Parameter Error Identification Research Articles

Error compensation for industrial robots combining kinematics characterized by conformal geometric algebra and fused observability-index-based measurement strategy

Abstract The geometric errors of industrial robots are key factors affecting positioning accuracy. A new compensation method for industrial robots is proposed based on the kinematics characterizing with Conformal Geometric Algebra (CGA) and measurement strategy with Double Ball Bar (DBB) path point optimization. Firstly, a kinematic error model for the industrial robot is established using CGA, the starting point of the CGA model is modified to simplify the modeling process and reduce computational complexity. Secondly, fused observability index is proposed and the relationship between the number of sampling points on the DBB path and the effectiveness of error parameter is obtained. Thirdly, the adaptive golden spiral optimization algorithm for error parameter identification is proposed, achieving efficient and stable identification of error parameters. Finally, a case study is carried out on a six-degree-of-freedom industrial robot. The validity of measurement strategy and error parameter identification algorithm are confirmed by comparing the residuals and uncertainties of predicted point positions in space with different methods. The spatial compensation results show that, after compensation, the average error and root mean square error of measurement paths are reduced by 36.76% and 33.96%, respectively.

Online optimal tracking control of unknown nonlinear singularly perturbed systems using single network adaptive critic with improved learning

This study is the first time devoted to seek an online optimal tracking solution for unknown nonlinear singularly perturbed systems based on single network adaptive critic (SNAC) design. Firstly, a novel identifier with more efficient parametric multi-time scales differential neural network (PMTSDNN) is developed to obtain the unknown system dynamics. Then, based on the identification results, the online optimal tracking controller consists of an adaptive steady control term and an optimal feedback control term is developed by using SNAC to solve the Hamilton–Jacobi–Bellman (HJB) equation online. New learning law considering filtered parameter identification error is developed for the PMTSDNN identifier and the SNAC, which can realize online synchronous learning and fast convergence. The Lyapunov approach is synthesized to ensure the convergence characteristics of the overall closed loop system consisting of the PMTSDNN identifier, the SNAC and the optimal tracking control policy. Three examples are provided to illustrate the effectiveness of the investigated method.

Pose Selection Based on a Hybrid Observation Index for Robotic Accuracy Improvement

The problem of the insufficient accuracy performance of industrial robots in high-precision manufacturing is addressed in this paper. Firstly, a kinematic error model based on an M-DH model was presented. Secondly, a hybrid observability index O6 was proposed to select the optimal poses for parameter identification. O6 is the combination of O1 and O3. The optimal poses were obtained by using the IOOPS algorithm. Thirdly, the fitness function for parameter identification was established, and the Levenberg–Marquardt (LM) algorithm was applied for the accurate identification of kinematic parameter errors. Finally, several experiments were conducted to evaluate the performance of the proposed hybrid observability index O6. The average position error and average attitude error of Staubli TX60 robot were reduced by 89% and 49%. The results show that the proposed hybrid observability index O6 has great stability and effectiveness for robot calibration.

Control Strategy of Flywheel Energy Storage System for Improved Model Reference Adaptive System Based on Tent-Sparrow Search Algorithm

This study addresses speed sensor aging and electrical parameter variations caused by prolonged operation and environmental factors in flywheel energy storage systems (FESSs). A model reference adaptive system (MRAS) flywheel speed observer with parameter identification capabilities is proposed to replace traditional speed sensors. The proposed method uses reference and adjustable models to identify the stator resistance and permanent magnet flux (PM Flux) to mitigate the adverse effects of electrical parameter changes on control performance. The Tent chaotic mapping-improved Sparrow Search Algorithm (SSA) optimizes the Proportional-Integral (PI) controller parameters for the dual closed-loop and MRAS speed adaptation laws of the flywheel motor. Moreover, a self-switching parameter identification (SSPI) scheme, which constructs a cost function based on the current, parameter identification, and speed errors, is proposed to prevent inaccuracies in parameter identification. The MRAS observer selects the appropriate PI adaptive mechanism based on the error values, thereby enhancing identification accuracy. Simulink simulations show significant improvements in the rapidity and accuracy of the Tent-SSA optimized MRAS flywheel speed observer, enhancing the stability and robustness of the flywheel rotor. Experimental validation on a constructed FESS platform confirms the feasibility of this method.

