Rapid learning of humanoid body schemas with kinematic Bezier maps

Trabajo presentado al 9th IEEE-RAS celebrado en París del 7 al 10 de diciembre de 2009.This paper addresses the problem of hand-eye coordination and, more specifically, tool-eye recalibration of humanoid robots. Inspired by results from neuroscience, a novel method to learn the forward kinematics model as part of the body schema of humanoid robots is presented. By making extensive use of techniques borrowed from the field of computer-aided geometry, the proposed Kinematic Be ́zier Maps (KB-Maps) permit reducing this complex problem to a linearly-solvable, although high-dimensional, one. Therefore, in the absence of noise, an exact kinematic model is obtained. This leads to rapid learning which, unlike in other approaches, is combined with good extrapolation capabilities. These promising theoretical advantages have been validated through simulation, and the applicability of the method to real hardware has been demonstrated through experiments on the humanoid robot ARMAR-IIIa.This work was supported by projects: 'Perception, action & cognition through learning of object-action complexes.' (4915), 'Analysis and motion planning of complex robotic systems' (4802), 'Grup de recerca consolidat - Grup de Robòtica' (4810). The work described in this paper was partially conducted within the EU Cognitive Systems projects GRASP (FP7-215821) and PACO-PLUS (FP6-027657) funded by the European Commission. The authors acknowledge support from the Generalitat de Catalunya under the consolidated Robotics group, and from the Spanish Ministry of Science and Education, under the project DPI2007-60858Peer Reviewe

A unifying framework for tolerance analysis in sensing, design, and manufacturing

Journal ArticleIn this work we address the problem of tolerance representation and analysis across the domains of industrial inspection using sensed data, CAD design, and manufacturing. Instead of using geometric primitives in CAD models to define and represent tolerances, we propose the use of stronger methods that are completely based on the manufacturing knowledge for the objects to be inspected. We guide our sensing strategies based on the manufacturing process plans for the parts that are to be inspected and define, compute, and analyze the tolerances of the parts based on the uncertainty in the sensed data along the different toolpaths of the sensed part. We believe that our new approach is the best way to unify tolerances across sensing, CAD, and CAM, as it captures the manufacturing knowledge of the parts to be inspected, as opposed to just CAD geometric representations

Low level direct interpolation for parametric curves

This article presents an algorithm for the direct interpolation of parametric planar curves C(u) with a CNC machine. It expresses parametric planar curves as sequences of machine tool axes discrete movements of BLU size. Therefore, the curve C(u) is directly approximated by the pulse trains, hence eliminating one source of the machining errors

On the capture and representation of fonts

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The commercial need to capture, process and represent the shape and form of an outline has lead to the development of a number of spline routines. These use a mathematical curve format that approximates the contours of a given shape. The modelled outline lends itself to be used on, and for, a variety of purposes. These include graphic screens, laser printers and numerically controlled machines. The latter can be employed for cutting foil, metal. plastic and stone. One of the most widely used software design packages has been the lKARUS system. This, developed by URW of Hamburg (Gennany), employs a number of mathematical descriptions that facilitate the process of both modelling and representation of font characters. It uses a variety of curve formats, including Bezier cubics, general conics and parabolics. The work reported in this dissertation focuses on developing improved techniques, primarily. for the lKARUS system. This includes two algorithms which allow a Bezier cubic description, two for a general conic representation and, yet another, two for the parabolic case. In addition, a number of algorithms are presented which promote conversions between these mathematical forms; for example, Bezier cubics to a general conic form. Furthennore, algorithms are developed to assist the process of rasterising both cubic and quadratic arcs.This study was partly funded by the Science and Education Research Council (SERC)

Geostatistics without Stationarity Assumptions within Geographical Information Systems

The present work deals with two challenging problems of applied geostatistics: (i) Stationarity assumptions often do not hold under real-world conditions. (ii) Geostatistical methods have to be linked with spatial databases in order to be applicable in non-stationary situations. Solutions for both problems are proposed and implemented. (i) A central assumption in geostatistics is the stationarity of the process. However the spatial variability of many natural phenomena heavily depends on the local geology, which is nonstationary in most cases. To deal with this, the concept of process stationarity is replaced by a stationarity of the governing influence relating the local semivariogram and the local geology as stored in a Geographical Information System (GIS). A construction method is used, which can meaningfully incorporate additional spatial information from GIS, e.g. smoothly varying geology in the investigated area, spatially varying anisotropy induced by mountainous morphology, or geological faults interrupting continuity. Least-squares parameter estimation is used for fitting instationary semivariogram models in typical example situations, leading to non-linear optimization problems. Furthermore, a method for semivariogram parameter estimation in the present of linear trend is proposed. (ii) Geostatistical tools that make use of the local geology need direct access to the data stored in the GIS. A link between the presented geostatistical tools and the GIS software ArcView was established. Thus, spatial data such as measured contaminant concentrations, soil properties and morphology can be incorporated in geostatistical analyses. R code that fits instationary semivariogram models and performs kriging was implemented and can be obtained from the author. It is applied to simulated datasets.Die vorliegende Diplomarbeit befasst sich mit zwei wichtigen Problemen der angewandten Geostatistik: (i) Stationaritätsannahmen werden unter realweltlichen Bedingungen oft nicht erfüllt. (ii) Geostatistische Methoden müssen mit räumlichen Datenbanken verbunden werden, um unter nichtstationären Bedingungen anwendbar zu sein. Lösungen für beide Probleme werden vorgeschlagen und implementiert. (i) In der Geostatistik ist die Stationarität des Prozesses eine zentrale Annahme. Die räumliche Variabilität vieler Phänomene in unserer Umwelt hängt jedoch stark von lokalen geologischen Verhältnissen ab, die meist aber instationär sind. Um damit umgehen zu können, wird das Konzept der Stationarität des Prozesses ersetzt durch eine Stationarität des Einflusses der lokalen Geologie, wie sie in einem GIS gespeichert ist, auf das lokale Semivariogramm. Es wird eine Konstruktionsmethode benutzt, die auf sinnvolle Art räumliche Informationen aus dem GIS in Semivariogrammmodelle einbinden kann, etwa sich über das Untersuchungsgebiet gleichmäßig verändernde geologische Verhältnisse, sich räumlich verändernde Anisotropie im Gebirgsrelief oder geologische Störungen, die die Kontinuität unterbrechen. Kleinste-Quadrate Schätzung wird für die Anpassung instationärer Semivariogrammmodelle in typischen Beispielsituationen verwendet. Dies führt zu nichtlinearen Optimierungsproblemen. Des weiteren wird eine Methode der Schätzung von Semivariogrammparametern in Modellen mit linearem Trend vorgestellt. (ii) Geostatistische Werkzeuge, die lokalen geologischen Verh¨ältnisse berücksichtigen, benötigen einen direkten Zugang zu Daten, die in einem GIS gespeichert sind. Im Rahmen dieser Arbeit wurde eine Verbindung zwischen den vorgestellten geostatistischen Werkzeugen und dem GIS Programm ArcView erstellt. Auf diese Weise können räumliche Daten wie etwa Schadstoffkonzentrationen, Bodeneigenschaften oder die Morphologie in geostatistische Analysen einbezogen werden. R-Code, der instationäre Semivariogrammmodelle anpasst und Kriging durchführt, wurde erstellt und auf simulierte Datensätze angewandt. Der Code kann über den Author bezogen werden.researc

