Galois lattice theory for probabilistic visual landmarks

This paper presents an original application of the Galois lattice theory, the visual landmark selection for topological localization of an autonomous mobile robot, equipped with a color camera. First, visual landmarks have to be selected in order to characterize a structural environment. Second, such landmarks have to be detected and updated for localization. These landmarks are combinations of attributes, and the selection process is done through a Galois lattice. This paper exposes the landmark selection process and focuses on probabilistic landmarks, which give the robot thorough information on how to locate itself. As a result, landmarks are no longer binary, but probabilistic. The full process of using such landmarks is described in this paper and validated through a robotics experiment

A Spectral Learning Approach to Range-Only SLAM

We present a novel spectral learning algorithm for simultaneous localization and mapping (SLAM) from range data with known correspondences. This algorithm is an instance of a general spectral system identification framework, from which it inherits several desirable properties, including statistical consistency and no local optima. Compared with popular batch optimization or multiple-hypothesis tracking (MHT) methods for range-only SLAM, our spectral approach offers guaranteed low computational requirements and good tracking performance. Compared with popular extended Kalman filter (EKF) or extended information filter (EIF) approaches, and many MHT ones, our approach does not need to linearize a transition or measurement model; such linearizations can cause severe errors in EKFs and EIFs, and to a lesser extent MHT, particularly for the highly non-Gaussian posteriors encountered in range-only SLAM. We provide a theoretical analysis of our method, including finite-sample error bounds. Finally, we demonstrate on a real-world robotic SLAM problem that our algorithm is not only theoretically justified, but works well in practice: in a comparison of multiple methods, the lowest errors come from a combination of our algorithm with batch optimization, but our method alone produces nearly as good a result at far lower computational cost

Simple yet stable bearing-only navigation

This article describes a simple monocular navigation system for a mobile robot based on the map-and-replay technique. The presented method is robust and easy to implement and does not require sensor calibration or structured environment, and its computational complexity is independent of the environment size. The method can navigate a robot while sensing only one landmark at a time, making it more robust than other monocular approaches. The aforementioned properties of the method allow even low-cost robots to effectively act in large outdoor and indoor environments with natural landmarks only. The basic idea is to utilize a monocular vision to correct only the robot's heading, leaving distance measurements to the odometry. The heading correction itself can suppress the odometric error and prevent the overall position error from diverging. The influence of a map-based heading estimation and odometric errors on the overall position uncertainty is examined. A claim is stated that for closed polygonal trajectories, the position error of this type of navigation does not diverge. The claim is defended mathematically and experimentally. The method has been experimentally tested in a set of indoor and outdoor experiments, during which the average position errors have been lower than 0.3 m for paths more than 1 km long

Vision-Based Localization Algorithm Based on Landmark Matching, Triangulation, Reconstruction, and Comparison

Many generic position-estimation algorithms are vulnerable to ambiguity introduced by nonunique landmarks. Also, the available high-dimensional image data is not fully used when these techniques are extended to vision-based localization. This paper presents the landmark matching, triangulation, reconstruction, and comparison (LTRC) global localization algorithm, which is reasonably immune to ambiguous landmark matches. It extracts natural landmarks for the (rough) matching stage before generating the list of possible position estimates through triangulation. Reconstruction and comparison then rank the possible estimates. The LTRC algorithm has been implemented using an interpreted language, onto a robot equipped with a panoramic vision system. Empirical data shows remarkable improvement in accuracy when compared with the established random sample consensus method. LTRC is also robust against inaccurate map data

Topological visual localization using decentralized galois lattices

This paper presents a new decentralized method for selecting visual landmarks in a structured environment. Different images, issued from the different places, are analyzed, and primitives are extracted to determine whether or not features are present in the images. Subsequently, landmarks are selected as a combination of these features with a mathematical formalism called Galois - or concept - lattices. The main drawback of the general approach is the exponential complexity of lattice building algorithms. A decentralized approach is therefore defined and detailed here: it leads to smaller lattices, and thus to better performance as well as an improved legibility

Characterization of image sets: the Galois Lattice approach

This paper presents a new method for supervised image classification. One or several landmarks are attached to each class, with the intention of characterizing it and discriminating it from the other classes. The different features, deduced from image primitives, and their relationships with the sets of images are structured and organized into a hierarchy thanks to an original method relying on a mathematical formalism called Galois (or Concept) Lattices. Such lattices allow us to select features as landmarks of specific classes. This paper details the feature selection process and illustrates this through a robotic example in a structured environment. The class of any image is the room from which the image is shot by the robot camera. In the discussion, we compare this approach with decision trees and we give some issues for future research