A novel method to enhance the accuracy of parameter identification in elasto-geometrical calibration for industrial robots

Elasto-geometrical calibration is crucial for enhancing the absolute accuracy of robots in machining operations through the identification and compensation of parameter errors. However, the presence of inconsistent measurement units and improper selection of measuring poses can result in the ill-conditioned identification matrix (ICIM) issue, consequently impacting the accuracy of parameter identification. This paper introduces a novel method to tackle this challenge. Initially, an elasto-geometrical error model is developed based on the orientation-independent measurements (OIM), efficiently reducing the impact of mismatched positions and orientations on the ICIM problem. Subsequently, a PSO-SFFS algorithm is proposed to optimize the measurement configurations and minimize the influence of measurement noise. Furthermore, the incorporation of screw theory and the consideration of parallelogram mechanisms enhance the precision and comprehensiveness of the error model. Subsequent to the development of the error model, calibration comparison experiments are conducted on an industrial robot. Both simulation and experimental results validate the effectiveness of the proposed method in improving parameter identification accuracy.

A robust finite–time model reference adaptive controller for arbitrary order disturbed LTI systems

This manuscript deals with the trajectory-tracking problem for linear time-invariant systems with parameter uncertainties and time-dependent external perturbations. A robust finite-time model reference adaptive controller is proposed. In the absence of external perturbations, the proposed controller ensures finite-time convergence to zero of the tracking and parameter identification errors. In presence of time-dependent external perturbations, the tracking and parameter identification errors converge to a region around the origin in a finite time. The convergence proofs are developed based on Lyapunov and input-to-state stability theory. Finally, simulation results in an academic example and a flexible-joint robot manipulator show the feasibility of the proposed approach.

Adaptive parameter estimation for the expanded sandwich model

An expanded-sandwich system is a nonlinear extended block-oriented system in which memoryless elements in conventional block-oriented systems are displaced by memory submodels. Expanded-sandwich system identification has received extensive attention in recent years due to the powerful ability of these systems to describe actual industrial systems. This study proposes a novel recursive identification algorithm for an expanded-sandwich system, in which an estimator is developed on the basis of parameter identification error data rather than the traditional prediction error output information. In this scheme, a filter is introduced to extract the available system information based on miserly structure layout, and some intermediate variables are designed using filtered vectors. According to the developed intermediate variables, the parameter identification error data can be obtained. Thereafter, an adaptive estimator is established by integrating the identification error data compared with the classic adaptive estimator based on the prediction error output information. Thus, the design framework introduced in this research provides a new perspective for the design of identification algorithms. Under a general continuous excitation condition, the parameter estimation values can converge to the true values. Finally, experimental results and illustrative examples indicate the availability and usefulness of the proposed method.

Online Parameter Identification for Lithium-Ion Batteries: An Adaptive Moving Window Size Design Methodology for Least Square Fitting

Online state-of-charge estimations are critical to lithium-ion batteries in electric vehicles for safe and reliable operations. To ensure accurate online state estimations, an online battery parameter identification algorithm, such as the least square fitting approach, along with a shifting moving window, was developed and implemented, while the decision of the moving window size for general purpose is a technical issue not yet been well-addressed. This paper proposes an adaptive moving window size design methodology that adjusts the moving window size considering three important factors: load profile, state-of-charge to open-circuit voltage profile, and condition of data. The simulation results show that the proposed methodology helps to identify the parameters of the battery electric circuit model with high accuracy, where the results are compatible to the results using fine-tuned fixed window sizes. Also, the proposed methodology is general to driving profiles from moderate to severe without extra algorithm redesign. In the three standard driving profile cases, the parameter identification error is reduced by 59.15%, 69.02%, and 75.14%, respectively, compared to the worst case in experiments, which are compatible with the results after fine-tuning the fixed window sizes. With accurately identified parameters, the modeling error is minimized, and three typical linear SOC estimation algorithms thus render accurate SOC estimation, rendering an average of 13.4%, 64.43% 57.48% reduction from the worst case in experiments, respectively.

