Included here are figures and relevant data for the work "Estimating Uncertainty in Robot Kinematics and Pose Measurements with Expectation-Maximization". We present a method to validate the measurement uncertainty of a metrology instrument without a priori estimates in the context of a kinematic calibration using Expectation-Maximization methods and extend our results to characterize post-calibration pose uncertainty for the manipulator throughout a workspace. This technique permits the robot kinematic model to be fitted simultaneously with a parameterized uncertainty model derived from direct-drive laser tracker kinematics. We demonstrate the performance of this algorithm in a simulated and experimental setting, achieving 6.4um position and 70.8 urad rotation error for kinematic calibration and statistically validating the fitted uncertainty model for points throughout the calibrated workspace.

This article presented a discussion on uncertainty representation and management for model-based prog- nostics methodologies based on the Bayesian tracking framework and specifically for a Kalman filter appli- cation to electronics components. In particular, it explores the implication of modeling remaining useful life prediction as a stochastic process and how it relates to remaining useful life computation by statistical models, to uncertainty representation and management, and to the role of prognostics in decision-making. A discussion on how uncertainty propagates from the health state estimation process through the health state forecasting process is provided. Remaining useful life computation steps under uncertainty are pre- sented and analytical results on uncertainty quantification are provided under a simplified scenario. A proper propagation of uncertainty through the RUL prediction step as well as its correct interpretation are key to developing decision-making methodologies that make use of the remaining useful life prediction estimates and their corresponding uncertainties in order to make actionable choices that will optimize reliability, operations or safety in view of the prognostics information.

This software is a Python module for estimating uncertainty in predictions of machine learning models. It is a Python package that calculates uncertainties in machine learning models using bootstrapping and residual bootstrapping. It is intended to interface with scikit-learn but any Python package that uses a similar interface should work.

A method and system to provide improved accuracies in multi jointed robots through kinematic robot model parameters determination are disclosed. The present invention calibrates multi-jointed robots by using the chain rule for differentiation in the Jacobian derivation for variations in calculated poses of reference points of a reference object as a function of variations in robot model parameters. The present invention also uses two such reference objects and the known distance therebetween to establish a length scale, thus avoiding the need to know one link length of the robot. In addition, the present invention makes use of iterative methods to find the optimum solution for improved accuracy of the resultant model parameters. Furthermore, the present invention provides for determination of the end joint parameters of the robot, including parameters defining the tool attachment mechanism frame, which allows for interchange of tools without subsequent calibration.

Uncertainty Representation and Management (URM) are an integral part of the prognostic system development.1As capabilities of prediction algorithms evolve, research in developing newer and more competent methods for URM is gaining momentum.2Beyond initial concepts, more sophisticated prediction distributions are obtained that are not limited to assumptions of Normality and unimodal characteristics. Most prediction algorithms yield non-parametric distributions that are then approximated as known ones for analytical simplicity, especially for performance assessment methods. Although applying the prognostic metrics introduced earlier with their simple definitions has proven useful, a lot of information about the distributions gets thrown away. In this paper, several techniques have been suggested for incorporating information available from Remaining Useful Life (RUL) distributions, while applying the prognostic performance metrics. These approaches offer a convenient and intuitive visualization of algorithm performance with respect to metrics like prediction horizon and α-λ performance, and also quantify the corresponding performance while incorporating the uncertainty information. A variety of options have been shortlisted that could be employed depending on whether the distributions can be approximated to some known form or cannot be parameterized. This paper presents a qualitative analysis on how and when these techniques should be used along with a quantitative comparison on a real application scenario. A particle filter based prognostic framework has been chosen as the candidate algorithm on which to evaluate the performance metrics due to its unique advantages in uncertainty management and flexibility in accommodating non-linear models and non-Gaussian noise. We investigate how performance estimates get affected by choosing different options of integrating the uncertainty estimates. This allows us to identify the advantages and limitations of these techniques and their applicability towards a standardized performance evaluation method.

The dataset contains both the robot's high-level tool center position (TCP) health data and controller-level components' information (i.e., joint positions, velocities, currents, temperatures, currents). The datasets can be used by users (e.g., software developers, data scientists) who work on robot health management (including accuracy) but have limited or no access to robots that can capture real data. The datasets can support the: - Development of robot health monitoring algorithms and tools - Research of technologies and tools to support robot monitoring, diagnostics, prognostics, and health management (collectively called PHM) - Validation and verification of the industrial PHM implementation. For example, the verification of a robot's TCP accuracy after the work cell has been reconfigured, or whenever a manufacturer wants to determine if the robot arm has experienced a degradation. For data collection, a trajectory is programmed for the Universal Robot (UR5) approaching and stopping at randomly-selected locations in its workspace. The robot moves along this preprogrammed trajectory during different conditions of temperature, payload, and speed. The TCP (x,y,z) of the robot are measured by a 7-D measurement system developed at NIST. Differences are calculated between the measured positions from the 7-D measurement system and the nominal positions calculated by the nominal robot kinematic parameters. The results are recorded within the dataset. Controller level sensing data are also collected from each joint (direct output from the controller of the UR5), to understand the influences of position degradation from temperature, payload, and speed. Controller-level data can be used for the root cause analysis of the robot performance degradation, by providing joint positions, velocities, currents, accelerations, torques, and temperatures. For example, the cold-start temperatures of the six joints were approximately 25 degrees Celsius. After two hours of operation, the joint temperatures increased to approximately 35 degrees Celsius. Control variables are listed in the header file in the data set (UR5TestResult_header.xlsx). If you'd like to comment on this data and/or offer recommendations on future datasets, please email guixiu.qiao@nist.gov.

,These datasets were generated for calibrating robot-camera systems. In an extension, we also considered the problem of calibrating robots with more than one camera.,These datasets are provided as a companion to the paper "Solving the Robot-World Hand-Eye(s) Calibration Problem with Iterative Methods" by Amy Tabb and Khalil M. Ahmad Yousef.,Included are eight datasets in zipped files, numbered DS1.zip, DS2.zip, etc.,Explanations of the format of the datasets is provided in the README resource in the file "README_input_format.txt". Generally, each zipped folder consists of images and a text file of robot positions when those images were acquired.,Open source code can be found at: https://github.com/amy-tabb/RWHEC-Tabb-AhmadYousef,We also include the results of using our code on one of the datasets so that you can be sure that the code worked correctly. This folder is named DS1_write.zip and can be found in the resource titled "Output from running methods on Dataset 1".,Problems/Comments/Bugs should be addressed to amy.tabb@ars.usda.gov,,

The data used to generate the graphs in figures 1-9 of the paper "Evaluating Uncertainty of Microwave Calibrations from Regression Residuals".The full citation is D. F. Williams, B. F. Jamroz, J. D. Rezac and R. D. Jones, "Evaluating Uncertainty of Microwave Calibration Models With Regression Residuals," in IEEE Transactions on Microwave Theory and Techniques, vol. 68, no. 6, pp. 2454-2467, June 2020, doi: 10.1109/TMTT.2020.2983358.The files are named as follows: 1. CI_figX.plt - Contains EasyPlot V 4.0.4 file used to create the plot, columns used in each file, legend, etc. 2. FigX_FY_name - Contains TAB-delimited data file Y used to construct figure X with original file name "name". First two lines repeats key information found in EasyPlot file. First line specifies columns used in EasyPlot column-selection format. Second line contains original location.EasyPlot column-selection format is as follows: "xyiiyy" or "xy..yy" means that column 1 was used for x axis, column 2 for first curve y values, column 5 for second curve y values, column 6 for third curve y values