Comparative Study of Two Pose Measuring Systems Used to Reduce Robot Localization Error.

The performance of marker-based, six degrees of freedom (6DOF) pose measuring systems is investigated. For instruments in this class, the pose is derived from locations of a few three-dimensional (3D) points. For such configurations to be used, the rigid-body condition-which requires that the distance between any two points must be fixed, regardless of orientation and position of the configuration-must be satisfied. This report introduces metrics that gauge the deviation from the rigid-body condition. The use of these metrics is demonstrated on the problem of reducing robot localization error in assembly applications. Experiments with two different systems used to reduce the localization error of the same industrial robot yielded two conflicting outcomes. The data acquired with one system led to substantial reduction in both position and orientation error of the robot, while the data acquired with a second system led to comparable reduction in the position error only. The difference is attributed to differences between metrics used to characterize the two systems.

Design of a six-DOF motion tracking system based on a Stewart platform and ball-and-socket joints.

This paper presents a six degree-of-freedom (DOF) real-time motion tracking system of measuring the position and the orientation for industrial robots in three-dimensional (3D) space. The proposed system is based on a typical Stewart platform design and utilizes six low-cost displacement sensors to monitor the motion of the Stewart platform. The advantage of the proposed system is its simple calibration and easy accessibility; the magnetic ball-and-socket joints used for rotational joints. With special measurement tools, the center of rotation of all twelve joints can be measured in 3D space at a glance. Following more than fifty measurements, the average root mean square (RMS) position accuracy error of the proposed device is less than 0.186 mm and the average of angular accuracy error is less than 0.160 °, making it suitable for monitoring the performance of industrial robot. A commercial robot is also tested by the proposed system to verify its usefulness.

Efficiently Improving and Quantifying Robot Accuracy In Situ.

The advancement of simulation-assisted robot programming, automation of high-tolerance assembly operations, and improvement of real-world performance engender a need for positionally accurate robots. Despite tight machining tolerances, good mechanical design, and careful assembly, robotic arms typically exhibit average Cartesian positioning errors of several millimeters. Fortunately, the vast majority of this error can be removed in software by proper calibration of the so-called "zero-offsets" of a robot's joints. This research developed an automated, inexpensive, highly portable, in situ calibration method that fine tunes these kinematic parameters, thereby, improving a robot's average positioning accuracy four-fold throughout its workspace. In particular, a prospective low-cost motion capture system and a benchmark laser tracker were used as reference sensors for robot calibration. Bayesian inference produced optimized zero-offset parameters alongside their uncertainty for data from both reference sensors. Relative and absolute accuracy metrics were proposed and applied for quantifying robot positioning accuracy. Uncertainty analysis of a validated, probabilistic robot model quantified the absolute positioning accuracy throughout its entire workspace. Altogether, three measures of accuracy conclusively revealed multi-fold improvement in the positioning accuracy of the robotic arm. Bayesian inference on motion capture data yielded zero-offsets and accuracy calculations comparable to those derived from laser tracker data, ultimately proving this method's viability towards robot calibration.

Concept to Commercialization of an Artifact for Evaluating Three-Dimensional Imaging Systems per ASTM E3125-17.

The relative-range error test is one of several tests described in the ASTM E3125-2017 standard for performance evaluation of spherical coordinate three-dimensional (3D) imaging systems such as terrestrial laser scanners (TLS). We designed a new artifact, called the plate-sphere target, that allows the realization of the relative-range error tests quickly and efficiently without the need for alignment at each position of the test.Use of a simple planar/plate target requires careful alignment of the target at each position of the relative-range error test, which is labor-intensive and time-consuming. This new artifact significantly reduces the time required to perform the test, from a matter of about 2 h to less than 30 min while resulting in similar test uncertainty values.The plate-sphere target was conceived and initially developed at the National Institute of Standards and Technology (NIST), improved based on feedback from collaborators at the National Research Council (NRC) of Canada and TLS manufacturers, and commercialized by Bal-tec Inc.This new artifact will save users and manufacturers of TLSs considerable time and money.