Identification of the periodontal ligament material parameters using response surface method

The orthodontic treatment can be guided by the finite element (FE) simulation of periodontal ligament (PDL) mechanical properties, and the biomimetic degree of FE simulation can be primarily affected by the material properties of the PDL. According to the principle of parameter inverse, a method: response surface (RS) method and FE inverse method were proposed to identify the material parameters of PDL. The Prony series viscoelastic FE model was established based on the relaxation experiment. With root mean square error of simulation results and experimental results as the objective function, the optimal parameter combination was obtained by RS method, and the FE simulation result were compared with the experimental result. The result showed that the optimal parameters of the PDL were elastic modulus: 3.791 MPa, Poisson's ratio: 0.42, temperature: 29.294°C separately, and the simulation result of optimal combination maintained consistency with experiment with the correlation coefficient of 0.97258, indicating that the method proposed in this paper could well identify of PDL material parameters. The parameter identification method used in this paper can significantly improve the calculation efficiency, and reduce the parameter identification error compared with the simple FE inverse method, which has scientific significance and theoretical value.

Filtering‐based concurrent learning adaptive attitude tracking control of rigid spacecraft with inertia parameter identification

SummaryThis paper investigates the attitude tracking control problem of rigid spacecraft with inertia parameter identification. Based on the relative attitude and angular velocity error dynamics, a basic adaptive backstepping based attitude tracking control scheme is firstly designed such that asymptotic attitude tracking can be achieved. However, the parameter identification error cannot decay to zero if the persistent excitation (PE) condition is not satisfied. To solve this issue, a filtering‐based concurrent learning adaptive backstepping control scheme is then proposed, by incorporating torque filtering technique with concurrent learning technique. A more mild rank condition, which consists of some collectable historical data, is provided to guarantee the convergence of parameter identification error. In addition, a valid data collection algorithm is given. It should be mentioned that a distinctive feature of the proposed filtering‐based concurrent learning adaptive control scheme is that the convergence rate of attitude tracking errors can be improved from asymptotical to exponential. Finally, simulation results are provided to illustrate the effectiveness of the proposed control schemes.

Elasto-geometrical calibration of a hybrid mobile robot considering gravity deformation and stiffness parameter errors

• An elasto-geometrical calibration method taking into account structural and stiffness parameter errors is proposed for a hybrid mobile robot. • A compensation strategy comprehensively considering the pose errors of the 3-RCU parallel module and 2-DoF robotic arm is put forward to improve the accuracy of the robot. • Calibration experiments based on three different models are conducted and the accuracy of the robot before and after calibration is tested to show the validity of the proposed method. Hybrid mobile robots, which combine the advantages of serial and parallel robots and have the ability to realize processing in situ , have considerable application potential in the field of processing and manufacturing. In this paper, a hybrid mobile robot used for wind turbine blade polishing is presented. The robot combines an automated guided vehicle, a 2-DoF robotic arm, and a 3-RCU parallel module. To improve the accuracy, investigating the elasto-geometrical calibration of the robot is necessary. Considering that the 3-RCU parallel module has weak stiffness along the gravitational direction, the stiffness model was established to estimate the deformation caused by the gravity of the mobile platform, ball screws, and motors. Subsequently, a rigid-flexible coupling error model considering structural and stiffness parameter errors is established. Based on these, a parameter identification method for the simultaneous identification of structural and stiffness parameter errors is proposed herein. For the 2-DoF robotic arm with parallelogram mechanisms, an intuitive error model considering the posture error caused by the parallelogram mechanism errors is established. The regularized nonlinear least squares method was adopted for parameter identification. Thereafter, a compensation strategy for the hybrid mobile robot that comprehensively considers the pose errors of the 3-RCU parallel module and 2-DoF robotic arm is proposed. Finally, a verification experiment was performed on the prototype, and the results indicated that after elasto-geometrical calibration, the maximum/mean of the position and posture errors of the hybrid mobile robot decreased from 3.738 mm/2.573 mm to 0.109 mm/0.063 mm and 0.236°/0.179° to 0.030°/0.013°, respectively. Owing to the decrease in the robot pose errors, the quality of the polished surface was more uniform. The range and standard deviation of roughness distribution of the polished surface were reduced from 0.595 μm and 0.248 μm to 0.397 μm and 0.127 μm. The methods proposed herein have reference significance for elasto-geometrical calibration of other parallel or hybrid robots.

