A new three object triangulation algorithm based on the power center of three circles

peer reviewedaudience: researcher, professional, popularizationPositioning is a fundamental issue in mobile robot applications that can be achieved in multiple ways. Among these methods, triangulation is a proven technique. As it exists for a long time, many variants of triangulation have been proposed. Which variant is most appropriate depends on the application because some methods ignore the beacon ordering while other have blind spots. Some methods are reliable but at a price of increasing complexity or special cases study. In this paper, we present a simple and new three object triangulation algorithm. Our algorithm works in the whole plane (except when the beacons and the robot are concyclic or colinear), and for any beacon ordering. Moreover, it does not need special cases study and has a strong geometrical meaning. Benchmarks show that our algorithm is faster than existing and comparable algorithms. Finally, a quality measure is intrinsically derived for the triangulation result in the whole plane, which can be used to identify the pathological cases, or as a validation gate in Kalman filters

A New Three Object Triangulation Algorithm for Mobile Robot Positioning

Positioning is a fundamental issue in mobile robot applications. It can be achieved in many ways. Among them, triangulation based on angles measured with the help of beacons is a proven technique. Most of the many triangulation algorithms proposed so far have major limitations. For example, some of them need a particular beacon ordering, have blind spots, or only work within the triangle defined by the three beacons. More reliable methods exist; however, they have an increasing complexity or they require to handle certain spatial arrangements separately. In this paper, we present a simple and new three object triangulation algorithm, named ToTal, that natively works in the whole plane, and for any beacon ordering. We also provide a comprehensive comparison between many algorithms, and show that our algorithm is faster and simpler than comparable algorithms. In addition to its inherent efficiency, our algorithm provides a very useful and unique reliability measure, assessable anywhere in the plane, which can be used to identify pathological cases, or as a validation gate in Kalman filters.Peer reviewe

Information-theoretic environment modeling for mobile robot localization

To enhance robotic computational efficiency without degenerating accuracy, it is imperative to fit the right and exact amount of information in its simplest form to the investigated task. This thesis conforms to this reasoning in environment model building and robot localization. It puts forth an approach towards building maps and localizing a mobile robot efficiently with respect to unknown, unstructured and moderately dynamic environments. For this, the environment is modeled on an information-theoretic basis, more specifically in terms of its transmission property. Subsequently, the presented environment model, which does not specifically adhere to classical geometric modeling, succeeds in solving the environment disambiguation effectively. The proposed solution lays out a two-level hierarchical structure for localization. The structure makes use of extracted features, which are stored in two different resolutions in a single hybrid feature-map. This enables dual coarse-topological and fine-geometric localization modalities. The first level in the hierarchy describes the environment topologically, where a defined set of places is described by a probabilistic feature representation. A conditional entropy-based criterion is proposed to quantify the transinformation between the feature and the place domains. This criterion provides a double benefit of pruning the large dimensional feature space, and at the same time selecting the best discriminative features that overcome environment aliasing problems. Features with the highest transinformation are filtered and compressed to form a coarse resolution feature-map (codebook). Localization at this level is conducted through place matching. In the second level of the hierarchy, the map is viewed in high-resolution, as consisting of non-compressed entropy-processed features. These features are additionally tagged with their position information. Given the identified topological place provided by the first level, fine localization corresponding to the second level is executed using feature triangulation. To enhance the triangulation accuracy, redundant features are used and two metric evaluating criteria are employ-ed; one for dynamic features and mismatches detection, and another for feature selection. The proposed approach and methods have been tested in realistic indoor environments using a vision sensor and the Scale Invariant Feature Transform local feature extraction. Through experiments, it is demonstrated that an information-theoretic modeling approach is highly efficient in attaining combined accuracy and computational efficiency performances for localization. It has also been proven that the approach is capable of modeling environments with a high degree of unstructuredness, perceptual aliasing, and dynamic variations (illumination conditions; scene dynamics). The merit of employing this modeling type is that environment features are evaluated quantitatively, while at the same time qualitative conclusions are generated about feature selection and performance in a robot localization task. In this way, the accuracy of localization can be adapted in accordance with the available resources. The experimental results also show that the hybrid topological-metric map provides sufficient information to localize a mobile robot on two scales, independent of the robot motion model. The codebook exhibits fast and accurate topological localization at significant compression ratios. The hierarchical localization framework demonstrates robustness and optimized space and time complexities. This, in turn, provides scalability to large environments application and real-time employment adequacies