Automatic G1 Parametric Fitting Of Curves And Surfaces To Outlines Of Images

Rapid advancement in imaging technologies produces massive amount of data which can be harnessed for information and knowledge gathering. Mathematical representations of objects of interest from these images are amenable to manipulation of shapes and sizes, thus aiding analysis and design. As a process in reverse engineering, we aim to automatically reproduce a mathematical outline of a 2D contour based image of an object. Next we will reconstruct a 3D object (surface) from its cross-sectional images. It is our objective to have a representation which is reliable, reasonably fast and with flexible accuracy

Study and implementation in C of the Finite Element Method in dimension 2

This document explains the finite element method for solving linear partial differentialequations in one and two dimensional domains. It consists of seven chapters. Thisfirst one acts as a description of the project. The second one explains the problem tobe solved. The third chapter explains necessary concepts to understand chapters 5and 6, where the problem is solved. The fourth chapter is independent, and needs notbe read in order to understand later chapters. Finally, the seventh chapter acts as asmall conclusion, although the main results are in chapters 5 and

Nonlinear tube-fitting for the analysis of anatomical and functional structures

We are concerned with the estimation of the exterior surface and interior summaries of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT) and to a white-matter tract image produced using diffusion tensor imaging (DTI).Comment: Published in at http://dx.doi.org/10.1214/10-AOAS384 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Mapping and Navigation of Small Bodies In The Presence of Uncertainty

Missions to small bodies in the Solar System face a number of challenges as early as their inception begins, due to the lack of information that usually characterizes asteroids and comets that have never been the target of an in-situ mission or been observed from Earth in a favorable geometry. Robust mission design to these targets can only be achieved if uncertainties affecting the a-priori knowledge - or lack thereof - in the small body shapes and dynamical environments are correctly handled. Small body shape models, customarily represented as a collection of triangular facets or generalized through higher-order elements are a function of a mesh of control points effectively defining the shape. Describing this ensemble of control points as a multidimensional random variable, obeying a Gaussian distribution of known mean and covariance, enables performing linearized uncertainty quantification in the small body's inertia parameters and gravitational field, allowing valuable insight into the small body dynamical environment to be gained, at a lesser computational cost than a traditional Monte-Carlo sampling of the shape, to the benefit of mission designers and planetary scientists alike. Moving closer to the shape, the capability to autonomously survey a small body by means of Lidar observations given little to no a-priori information is demonstrated, in addition to the capacity to deliver a consistent shape estimate accounting for underlying errors in the reconstructed shape. This consistent pair of a shape estimate augmented with its uncertainty metric allows model-based navigation to take place in a robust manner, through the use of an Iterated Extended Kalman Filter taking in position and attitude measurements from a Consider Batch Filter augmenting the measurement covariance with a commensurate consider contribution coming from the shape uncertainty model. A sensitivity analysis covering a subset of the parameter space has validated the proposed framework's robustness, paving the way for autonomous mapping and navigation of small bodies in the presence of uncertainty.</p

On the Fast Track: Rapid construction of stellar stream paths

Stellar streams are sensitive probes of the Galactic potential. The likelihood of a stream model given stream data is often assessed using simulations. However, comparing to simulations is challenging when even the stream paths can be hard to quantify. Here we present a novel application of Self-Organizing Maps and first-order Kalman Filters to reconstruct a stream's path, propagating measurement errors and data sparsity into the stream path uncertainty. The technique is Galactic-model independent, non-parametric, and works on phase-wrapped streams. With this technique, we can uniformly analyze and compare data with simulations, enabling both comparison of simulation techniques and ensemble analysis with stream tracks of many stellar streams. Our method is implemented in the public Python package TrackStream, available at https://github.com/nstarman/trackstream.Comment: 16 pages, 11 figures, preprin