Feedrate planning for machining with industrial six-axis robots

The authors want to thank Stäubli for providing the necessary information of the controller, Dynalog for its contribution to the experimental validations and X. Helle for its material contributions.Nowadays, the adaptation of industrial robots to carry out high-speed machining operations is strongly required by the manufacturing industry. This new technology machining process demands the improvement of the overall performances of robots to achieve an accuracy level close to that realized by machine-tools. This paper presents a method of trajectory planning adapted for continuous machining by robot. The methodology used is based on a parametric interpolation of the geometry in the operational space. FIR filters properties are exploited to generate the tool feedrate with limited jerk. This planning method is validated experimentally on an industrial robot

Modeling and replicating statistical topology, and evidence for CMB non-homogeneity

Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this challenge is `TDA', or `Topological Data Analysis', one of the primary aims of which is providing non-metric, but topologically informative, pre-analyses of data sets which make later, more quantitative analyses feasible. While TDA rests on strong mathematical foundations from Topology, in applications it has faced challenges due to an inability to handle issues of statistical reliability and robustness and, most importantly, in an inability to make scientific claims with verifiable levels of statistical confidence. We propose a methodology for the parametric representation, estimation, and replication of persistence diagrams, the main diagnostic tool of TDA. The power of the methodology lies in the fact that even if only one persistence diagram is available for analysis -- the typical case for big data applications -- replications can be generated to allow for conventional statistical hypothesis testing. The methodology is conceptually simple and computationally practical, and provides a broadly effective statistical procedure for persistence diagram TDA analysis. We demonstrate the basic ideas on a toy example, and the power of the approach in a novel and revealing analysis of CMB non-homogeneity

Cluster Lenses

Clusters of galaxies are the most recently assembled, massive, bound structures in the Universe. As predicted by General Relativity, given their masses, clusters strongly deform space-time in their vicinity. Clusters act as some of the most powerful gravitational lenses in the Universe. Light rays traversing through clusters from distant sources are hence deflected, and the resulting images of these distant objects therefore appear distorted and magnified. Lensing by clusters occurs in two regimes, each with unique observational signatures. The strong lensing regime is characterized by effects readily seen by eye, namely, the production of giant arcs, multiple-images, and arclets. The weak lensing regime is characterized by small deformations in the shapes of background galaxies only detectable statistically. Cluster lenses have been exploited successfully to address several important current questions in cosmology: (i) the study of the lens(es) - understanding cluster mass distributions and issues pertaining to cluster formation and evolution, as well as constraining the nature of dark matter; (ii) the study of the lensed objects - probing the properties of the background lensed galaxy population - which is statistically at higher redshifts and of lower intrinsic luminosity thus enabling the probing of galaxy formation at the earliest times right up to the Dark Ages; and (iii) the study of the geometry of the Universe - as the strength of lensing depends on the ratios of angular diameter distances between the lens, source and observer, lens deflections are sensitive to the value of cosmological parameters and offer a powerful geometric tool to probe Dark Energy. In this review, we present the basics of cluster lensing and provide a current status report of the field.Comment: About 120 pages - Published in Open Access at: http://www.springerlink.com/content/j183018170485723/ . arXiv admin note: text overlap with arXiv:astro-ph/0504478 and arXiv:1003.3674 by other author

Hubble Space Telescope Combined Strong and Weak Lensing Analysis of the CLASH Sample: Mass and Magnification Models and Systematic Uncertainties

