Uncertainty estimation and multi sensor fusion for kinematic laser tracker measurements

This paper presents an automated calibration method for industrial robots, based on the use of (1) a novel, low-cost, wireless, 3D measuring device mounted on the robot end-effector and (2) a portable 3D ball artifact fixed with respect to the robot base. The new device, called TriCal, is essentially a fixture holding three digital indicators (plunger style), the axes of which are orthogonal and intersect at one point, considered to be the robot tool center point (TCP). The artifact contains four 1-inch datum balls, each mounted on a stem, with precisely known relative positions measured on a Coordinate Measuring Machine (CMM). The measurement procedure with the TriCal is fully automated and consists of the robot moving its end-effector in such as a way as to perfectly align its TCP with the center of each of the four datum balls, with multiple end-effector orientations. The calibration method and hardware were tested on a six-axis industrial robot (KUKA KR6 R700 sixx). The calibration model included all kinematic and joint stiffness parameters, which were identified using the least-squares method. The efficiency of the new calibration system was validated by measuring the accuracy of the robot after calibration in 500 nearly random end-effector poses using a laser tracker. The same validation was performed after the robot was calibrated using measurements from the laser tracker only. Results show that both measurement methods lead to similar accuracy improvements, with the TriCal yielding maximum position errors of 0.624 mm and mean position errors of 0.326 mm.

In this paper, a novel multilateral synthetic aperture secondary radar concept and its application for precise 3D localization of a robot tool center point (TCP) are introduced. A backscatter transponder is attached to the TCP of a robot. Spatially distributed FMCW secondary radar units pick up the backscattered phase coherent transponder signals. Based on assisting relative sensors, a synthetic aperture is created with the TCP. The developed multilateral inverse synthetic aperture reconstruction algorithm then determines a probability density function (PDF) of the spatial transponder position. By simulations and experimental results using a 5.8 GHz system with 140 MHz bandwidth it is shown, that 3D localization precision in the mm range can be achieved with the novel wireless local positioning concept even with narrowband radar systems in dense multipath environments. Heretofore, accuracies of this magnitude were only attainable with ultrawideband (UWB) systems utilizing a ten times wider bandwidth. It is shown, that the multilateral synthetic aperture locating system has the potential for a quantum leap in precise 3D wireless local positioning.

The Wide Field Phasing Testbed for the Giant Magellan Telescope1 is comprised of six pairs of off-axis parabolas, an Offner relay and several additional fold mirrors. To align this optical system we used a Leica laser tracker and a 4D interferometer. The laser tracker was used to accurately position each fold mirror on the optical bench by measuring the position of a spherically mounted retroreflector with the laser tracker, first directly and then in reflection off the mirror to be aligned. The mirror was adjusted until the reflected image was in the correct location. Key to this operation was custom software that read in the Zemax prescription file specifying the location of each optic; interfaced with the laser tracker to measure the location of fiducial SMRs on the optical bench; performed transformations between coordinate systems attached to the laser tracker, the optical bench, the Zemax model, and the individual optics; and finally displayed the real-time position errors in a large font so that the optic could be easily adjusted to the correct location. The OAPs were also positioned using the laser tracker in conjunction with the interferometer. An SMR was placed at the desired focal position of the OAP using the laser tracker. This same SMR served as the return sphere for the interferometer which was used to adjust out tilt and astigmatism errors. With this system we were able to align the full optical system efficiently and in a deterministic way.

This paper introduces an enhanced method to analytically identify an unknown tool centre point (TCP) of standard industrial robots with six degrees of freedom. The method uses a mathematical closed form to determine the position and orientation (pose) of a mounted robot tool frame in relation to the robot flange frame. This unknown pose is represented by a homogeneous transformation that is calculated by performing two robot movements. The position and orientation of the robot is measured after each movement, which leads to an equation of the form , where represents the unknown homogeneous transformation from the robot flange to the TCP. The achievable accuracy in comparison to existing methods is enhanced by using relative movements with orthogonal rotational axes. This ensures optimal error propagation for solving the resulting equation and leads to a very accurate calculation of the unknown transformation. The described method was evaluated and tested on a standard industrial robot. All measurements to determine the position and orientation of the robot tool were done with a laser tracker. A typical application example from the field of automated machining demonstrates the use of the developed method. 

This paper presents a Monte Carlo simulation of the self-calibration method for the multi laser tracker system (MLTS) which can track a retroreflector mounted on a kinematical system (e.g. positioning stage, robot manipulator etc.). Four laser trackers build up the MLTS. In the first part of the study the required algorithms enabling the MLTS to measure the position of the retroreflector are presented. The algorithms include the localization of the retroreflector, the communication between the laser trackers and the tracking controller as well as the calculation of the Tool Centre Point (TCP) position. In the second part of this study a deeper analysis of the self-calibration algorithm is carried out. A Monte Carlo simulation shows that the quality of the parameter estimation highly depends on the optimal arrangement of the MTLS.

