods are mainly offline and will be no longer applicable when the pose of the end-effector in the workspace changes dramatically or the working performance of the robot degrades. Thus, to compensate the positioning error of an industrial robot during long-term operation, this research proposes an adaptive hierarchical compensation method based on fixed-length memory window incremental learning and incremental model reconstruction. Firstly, the correlation between positioning errors and robot poses is studied, a calibration sample library is created, and thus the actively evaluating mechanism of the pose mapping model is established to overcome the problem of the robot’ workspace having a differential distribution of error levels. Then, an incremental learning algorithm with fixed-length memory window and an incremental model reconstruction algorithm are designed to optimize the pose mapping model in terms of its parameters and architecture and overcome the problem that the performance degradation of the robot exacerbates the positioning error and affects the applicability of the pose mapping model, ensuring that the pose mapping model runs stably above the target accuracy level. Finally, the proposed method is applied to the long-term compensation case of a Stäubli industrial robot and a UR robot, and compared to state-of-art methods. Verification results show the proposed method reduces the position error of the Stäubli robot from 0.85mm to 0.13mm and orientation error from 0.68° to 0.07°, as well as reduces the position error of the UR robot from 2.11mm to 0.17mm, demonstrating that the proposed method works in real world scenarios and outperforms similar methods.

A New Error Compensation Method for Delta Robots Combining Geometric Error Modeling With Spatial Interpolating

Abstract Robots are playing an important role in precision manufacturing and automated inspection, which places higher demands on the positioning accuracy. The Delta robot is the most widely used parallel robot with high speed and small cumulative error. In this way, improving the positioning accuracy of the Delta robot can expand its application scenarios. According to the parameter mapping relationship, the position error can be divided into geometric error and non-geometric error. Considering the influence of the orientation errors on the actual position of the robot end, an error model to recognize the geometric error is established, and the parameter identification is performed based on an iterative approach. For the non-geometric error, the 3D annular sector grid division method and the interpolation rule are established based on the error similarity. And then, a new error compensation method for Delta robots is proposed by combining geometric error modeling with spatial interpolating. After compensation, the positioning accuracy of the Delta robot is improved significantly. The maximum absolute positioning error of the robot is reduced by 86.08% from 2.084 mm to 0.290 mm, the average absolute positioning error of the robot is reduced by 81.77% from 0.790 mm to 0.144 mm, and the error trend in the workspace is eliminated, so as to enable the expansion of Delta robot applications.

Ultrasound-guide prostate biopsy robot and calibration based on dynamic kinematic error model with POE formula

In the transrectal ultrasound-guided transperineal prostate biopsy, the application of robots can effectively reduce the interference of low-quality ultrasound images on the physician to determine the biopsy route and improve the positive detection rate. In this paper, an 8-degree-of-freedom (DOF) prostate biopsy robot for clinical is developed to realize the operation of ultrasonic probe scanning, the inserting point and target lesion point positioning, and the needle insertion. Considering the dynamic errors caused by different motions of robot joints, a dynamic product-of-exponentials (POE) based kinematic model that can reflect non-geometric errors is proposed by integrating the errors into each joint. Moreover, the parameters in the model are identified by linearizing the dynamic POE-based kinematic model. Finally, the experiment shows the maximum errors can be limited to 0.60 and 1.16 mm for inserting point and needle endpoint after compensation, and the maximum inserting angle error is limited to 1.381°. It proves the feasibility of the kinematic model proposed in this paper and indicates that the robot system can meet the requirements of clinical biopsy.

An Enhanced Positional Error Compensation Method for Rock Drilling Robots Based on LightGBM and RBFN.

Rock drilling robots are able to greatly reduce labor intensity and improve efficiency and quality in tunnel construction. However, due to the characteristics of the heavy load, large span, and multi-joints of the robot manipulator, the errors are diverse and non-linear, which pose challenges to the intelligent and high-precision control of the robot manipulator. In order to enhance the control accuracy, a hybrid positional error compensation method based on Radial Basis Function Network (RBFN) and Light Gradient Boosting Decision Tree (LightGBM) is proposed for the rock drilling robot. Firstly, the kinematics model of the robotic manipulator is established by applying MDH. Then a parallel difference algorithm is designed to modify the kinematics parameters to compensate for the geometric error. Afterward, non-geometric errors are analyzed and compensated by applying RBFN and lightGBM including features and kinematics model. Finally, the experiments of the error compensation by combing combining the geometric and non-geometric errors verify the performance of the proposed method.

