Robust autonomous robot localization using interval analysis

International audienceThis paper deals with the determination of the position and orientation of a mobile robot from distance measurements provided by a belt of onboard ultrasonic sensors. The environment is assumed to be two-dimensional, and a map of its landmarks is available to the robot. In this context, classical localization methods have three main limitations. First, each data point provided by a sensor must be associated with a given landmark. This data-association step turns out to be extremely complex and time-consuming, and its results can usually not be guaranteed. The second limitation is that these methods are based on linearization, which makes them inherently local. The third limitation is their lack of robustness to outliers due, e.g., to sensor malfunctions or outdated maps. By contrast, the method proposed here, based on interval analysis, bypasses the data-association step, handless the problem as nonlinera and in a global way and is (extraordinarily) robust to outliers

Mobile robot localization using robust extended H-infinity filtering

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2009 Institution of Mechanical Engineers.In this paper, a novel methodology is provided for accurate localization of a mobile robot using autonomous navigation based on internal and external sensors. A new robust extended H∞ filter is developed to deal with the non-linear kinematic model of the robot and the non-linear distance measurements, together with process and measurement noises. The proposed filter relies on a two-step prediction-correction structure, which is similar to a Kalman filter. Simulations are provided to demonstrate the effectiveness of the proposed method.EPSRC, the Nuffield Foundation, and the Alexander von Humboldt Foundation

A Polar Representation for Complex Interval Numbers

The present work defines the basic elements for the introduction to the Study of Complex variables under the mathematical interval context with the goal of using it as a foundation for the understanding of pure mathematical problems, associating the mathematical interval to support the results. The present article contributes to the complex interval theory taking into consideration Euler’s Identity and redefining the polar representation of interval complex numbers. In engineering, the present article could be used as a subsidy for many applications where complex variable theory is applicable and requires accurate results

Reliable bounding zones and inconsistency measures for GPS positioning using geometrical constraints

Reliable confidence domains for positioning with Global Navigation Satellite System (GNSS) and inconsistency measures for the observations are of great importance for any navigation system, especially for safety critical applications. In this work, deterministic error bounds are introduced in form of intervals to assess remaining observation errors. The intervals can be determined based on expert knowledge or - as in our case - based on a sensitivity analysis of the measurement correction process. Using convex optimization, bounding zones are computed for GPS positioning, which satisfy the geometrical constraints imposed by the observation intervals. The bounding zone is a convex polytope. When exploiting only the navigation geometry, a confidence domain is computed in form of a zonotope. We show that the relative volume between the polytope and the zonotope can be considered as an inconsistency measure. A small polytope volume indicates bad consistency of the observations. In extreme cases, empty sets are obtained which indicates large outliers. We explain how shape and volume of the polytopes are related to the positioning geometry. Furthermore, we propose a new concept of Minimum Detectable Biases. Using the example of the Klobuchar ionospheric model and Saastamoinen tropospheric model, we show how observation intervals can be determined via sensitivity analysis of these correction models for a real measurement campaign. Taking GPS code data from simulations and real experiments, a comparison analysis between the proposed deterministic bounding method and the classical least-squares adjustment has been conducted in terms of accuracy and reliability. It shows that the computed polytopes always enclose the reference trajectory. In case of large outliers, large position deviations persist in the least-squares solution while the polytope algorithm yields empty sets and thus successfully detects the cases with outliers

Robust robot localization and tracking using interval analysis

This paper presents a new solution to the problem of localizing and tracking a robot from distance measurements provided by on-board ultrasonic sensors. The measurement errors and state perturbations are assumed to be bounded. A parameter and state estimation technique based on interval analysis is employed to compute, as a function of time, a set guaranteed to contain all robot configurations (position and orientation) that are consistent with the measurements provided by the ultrasonic sensors, given bounds on the acceptable errors. The unavoidable presence of many outliers is taken into account to provide robust estimates. A realistic simulated example is treated in detail to illustrate the properties of the technique.Cet article présente une solution originale au problème de localisation et de suivi d'un robot mobile à partir de données télémétriques fournies par des capteurs à ultrasons. Le problème est traité dans un contexte d'erreurs de mesure et d'incertitudes sur l'état bornées. Grâce à une technique d'estimation de paramètres et d'état utilisant l'analyse par intervalles, les mesures provenant des capteurs à ultrasons sont fusionnées en tenant compte de la présence inévitable de nombreuses données aberrantes. Un ensemble contenant la configuration (position et orientation) du robot est fourni à chaque instant. Un exemple simulé réaliste est présenté en détail pour illustrer les propriétés de la technique

Des cartes combinatoires pour la construction automatique de modèles d'environnement par un robot mobile

Ce travail s'inscrit dans la problématique classique de localisation et de cartographie simultanées pour un robot mobile évoluant en milieu intérieur supposé inconnu. Son originalité réside dans la définition d'un modèle de carte très structuré fondé sur un outil algébrique appelé « carte combinatoire », qui combine plusieurs types de représentations géométriques (modèles surfaciques et cartes basées sur des primitives géométriques) et fournit des informations topologiques telles que les liens d'adjacence. Nous détaillons la chaîne algorithmique permettant de construire des cartes en ligne suivant ce modèle, avec un robot équipé d'un télémètre laser à balayage : il s'agit d'adapter les techniques habituelles basées sur le filtrage de Kalman afin de gérer les relations d'adjacence (appariement de chaînes polygonales, définition de points de cassure virtuels, mises à jour géométrique et topologique spécifiques). Des résultats expérimentaux illustrent et valident les divers mécanismes mis en oeuvre. ABSTRACT : This thesis focuses on the well-known Simultaneous Localization And Map-building (SLAM) problem for indoor mobile robots. The novelty of this work lies in the definition of a well-structured map model based on an algebraic tool called « combinatorial map » which combines different kinds of geometric representations (space-based, grid-based as well as feature-based formats) and provides topological information such as adjacency links between map elements. We describe the whole algorithm designed to build maps on line according to this model, using a robot equipped with a laser scanner. Classical techniques relying on Kalman filtering are adapted in order to deal with adjacency relationships (via polyline matching, the use of virtual break-points and specific geometric and topological update operations). Exeprimental results are presented to illustrate and validate the various mecanisms involved in this process