Lukas Luft

Alexander Schaefer, Daniel Büscher, Lukas Luft et al.

Man-made environments such as households, offices, or factory floors are typically composed of linear structures. Accordingly, polylines are a natural way to accurately represent their geometry. In this paper, we propose a novel probabilistic method to extract polylines from raw 2-D laser range scans. The key idea of our approach is to determine a set of polylines that maximizes the likelihood of a given scan. In extensive experiments carried out on publicly available real-world datasets and on simulated laser scans, we demonstrate that our method substantially outperforms existing state-of-the-art approaches in terms of accuracy, while showing comparable computational requirements. Our implementation is available under https://github.com/acschaefer/ple.

Alexander Schaefer, Lukas Luft, Wolfram Burgard

Most robot mapping techniques for lidar sensors tessellate the environment into pixels or voxels and assume uniformity of the environment within them. Although intuitive, this representation entails disadvantages: The resulting grid maps exhibit aliasing effects and are not differentiable. In the present paper, we address these drawbacks by introducing a novel mapping technique that does neither rely on tessellation nor on the assumption of piecewise uniformity of the space, without increasing memory requirements. Instead of representing the map in the position domain, we store the map parameters in the discrete frequency domain and leverage the continuous extension of the inverse discrete cosine transform to convert them to a continuously differentiable scalar field in the position domain, which we call DCT map. A DCT map assigns to each point in space a lidar decay rate, which models the local permeability of the space for laser rays. In this way, the map can describe objects of different laser permeabilities, from completely opaque to completely transparent. DCT maps represent lidar measurements significantly more accurate than grid maps, Gaussian process occupancy maps, and Hilbert maps, all with the same memory requirements, as demonstrated in our real-world experiments.

Alexander Schaefer, Lukas Luft, Wolfram Burgard

Two core competencies of a mobile robot are to build a map of the environment and to estimate its own pose on the basis of this map and incoming sensor readings. To account for the uncertainties in this process, one typically employs probabilistic state estimation approaches combined with a model of the specific sensor. Over the past years, lidar sensors have become a popular choice for mapping and localization. However, many common lidar models perform poorly in unstructured, unpredictable environments, they lack a consistent physical model for both mapping and localization, and they do not exploit all the information the sensor provides, e.g. out-of-range measurements. In this paper, we introduce a consistent physical model that can be applied to mapping as well as to localization. It naturally deals with unstructured environments and makes use of both out-of-range measurements and information about the ray path. The approach can be seen as a generalization of the well-established reflection model, but in addition to counting ray reflections and traversals in a specific map cell, it considers the distances that all rays travel inside this cell. We prove that the resulting map maximizes the data likelihood and demonstrate that our model outperforms state-of-the-art sensor models in extensive real-world experiments.

R. Chaves, L. Luft, T. O. Maciel et al.

One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial constraints on the observed distribution. Here, we propose an information-theoretic approach, based on the insight that conditions on entropies of Bayesian networks take the form of simple linear inequalities. We describe an algorithm for deriving entropic tests for latent structures. The well-known conditional independence tests appear as a special case. While the approach applies for generic Bayesian networks, we presently adopt the causal view, and show the versatility of the framework by treating several relevant problems from that domain: detecting common ancestors, quantifying the strength of causal influence, and inferring the direction of causation from two-variable marginals.