A rule-based system to automatically validate IFC second-level space boundaries for building energy analysis

To facilitate BIM-to-Building Energy Modeling (BEM) geometric transformation, IFC provides a concept of second-level space boundary (SB). In the current practice, however, quality issues of second-level SBs in IFC models are often found, which makes it critical to evaluate their quality before retrieving them for energy analysis. Each second-level SB is objectified by carrying surface geometry and rich semantic data. Manually checking a large number of second-level SBs thus becomes error-prone and impracticable, while automatic and reliable approaches are still not available. This study presents an automated system to validate IFC second-level SBs with 38 rules in terms of syntactic and semantic correctness, geometric correctness, and consistency. The test results with an IFC model of a real-world building show that the system allows users to reliably evaluate the quality of second–level SBs as well as conveniently locate and visualize detected geometric and non-geometric errors.

A Robot Calibration Method Using a Neural Network Based on a Butterfly and Flower Pollination Algorithm

This article proposes a robot calibration method using an extended Kalman filter (EKF) and an artificial neural network (ANN) based on a butterfly and flower pollination algorithm (ANN-BFPA) to improve the robot’s absolute pose (position and orientation) accuracy. After establishing a geometric error model, the EKF, a robust optimization algorithm for a nonlinear system with Gaussian noise, was used to estimate geometric parameter errors and compensate for geometric errors. However, nongeometric errors caused by joint clearance, gear backlash, and link deflection could still affect the pose accuracy and interfere with the correctness of the model. Therefore, the ANN-BFPA was proposed to compensate for these errors. The ANN model was used to establish the complex relationship between joint lengths and pose error. In addition, BFPA was used to optimize weights and bias of the neural network. The efficiency of the proposed calibration method was evaluated using a Stewart platform. Experimental results demonstrated that the proposed method significantly improved the robot’s pose accuracy and showed better performance than previous techniques.

Uncertainty solution of robot parameters using fuzzy position control applied for an automotive cracked exhaust system inspection

This paper presents a new strategy for robotic manipulator inverse kinematics, which senses the final position error of the end-effector through an observational error model based on an Internet Protocol (IP) camera and calculates the joint variable errors through two fuzzy control techniques. Single Stage Fuzzy Controller (SSFC) and Three Stages Fuzzy Controller (TSFC) served as an inverse kinematic model to 3 degrees of freedom (DOF) robot manipulator. The inputs to the controller were the errors in the end-effector position Δx, Δy, Δz and the outputs of the controller were the controlled changes in the angular displacements of the joints. The fuzzy controller was utilized to compensate for geometric errors and non-geometric errors in the robot manipulator. Autodesk Inventor software was used for modeling the robot manipulator and make the transition to Simulink through the SimMechanics link for trajectory simulation. The simulation during the uncertainty of link length and end-effector load was implemented to show the proposed control model effectiveness. The gas leak test in an automotive exhaust system was applied to locate the crack position as an experimental validation of the proposed model in real-world applications.

Non-Geometric Error Compensation for Long-Stroke Cartesian Robot With Semi-Analytical Beam Deformation and Gaussian Process Regression Model

Till now, most calibration methods only compensate geometric error caused by inaccurate kinematic parameters, while the desired accuracy may still not be achieved when the robot is performing long-stroke, heavy-duty loading and unloading tasks. In this paper, a generalized semi-analytical beam deformation model is firstly proposed for the Cartesian robot to compensate the non-geometric error due to structural deformation under both distributed and concentrated loads. The adjustment factors are introduced in this model to deal with the over-constrained boundary conditions for both intermediate and side modules of the long-stroke Cartesian robot. This improves the fitness of the coming geometric error model, which assumes the beam to be rigid and straight. In addition, as the major error components which do not conform to the Gaussian distribution have been extracted in earlier steps, the Gaussian process regression model is imported to predict the residual error more accurately. In this way, comprehensive geometric and non-geometric error modeling and compensation procedures are formed for the multi-module, long-stroke Cartesian robot. Simulations and real-time experiments are conducted to validate the effectiveness of the proposed method.