An Online Condition-Based Parameter Identification Switching Algorithm for Lithium-Ion Batteries in Electric Vehicles

Safely and reliably managing the lithium-ion batteries in electric vehicles for daily operations relies on accurate state-of-charge estimation. To pursue accurate state-of-charge estimation, battery electric circuit model-based algorithms demand minimized modeling error from accurate parameter identifications. Typical online parameter identification algorithms: least square fitting approach and recursive least square fitting are commonly adopted but have their limitations and issues with continuously providing accurate identification results. To overcome their problems and utilize their strengths, this paper proposes a condition-based parameter identification switching algorithm. The proposed algorithm accurately and robustly identifies the lithium-ion batteries' parameters based on the battery data condition and the adoption of Bollinger bands. By minimizing the modeling error, the accuracy of the state-of-charge estimation is thus improved. The electric vehicle simulation results indicate that the proposed algorithm can improve the parameter identification accuracy by an average of 70.80% and 44.95% reduction in the mean absolute parameter identification error, compared to typical least square fitting and recursive least square fitting approaches. With the help of the minimized modeling error, the state-of-charge estimation accuracy can thus be improved, rendering an average of 62.44% and 21.49% improvement.

Optimization and application of parameter identification error algorithm for steam turbine governing system

The parameter identification of the steam turbine speed governing system needs to be realized by the fitting of the measured response curve of the steam turbine active power. The national standard puts forward strict requirements on the error of the identification result. At present, error calculation is often realized by manual punctuation, which is a complicated process and greatly influenced by human judgment. Hence it needs to be improved urgently. In this paper, polynomial fitting and improved sliding window method are used to optimize the error identification algorithm of the steam turbine active power response curve. The visualization of the program is realized based on the Python language. The algorithm improves the data processing efficiency and reduces the influence of human judgment. The calculation results meet the standard requirements.

A New Adaptive Controller for Linear Systems: A Model Reference Approach

In this paper, a finite-time model reference adaptive controller is proposed to solve the tracking problem for a class of linear time-invariant systems with parameter uncertainties. The convergence to zero in a finite time for the tracking and parameter identification errors is ensured. The convergence proofs are developed based on Lyapunov function approach. Finally, some simulation results show the feasibility of the proposed approach.

Adaptive Observer for Regression Models with External Time–Dependent Disturbances

In this paper, a robust adaptive observer is proposed for dynamical disturbed regression models. For the constant unknown parameters case, the proposed algorithm ensures asymptotic convergence to zero of the parameter identification error in presence of time-dependent external disturbances. For the case of the time-varying parameters, the parameter identification error converges asymptotically to an arbitrarily small region around the origin in presence of time-dependent external disturbances. The synthesis of the adaptive observer is based on the solution of a linear matrix inequality. Numerical simulations illustrate the convergence properties of the proposed algorithm.

Finite-time composite learning control for trajectory tracking of dynamic positioning vessels

This paper studies the trajectory tracking control method for dynamic positioning vessels with state constraints and parameter uncertainties. A composite learning method is introduced to identify unknown parameters online. Regressor filtering together with dynamic regressor extension and mixing procedure are combined not only to relax the dependence of parameter estimation convergence process on the persistent excitation condition, but also to ensure the independence and flexibility of each parameter. Subsequently, a finite-time composite learning controller is designed based on asymmetric integral barrier Lyapunov functions, which guarantees the asymmetric constraints on vessel states. Furthermore, Lyapunov stability shows that the parameter identification and tracking errors can converge to zero in finite-time. Finally, tracking control task for dynamic positioning systems is carried out to illustrate the merits of the proposed method.