Inertial-based motion capture (IMC) has been suggested to overcome many of the limitations of traditional motion capture systems. The validity of IMC is, however, suggested to be dependent on the methodologies used to process the raw data collected by the inertial device. The aim of this technical summary is to provide researchers and developers with a starting point from which to further develop the current IMC data processing methodologies used to estimate human spatiotemporal and kinematic measures. The main workflow pertaining to the estimation of spatiotemporal and kinematic measures was presented, and a general overview of previous methodologies used for each stage of data processing was provided. For the estimation of spatiotemporal measures, which includes stride length, stride rate, and stance/swing duration, measurement thresholding and zero-velocity update approaches were discussed as the most common methodologies used to estimate such measures. The methodologies used for the estimation of joint kinematics were found to be broad, with the combination of Kalman filtering or complimentary filtering and various sensor to segment alignment techniques including anatomical alignment, static calibration, and functional calibration methods identified as being most common. The effect of soft tissue artefacts, device placement, biomechanical modelling methods, and ferromagnetic interference within the environment, on the accuracy and validity of IMC, was also discussed. Where a range of methods have previously been used to estimate human spatiotemporal and kinematic measures, further development is required to reduce estimation errors, improve the validity of spatiotemporal and kinematic estimations, and standardize data processing practices. It is anticipated that this technical summary will reduce the time researchers and developers require to establish the fundamental methodological components of IMC prior to commencing further development of IMC methodologies, thus increasing the rate of development and utilisation of IMC.

In robotic drilling of aircraft structures, reference holes are pre-drilled on aircraft structures and then detected by vision systems in the drilling process to compensate for the relative positioning errors between the robot tool center point and the workpiece, thus achieving improved position accuracy of drilled holes. In this paper, a novel elliptic contour extraction method based on salient region detection and optimization with snakes model is proposed for reference hole detection. Firstly, salient region detection is used for segmenting the region of reference hole from the background, and the resultant image of this operation is used for contours retrieving. Secondly, the initial contour of the reference hole is obtained from the retrieved contours using the voting method. Then the initial contour of the reference hole is further refined with the snakes model through energy minimizing of the snake. Finally, the elliptical parameters of the reference hole are computed by fitting an ellipse to the evolving result of the snake. The robustness and accuracy of reference hole detection with respect to noise and environmental disturbance are enhanced significantly through saliency estimation and optimization with the snakes model. Experimental results reveal that the proposed method can be applied to detect reference holes accurately and robustly in the jamming environment of aircraft assembly.

For multi-target tracking, the IMM (interactive multiple model) algorithm has been proposed. The IMM is expected to reduce tracking errors for both nonmaneuvering and maneuvering targets. However, the IMM requires a heavy computational burden, because it utilizes multiple Kalman filters in parallel. On the other hand, the Kalman filter with a turning acceleration estimator, which can adapt a maneuvering target, has been proposed. The Kalman filter with a turning acceleration estimator is a single two-stage type filter and has a problem of setting threshold for the maneuver detector. In this paper, we propose the hybrid filter with a constant-velocity (CV) filter and a turning acceleration estimation filter. The proposed filter does not require a maneuver detector, because it integrates the outputs of two filters using the likelihood of each filter. And its computational requirement is smaller than the IMM, since it consists of only two Kalman based filters. The proposed method can prevent deteriorating tracking accuracy by reducing the risk of maneuver misdetection when a target maneuvers. We evaluate the performance of the proposed filter by computer simulation, and show the effectiveness of the proposed filter, comparing with the conventional Kalman filter and the two-stage Kalman filter.

Research on an inertial positioning system for a parallel kinematic machine

This paper examines and contrasts two estimation methods, Kalman filtering and linear smoothing, for creating interpolated data products from bathymetry measurements. Using targeted examples, we demonstrate previously obscured behavior showing the dependence of linear smoothers on the spatial arrangement of the measurements, yielding markedly different estimation results than the Kalman filter. For bathymetry data, we have modified the variance estimates from both the Kalman filter and linear smoothers to obtain comparable estimators for dense data. These comparable estimators produce uncertainty estimates that have statistically insignificant differences via hypothesis testing. Achieving comparable estimation is accomplished by applying the “propagated uncertainty” concept and a numerical realization of Tobler's principle to the measurement data prior to the computation of the estimate. We show new mathematical derivations for these modifications. In addition, we show test results with (a) synthetic data and (b) gridded bathymetry in the area of the Scripps and La Jolla Canyons. Our tenfold cross‐validation for case (b) shows that the modified equations create comparable uncertainty for both gridding algorithms with null hypothesis acceptance rates of greater than 99.95% of the data points. In contrast, bilinear interpolation has 10 times the amount of rejection. We then discuss how the uncertainty estimators are, in principle, applicable to interpolate geophysical data other than bathymetry.