We present results from a comprehensive lensing analysis in HST data, of the complete CLASH cluster sample. We identify new multiple-images previously undiscovered allowing improved or first constraints on the cluster inner mass distributions and profiles. We combine these strong-lensing constraints with weak-lensing shape measurements within the HST FOV to jointly constrain the mass distributions. The analysis is performed in two different common parameterizations (one adopts light-traces-mass for both galaxies and dark matter while the other adopts an analytical, elliptical NFW form for the dark matter), to provide a better assessment of the underlying systematics - which is most important for deep, cluster-lensing surveys, especially when studying magnified high-redshift objects. We find that the typical (median), relative systematic differences throughout the central FOV are $\sim40\%$ in the (dimensionless) mass density, $\kappa$, and $\sim20\%$ in the magnification, $\mu$. We show maps of these differences for each cluster, as well as the mass distributions, critical curves, and 2D integrated mass profiles. For the Einstein radii ($z_{s}=2$) we find that all typically agree within $10\%$ between the two models, and Einstein masses agree, typically, within $\sim15\%$. At larger radii, the total projected, 2D integrated mass profiles of the two models, within r\sim2\arcmin, differ by $\sim30\%$. Stacking the surface-density profiles of the sample from the two methods together, we obtain an average slope of $d\log (\Sigma)/d\log(r)\sim-0.64\pm0.1$, in the radial range [5,350] kpc. Lastly, we also characterize the behavior of the average magnification, surface density, and shear differences between the two models, as a function of both the radius from the center, and the best-fit values of these quantities.Comment: 35 pages (20 main text pages, plus 15 pages for additional figures and tables); 2 Tables, 17 Figures. V3: accepted version; some minor corrections and additions made. V4: corrected several entries in Table 2. All mass models and magnification maps are made publicly available for the communit

Index to NASA Tech Briefs, 1975

This index contains abstracts and four indexes--subject, personal author, originating Center, and Tech Brief number--for 1975 Tech Briefs

The Sloan Lens ACS Survey. VI: Discovery and analysis of a double Einstein ring

We report the discovery of two concentric Einstein rings around the gravitational lens SDSSJ0946+1006, as part of the Sloan Lens ACS Survey. The main lens is at redshift zl=0.222, while the inner ring (1) is at zs1=0.609 and Einstein radius $Re_1=1.43\pm0.01"$. The wider image separation ($Re_2=2.07\pm 0.02"$) of the outer ring (2) implies that it is at higher redshift. Its detection in the F814W filter implies zs2<6.9. The configuration can be well described by a total density profile $\rho_{tot} ~ r^-g'$ with $g'=2.00\pm0.03$ and velocity dispersion \sigma_{SIE}=287\pm5\kms. [...] We consider whether this configuration can be used to constrain cosmological parameters exploiting angular distance ratios entering the lens equations. Constraints for SDSSJ0946+1006, are uninteresting due to the sub-optimal lens and source redshifts. We then consider the perturbing effect of the mass associated with Ring 1 building a double lens plane compound lens model. This introduces minor changes to the mass of the main lens and allows to estimate the mass of Ring 1 (\sigma_{SIE,s1}=94\pm30\kms). We examine the prospects of doing cosmography with a sample of 50 double lenses, expected from future space based surveys such as DUNE or JDEM. Taking full account of the model uncertainties, such a sample could be used to measure $\Omega_m$ and $w$ with 10% accuracy, for a flat cosmology

Weak lensing analysis of MS 1008-1224 with the VLT

We present a gravitational lensing analysis of the cluster of galaxies MS 1008-1224 (z=0.30), based on very deep observations obtained using the VLT with FORS and ISAAC during the science verification phase. We reconstructed the projected mass distribution from B,V,R,I bands using two different methods independently. The mass maps are remarkably similar, which confirm that the PSF correction worked well. The ISAAC and FORS data were combined to measure the photometric redshifts and constrain the redshift distribution of the lensed sources. The total mass inferred from weak shear is 2.3 10^{14} h^{-1} Mo on large scales, in agreement with the X-ray mass. The measured mass profile is well fit by both Navarro, Frenk and White and isothermal sphere with core radius models although the NFW is slightly better. In the inner regions, the lensing mass is about 2 times higher than the X-ray mass, which supports the view that complex physical processes in the innermost parts of clusters are responsible for the X-ray/lensing mass discrepancy. The central part of the cluster is composed of two mass peaks whose the center of mass is 15 arcsecond north of the cD galaxy. This provides an explanation for the 15 arcsecond offset between the cD and the center of the X-ray map reported elsewhere. The optical, X-ray and the mass distributions show that MS 1008-1224 is composed of many subsystems which are probably undergoing a merger. MS 1008-1224 shows a remarkable case of cluster-cluster lensing. The photometric redshifts show an excess of galaxies located 30 arcseconds south-west of the cD galaxy at a redshift of about 0.9 which is lensed by MS 1008-1224. These results show the importance of getting BVRIJK images silmultenously. The VLT is a unique tool to provide such datasets.Comment: 22 pages, submitted to A&A, paper with `big' figures available at ftp://ftp.cita.utoronto.ca/pub/waerbeke/ms1008paper