Calibration Method Based on Models and Least-Squares Support Vector Regression Enhancing Robot Position Accuracy

The positioning accuracy of a robot directly affects the quality of its operations. In this study, a calibration method is proposed based on combining a model with least-squares support vector regression (LSSVR) to improve robot positioning accuracy. First, a geometric error model of the robot is established. Second, singular value decomposition (SVD) and physical model analysis method are employed to process the coupling parameters in the error model to improve the accuracy and efficiency of identification. Third, as nongeometric errors hinder the construction of an accurate and complete mathematical model and affect the residual positioning errors of the robot, LSSVR is used to compensate for the residual positioning errors caused by nongeometric errors. The proposed method thus improves the accuracy and robustness of finite sample estimation. Finally, an experiment is performed on an IRB1410 robot with a parallelogram mechanism. The maximum/mean positioning errors of the robot decrease from 2.0348/1.0978 mm to 0.1659/0.0733 mm, and the effectiveness of the proposed method is verified. The proposed method has higher prediction accuracy and stability for small samples than other methods.

Improving Robot Precision Positioning Using a Neural Network Based on Levenberg Marquardt–APSO Algorithm

This paper proposes a robot calibration method that uses an extended Kalman filter (EKF) and a neural network based on Levenberg-Marquardt combined accelerated particle swarm optimization (LMAPSO) to improve the accuracy of the robot's absolute position. After the EKF optimizes all geometric parameters, the robot position still contains non-geometric errors due to joint clearance, gear backlash, and link deflection that are impossible to model. Therefore, an artificial neural network model (ANN) is designed to compensate for these un-modeled errors. The Levenberg-Marquardt combined accelerated particle swarm optimization (LMAPSO) provides a robust optimization search algorithm to optimize the weight and bias of the neural network based on the training set. An experiment on a five-bar parallel robot shows that geometric and non-geometric calibration reduced the maximum absolute position error from (1.548 to 0.045) mm. The experimental results demonstrate the proposed calibration method's effectiveness with the robot's absolute position accuracy improving by 98%.

Intelligent Calibration of a Heavy-Duty Mechanical Arm in Coal Mine

Accurate positioning of an airborne heavy-duty mechanical arm in coal mine, such as a roof bolter, is important for the efficiency and safety of coal mining. Its positioning accuracy is affected not only by geometric errors but also by nongeometric errors such as link and joint compliance. In this paper, a novel calibration method based on error limited genetic algorithm (ELGA) and regularized extreme learning machine (RELM) is proposed to improve the positioning accuracy of a roof bolter. To achieve the improvement, the ELGA is firstly implemented to identify the geometric parameters of the roof bolter’s kinematics model. Then, the residual positioning errors caused by nongeometric facts are compensated with the regularized extreme learning machine (RELM) network. Experiments were carried out to validate the proposed calibration method. The experimental results show that the root mean square error (RMSE) and the mean absolute error (MAE) between the actual mast end position and the nominal mast end position are reduced by more than 78.23%. It also shows the maximum absolute error (MAXE) between the actual mast end position and the nominal mast end position is reduced by more than 58.72% in the three directions of Cartesian coordinate system.

An ANN-Based Precision Compensation Method for Industrial Manipulators via Optimization of Point Selection

Industrial manipulators are widely used in the manufacture of products due to their high flexibility and low costs. High absolute positioning accuracy is the key to guarantee the product quality, which is commonly improved through the error compensation technology. Due to the variety, complexity, and unpredictability of the error sources, the influence of the nongeometric errors on the absolute positioning accuracy of manipulators is uncertain. In result, the existing error compensation methods are difficult to obtain satisfying results, especially for manipulators with large joint flexibility that need to work in different task scenarios. In this paper, an artificial neural network- (ANN-) based precision compensation method via optimization of point selection is proposed, which deals with the kinematic errors and joint stiffness errors in different task scenarios. Firstly, the quasi-random sequence (QRS) method and the product of exponentials (POE) model are combined to identify and compensate the geometric parameters. The QRS method can select points evenly in the workspace. And the POE model can avoid the singularity problem of Denavit–Hartenberg (DH) model. Secondly, a continuous joint stiffness compensation model in the whole workspace is established through ANN. In order to get better compensation results for the current task scenario, the point selection method based on trajectory similarity is adopted to determine the training data of ANN. Finally, the experiments are conducted on a 6-DOF industrial manipulator to demonstrate the validity of the proposed method. The results show that the ANN-based method via optimization of point selection could be an effective solution for the precision compensation.