<div class="htmlview paragraph">In a CAS system, the distance and relative velocity between front and host vehicles are estimated to calculate time-to-collision (TTC). The distance estimates by different methods will certainly include noise which should be removed to ensure the accuracy of TTC calculations. Kalman filter is a good tool to filter such type of noise. Nevertheless, Kalman filter is a model based filter, which means a correct model is important to get the good filtering results. Usually, a vehicle is either moving with a constant velocity (CV) or constant acceleration (CA) maneuvers. This means the distance data between front and host vehicles can be described by either constant velocity or constant acceleration model. In this paper, first, CV and CA models are used to design two Kalman filters and an interacting multiple model (IMM) is used to dynamically combine the outputs from two filters. In detail, IMM technique is used to estimate the mode probabilities for CV and CA based Kalman filters and mix the two filter results based on the mode probabilities. Then the motion equation is used to calculate the TTC based on the distance and velocity estimates obtained from the IMM based filter. The experimental results on both simulated and real estimated distance data are found to be satisfactory and indicate that the proposed algorithm does improve the signal-to-noise ratio of distance data.</div>

A method for direct evaluation of the dynamic 3D path accuracy of NC machine tools

<strong class="journal-contentHeaderColor">Abstract.</strong> The paper presents a simplification to the Kalman smoother that can be run as a post processing step using only minimal stored information from a Kalman filter analysis, which is intended for use with large model products such as reanalyses of Earth system variability. A simple decay assumption is applied to cross time error covariances and we show how the resulting equations relate formally to the fixed-lag Kalman smoother, and how they can be solved to give a smoother analysis along with an uncertainty estimate. The method is demonstrated in the Lorenz 1963 idealised system, being applied with both an extended Kalman smoother and an Ensemble Kalman smoother. In each case the root mean square errors (RMSE) against truth, for both assimilated and unassimilated (independent) data, of the new smoother analyses are substantially smaller than for the original filter analyses, while being larger than for the full smoother solution. Typically 60 % of the full smoother error reduction with respect to the filter, is achieved. The uncertainties derived for the new smoother also agree remarkably well with the actual RMSE values throughout the assimilation period. The ability to run this smoother very efficiently as a post processor should allow it to be useful for real large model reanalysis products, especially ensemble products, that are already being developed by various operational centres.

Respiration induces significant movement of tumours in the vicinity of thoracic and abdominal structures. Real-time image-guided radiotherapy (IGRT) aims to adapt radiation delivery to tumour motion during irradiation. One of the main problems for achieving this objective is the presence of time lag between the acquisition of tumour position and the radiation delivery. Such time lag causes significant beam positioning errors and affects the dose coverage. A method to solve this problem is to employ an algorithm that is able to predict future tumour positions from available tumour position measurements. This paper presents a multiple model approach to respiratory-induced tumour motion prediction using the interacting multiple model (IMM) filter. A combination of two models, constant velocity (CV) and constant acceleration (CA), is used to capture respiratory-induced tumour motion. A Kalman filter is designed for each of the local models and the IMM filter is applied to combine the predictions of these Kalman filters for obtaining the predicted tumour position. The IMM filter, likewise the Kalman filter, is a recursive algorithm that is suitable for real-time applications. In addition, this paper proposes a confidence interval (CI) criterion to evaluate the performance of tumour motion prediction algorithms for IGRT. The proposed CI criterion provides a relevant measure for the prediction performance in terms of clinical applications and can be used to specify the margin to accommodate prediction errors. The prediction performance of the IMM filter has been evaluated using 110 traces of 4-minute free-breathing motion collected from 24 lung-cancer patients. The simulation study was carried out for prediction time 0.1–0.6 s with sampling rates 3, 5 and 10 Hz. It was found that the prediction of the IMM filter was consistently better than the prediction of the Kalman filter with the CV or CA model. There was no significant difference of prediction errors for the sampling rates 5 and 10 Hz. For these sampling rates, the errors of the IMM filter for 0.4 s prediction time were less than 2.1 mm in terms of the 95% CI criterion or 1.1 mm in terms of the standard deviation (SD) or root mean squared errors (RMSE) criterion. For the prediction time of 0.6 s the errors were less than 3.6 mm in terms of the 95% CI criterion or 1.8 mm in terms of the SD/RMSE criterion. The prediction error analysis showed that the average percentage of the target lies outside the 95% CI margin was 5.2% and outside the SD/RMSE margin was 24.3%. This indicates the effectiveness of the 95% CI criterion as a margining strategy to accommodate prediction errors.

When tracking maneuvering targets with a nearly constant acceleration (NCA) Kalman filter with discrete white noise acceleration (DWNA), the selection of the process noise variance is complicated by the fact that the process noise errors are modeled as white Gaussian, while target maneuvers are deterministic or highly correlated in time. In recent years for nearly constant velocity (NCV) Kalman filters, the deterministic tracking index was introduced and used to develop a relationship between the maximum acceleration of the target and the process noise variance that minimizes the maximum mean squared error (MMSE) in position. A lower bound on the process noise variance was also expressed in terms of the maximum acceleration and deterministic tracking index. In this paper, the design methods for NCV Kalman filters with DWNA are extended to develop design methods for NCA Kalman filters with DWNA tracking maneuvering targets. The effectiveness of the design methods are illustrated via Monte Carlo simulations.