Multi-area parameter error identification for large power systems

Power grid model parameters may contain errors due to various reasons. Detecting and correcting parameter errors typically requires significant computational effort due to the size and complexity of the parameter database. While the normalized Lagrange multiplier (NLM) method can effectively detect, identify and correct parameter errors, its computational burden could rapidly grow with increasing system size. This paper addresses this issue by proposing a multi-area parameter error identification method. Each area has its own outlier detection tool for detecting the incorrect parameters and measurements within the area. On the other hand, due to the reduced redundancy at area boundaries, parameter errors on branches incident to boundary buses may not be detected. Such errors are subsequently detected by a coordination level estimator completing the system-wide parameter detection procedure. Performance of the developed method is demonstrated using the IEEE 118-bus and 2000-bus Texas synthetic systems.

Kinematic modeling and error parameter identification of automated fiber placement machine based on measured data

This paper presents a novel kinematic modeling and error parameter identification method for a six-axis gantry automated fiber placement (AFP) machine. Multi-body system theory is used to model the kinematics of the AFP machine, and then use the homogeneous transformation matrix to represent the transfer relationship of the coordinate system. Based on 54 geometric errors of the AFP machine, a volumetric error transfer model is established. To eliminate the training bias caused by sampling randomness, 10-fold cross-validation combined with the Levenberg–Marquardt method is used to train the kinematic model of the AFP machine. Based on the coordinates of random points in space measured by a laser tracker, all the position-dependent geometric errors and position-independent geometric errors of the linear and rotary axes can be identified simultaneously. After the error parameters are identified, the average error of the random points in the X-direction is reduced from 0.72 to 0.08 mm, a drop of 88.9%. Corresponding experiments are carried out on the body diagonals and the winglet placement path. The experimental results show that the volumetric error transfer model and error parameter identification method proposed in the article can accurately predict the volumetric errors of the AFP machine, and can also meet the requirements of the AFP machine placement accuracy.

Simultaneous Identification and Correction of Multiple Network Parameter Errors by Mixed-Effects Models

Accurate parameter values are essential for the secure and stable operation of power systems. Parameters may be erroneous in real power systems, while existing methods may provide false results in the case of multiple interacting parameter errors. This paper proposes an LME-HTI method for the simultaneous identification of multiple parameter errors based on a linear mixed-effects (LME) model and hypothesis testing identification (HTI). The residual equations from multiple-snapshot state estimation are used to formulate the LME model in which the parameter errors are considered as the fixed effects and the measurement errors are considered as the random effects. By solving the LME model, all the parameter errors and the variances of the measurement errors can be simultaneously estimated. Then, hypothesis testing is performed to infer whether each parameter error is zero. An extended state augmentation (ESA) method is proposed to further remove the misidentified but correct parameters from the suspicious parameter set while correcting the left erroneous parameters by constrained nonlinear optimization. In this way, only a limited number of parameters with strong evid

Kinematic Calibration of Parallel Robots Based on L-Infinity Parameter Estimation

Pose accuracy is one of the most important problems in the application of parallel robots. In order to adhere to strict pose error bounds, a new kinematic calibration method is proposed, which includes a new pose error model with 60 error parameters and a different kinematic parameter error identification algorithm based on L-infinity parameter estimation. Parameter errors are identified by using linear programming to minimize the maximum difference between predictions and workspace measurements. Simulation results show that the proposed kinematic calibration has better kinematic parameter error estimation and fewer pose errors when measurement noise is less than kinematic parameter errors. Experimental results show that maximum position and orientation errors, respectively, based on the proposed method are decreased by 86.48% and 87.85% of the original values and by 14.32% and 18.23% of those based on the conventional least squares method. The feasibility and validity of the proposed kinematic calibration are verified by improved pose accuracy of the parallel robot.