Parameter Identification and Nonparametric Calibration of the Tri-Pyramid Robot

The Tri-pyramid Robot is a 3-degree-of-freedom overconstrained parallel robot designed for the rapid flexible forming of three-dimensional thin sheets without geometry-specific dies used in conventional forming processes. In this article, a combined parametric and nonparametric calibration method for the geometric and nongeometric errors of the Tri-pyramid Robot is presented. The geometry-based inverse and forward kinematic equations are derived. With the actuator values and the relative end-effector positions measured through experiments, the real structural parameters are identified using the nonlinear least-squares method. A neural network is trained to further calibrate the position- and direction-dependent nongeometric errors, such as backlash and link deformations. Combining the end-effector position calculated from the kinematic model and the nongeometric errors predicted with the trained neural network, the end-effector positions can be predicted. The validation experiments show that the accuracy of the robot can be improved by 60% with the proposed method.

A multilevel index optimization method for fast kinematic calibration configuration of serial manipulators based on Compute Unified Device Architecture parallel computing

The kinematic calibration accuracy of serial manipulators is affected by the error expression ability of the selected measurement configurations and non-geometric errors such as joint disturbance, measurement noise, etc. Based on the observability of configurations, deviation of identifiable parameters, and calibration robustness, this paper proposes a multilevel evaluation criterion for measurement configuration optimization. In addition, based on the Compute Unified Device Architecture (CUDA) parallel computing technique, the most time-consuming Jacobian matrix calculation program in the algorithm is modified, and an efficient optimization algorithm for measurement configurations is established, to guarantee the feasibility of the evaluation criterion. Combined with CUDA algorithm, fast calibration is implemented with fewer measurement points and relatively higher accuracy, by means of multilevel optimization. The results illustrate the effectiveness and the universality of the proposed multilevel evaluation criterion. The criterion can be applied in calibration experiments of multi-degree of freedom (DOF) serial manipulators with complex structures.

Improvement of Heavy Load Robot Positioning Accuracy by Combining a Model-Based Identification for Geometric Parameters and an Optimized Neural Network for the Compensation of Nongeometric Errors

The positioning accuracy of a robot is of great significance in advanced robotic manufacturing systems. This paper proposes a novel calibration method for improving robot positioning accuracy. First of all, geometric parameters are identified on the basis of the product of exponentials (POE) formula. The errors of the reduction ratio and the coupling ratio are identified at the same time. Then, joint stiffness identification is carried out by adding a load to the end-effector. Finally, residual errors caused by nongeometric parameters are compensated by a multilayer perceptron neural network (MLPNN) based on beetle swarm optimization algorithm. The calibration is implemented on a SIASUN SR210D robot manipulator. Results show that the proposed method possesses better performance in terms of faster convergence and higher precision.

Robot Manipulator Calibration Using a Model Based Identification Technique and a Neural Network With the Teaching Learning-Based Optimization

This paper proposes a new calibration method for enhancing robot positional accuracy of the industrial manipulators. By combining the joint deflection model with the conventional kinematic model of a manipulator, the geometric errors and joint deflection errors can be considered together to increase its positional accuracy. Then, a neural network is designed to additionally compensate the unmodeled errors, specially, non-geometric errors. The teaching-learning-based optimization method is employed to optimize weights and bias of the neural network. In order to demonstrate the effectiveness of the proposed method, real experimental studies are carried out on HH 800 manipulator. The enhanced position accuracy of the manipulator after the calibration confirms the feasibility and more positional accuracy over the other calibration methods.