Relative range error evaluation of terrestrial laser scanners using a plate, a sphere, and a novel dual-sphere-plate target.

Terrestrial laser scanners (TLS) are a class of 3D imaging systems that produce a 3D point cloud by measuring the range and two angles to a point. The fundamental measurement of a TLS is range. Relative range error is one component of the overall range error of TLS and its estimation is therefore an important aspect in establishing metrological traceability of measurements performed using these systems. Target geometry is an important aspect to consider when realizing the relative range tests. The recently published ASTM E2938-15 mandates the use of a plate target for the relative range tests. While a plate target may reasonably be expected to produce distortion free data even at far distances, the target itself needs careful alignment at each of the relative range test positions. In this paper, we discuss relative range experiments performed using a plate target and then address the advantages and limitations of using a sphere target. We then present a novel dual-sphere-plate target that draws from the advantages of the sphere and the plate without the associated limitations. The spheres in the dual-sphere-plate target are used simply as fiducials to identify a point on the surface of the plate that is common to both the scanner and the reference instrument, thus overcoming the need to carefully align the target.

Selection of Fiducial Locations and Performance Metrics for Point-Based Rigid-Body Registration.

A method is described to select the location and number of fiducials used in point-based, rigid-body registration of two coordinate frames. Two indices are introduced which are used to search for the optimum configuration of fiducials. They can be used to quickly evaluate a large number of configurations because no actual registration is involved in their calculation. Furthermore, configurations yielding small values of the indices correlate well with configurations which result in optimum registrations. Three registration performance metrics are discussed, and it is shown that optimization of different metrics leads to different selection of fiducial configurations. If an optimized configuration is selected as a starting configuration of N fiducials, the addition of extra fiducials does not significantly improve the registration in most cases. This work is based on 3D data acquired with three different instruments, each having different noise and bias characteristics.

Orientation Uncertainty Characteristics of Some Pose Measuring Systems.

We investigate the performance of pose measuring systems which determine an object's pose from measurement of a few fiducial markers attached to the object. Such systems use point-based, rigid body registration to get the orientation matrix. Uncertainty in the fiducials' measurement propagates to the uncertainty of the orientation matrix. This orientation uncertainty then propagates to points on the object's surface. This propagation is anisotropic, and the direction along which the uncertainty is the smallest is determined by the eigenvector associated with the largest eigenvalue of the orientation data's covariance matrix. This eigenvector in the coordinate frame defined by the fiducials remains almost fixed for any rotation of the object. However, the remaining two eigenvectors vary widely and the direction along which the propagated uncertainty is the largest cannot be determined from the object's pose. Conditions that result in such a behavior and practical consequences of it are presented.

METHODS AND CONSIDERATIONS TO DETERMINE SPHERE CENTER FROM TERRESTRIAL LASER SCANNER POINT CLOUD DATA.

The Dimensional Metrology Group (DMG) at the National Institute of Standards and Technology (NIST) is performing research to support the development of documentary standards within ASTM E57 committee. This committee is addressing the point-to-point performance evaluation of a subclass of 3D imaging systems called Terrestrial Laser Scanners (TLSs) which are laser-based and use spherical coordinate system. This paper discusses the usage of sphere targets for this effort and methods to minimize the errors due to the determination of their centers. The key contributions of this paper include the methods to segment sphere data from TLS point cloud and the study of some of the factors that influence the determination of sphere centers.

Propagation of Error from Registration Parameters to Transformed Data.

Methods to register two sets of data have existed for quite some time. However, these sets of data are rarely error-free. Consequently, any registration based on this data will be affected by the error. Moreover, if the corresponding registration matrix is then used to transform data from one coordinate system to another, any error from the registration will also get propagated to the transformed data. In this paper, we will characterize this propagation of random error, or noise, through a mathematical perspective and will illustrate its use with data obtained from physical experiments and with quasi-simulated sets of data. In addition, we will discuss the limitations of this propagation of error when systematic bias is present in the data.