VECTOR MAPS IN MOBILE ROBOTICS

The aim of this paper is to provide a brief overview of vector map techniques used in mobile robotics and to present current state of the research in this field at the Brno University of Technology. Vector maps are described as a part of the simultaneous localization and mapping (SLAM) problem in the environment without artificial landmarks or global navigation system. The paper describes algorithms from data acquisition to map building but particular emphasis is put on segmentation, line extraction and scan matching algorithms. All significant algorithms are illustrated with experimental results

A weighted MVDR beamformer based on SVM learning for sound source localization

3noA weighted minimum variance distortionless response (WMVDR) algorithm for near-field sound localization in a reverberant environment is presented. The steered response power computation of the WMVDR is based on a machine learning component which improves the incoherent frequency fusion of the narrowband power maps. A support vector machine (SVM) classifier is adopted to select the components of the fusion. The skewness measure of the narrowband power map marginal distribution is showed to be an effective feature for the supervised learning of the power map selection. Experiments with both simulated and real data demonstrate the improvement of the WMVDR beamformer localization accuracy with respect to other state-of-the-art techniques.partially_openopenSalvati, Daniele; Drioli, Carlo; Foresti, Gian LucaSalvati, Daniele; Drioli, Carlo; Foresti, Gian Luc

Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem

International audienceThe purpose of the present paper is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, we deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, we use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar in the Hamiltonian case, and we obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplicities of the index of general spin^c Dirac operators (see preprint arXiv:1411.7772)

Orientation-Aware 3D SLAM in Alternating Magnetic Field from Powerlines

Identifying new sensing modalities for indoor localization is an interest of research. This paper studies powerline-induced alternating magnetic field (AMF) that fills the indoor space for the orientation-aware three-dimensional (3D) simultaneous localization and mapping (SLAM). While an existing study has adopted a uniaxial AMF sensor for SLAM in a plane surface, the design falls short of addressing the vector field nature of AMF and is therefore susceptible to sensor orientation variations. Moreover, although the higher spatial variability of AMF in comparison with indoor geomagnetism promotes location sensing resolution, extra SLAM algorithm designs are needed to achieve robustness to trajectory deviations from the constructed map. To address the above issues, we design a new triaxial AMF sensor and a new SLAM algorithm that constructs a 3D AMF intensity map regularized and augmented by a Gaussian process. The triaxial sensor’s orientation estimation is free of the error accumulation problem faced by inertial sensing. From extensive evaluation in eight indoor environments, our AMF-based 3D SLAM achieves sub-1m to 3m median localization errors in spaces of up to 500 m2 , sub-2° mean error in orientation sensing, and outperforms the SLAM systems based on Wi-Fi, geomagnetism, and uniaxial AMF by more than 30%

A Constant-Time Algorithm for Vector Field SLAM using an Exactly Sparse Extended Information Filter

Abstract — Designing a localization system for a low-cost robotic consumer product poses a major challenge. In previous work, we introduced Vector Field SLAM [5], a system for simultaneously estimating robot pose and a vector field induced by stationary signal sources present in the environment. In this paper we show how this method can be realized on a low-cost embedded processing unit by applying the concepts of the Exactly Sparse Extended Information Filter [15]. By restricting the set of active features to the 4 nodes of the current cell, the size of the map becomes linear in the area explored by the robot while the time for updating the state can be held constant under certain approximations. We report results from running our method on an ARM 7 embedded board with 64 kByte RAM controlling a Roomba 510 vacuum cleaner in a standard test environment. NS spot1 X (sensor units) Spot1 X readings Node X1 estimate

On localization in holomorphic equivariant cohomology

We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the exposition. v4: final version to appear in Centr. Eur. J. Mat

Equivariant Kaehler Geometry and Localization in the G/G Model

We analyze in detail the equivariant supersymmetry of the $G/G$ model. In spite of the fact that this supersymmetry does not model the infinitesimal action of the group of gauge transformations, localization can be established by standard arguments. The theory localizes onto reducible connections and a careful evaluation of the fixed point contributions leads to an alternative derivation of the Verlinde formula for the $G_{k}$ WZW model. We show that the supersymmetry of the $G/G$ model can be regarded as an infinite dimensional realization of Bismut's theory of equivariant Bott-Chern currents on K\"ahler manifolds, thus providing a convenient cohomological setting for understanding the Verlinde formula. We also show that the supersymmetry is related to a non-linear generalization (q-deformation) of the ordinary moment map of symplectic geometry in which a representation of the Lie algebra of a group $G$ is replaced by a representation of its group algebra with commutator $[g,h] = gh-hg$. In the large $k$ limit it reduces to the ordinary moment map of two-dimensional gauge theories.Comment: LaTex file, 40 A4 pages, IC/94/108 and ENSLAPP-L-469/9