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Dellaert,
Frank
Dellaert,
Frank
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ItemSelecting Good Measurements via ℓ₁ Relaxation: A Convex Approach for Robust Estimation Over Graphs(Georgia Institute of Technology, 2014-09) Carlone, Luca ; Censi, Andrea ; Dellaert, FrankPose graph optimization is an elegant and efficient formulation for robot localization and mapping. Experimental evidence suggests that, in real problems, the set of measurements used to estimate robot poses is prone to contain outliers, due to perceptual aliasing and incorrect data association. While several related works deal with the rejection of outliers during pose estimation, the goal of this paper is to propose a grounded strategy for measurements selection, i.e., the output of our approach is a set of “reliable” measurements, rather than pose estimates. Because the classification in inliers /outliers is not observable in general, we pose the problem as finding the maximal subset of the measurements that is internally coherent. In the linear case, we show that the selection of the maximal coherent set can be (conservatively) relaxed to obtain a linear programming problem with ℓ₁ objective. We show that this approach can be extended to (nonlinear) planar pose graph optimization using similar ideas as our previous work on linear approaches to pose graph optimization. We evaluate our method on standard datasets, and we show that it is robust to a large number of outliers and different outlier generation models, while entailing the advantages of linear programming (fast computation, scalability).
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ItemMining Structure Fragments for Smart Bundle Adjustment(Georgia Institute of Technology, 2014-09) Carlone, Luca ; Alcantarilla, Pablo Fernandez ; Chiu, Han-Pang ; Kira, Zsolt ; Dellaert, FrankBundle Adjustment (BA) can be seen as an inference process over a factor graph. From this perspective, the Schur complement trick can be interpreted as an ordering choice for elimination. The elimination of a single point in the BA graph induces a factor over the set of cameras observing that point. This factor has a very low information content (a point observation enforces a low-rank constraint on the cameras). In this work we show that, when using conjugate gradient solvers, there is a computational advantage in “grouping” factors corresponding to sets of points (fragments) that are co-visible by the same set of cameras. Intuitively, we collapse many factors with low information content into a single factor that imposes a high-rank constraint among the cameras. We provide a grounded way to group factors: the selection of points that are co-observed by the same camera patterns is a data mining problem, and standard tools for frequent pattern mining can be applied to reveal the structure of BA graphs. We demonstrate the computational advantage of grouping in large BA problems and we show that it enables a consistent reduction of BA time with respect to state-of-the-art solvers (Ceres [1]).
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ItemPlanning Under Uncertainty in the Continuous Domain: A Generalized Belief Space Approach(Georgia Institute of Technology, 2014) Indelman, Vadim ; Carlone, Luca ; Dellaert, FrankThis work investigates the problem of planning under uncertainty, with application to mobile robotics. We propose a probabilistic framework in which the robot bases its decisions on the generalized belief , which is a probabilistic description of its own state and of external variables of interest. The approach naturally leads to a dual-layer architecture: an inner estimation layer, which performs inference to predict the outcome of possible decisions, and an outer decisional layer which is in charge of deciding the best action to undertake. The approach does not discretize the state or control space, and allows planning in continuous domain. Moreover, it allows to relax the assumption of maximum likelihood observations: predicted measurements are treated as random variables and are not considered as given. Experimental results show that our planning approach produces smooth trajectories while maintaining uncertainty within reasonable bounds.
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ItemEliminating Conditionally Independent Sets in Factor Graphs: A Unifying Perspective based on Smart Factors(Georgia Institute of Technology, 2014) Carlone, Luca ; Kira, Zsolt ; Beall, Chris ; Indelman, Vadim ; Dellaert, FrankFactor graphs are a general estimation framework that has been widely used in computer vision and robotics. In several classes of problems a natural partition arises among variables involved in the estimation. A subset of the variables are actually of interest for the user: we call those target variables. The remaining variables are essential for the formulation of the optimization problem underlying maximum a posteriori (MAP) estimation; however these variables, that we call support variables, are not strictly required as output of the estimation problem. In this paper, we propose a systematic way to abstract support variables, defining optimization problems that are only defined over the set of target variables. This abstraction naturally leads to the definition of smart factors, which correspond to constraints among target variables. We show that this perspective unifies the treatment of heterogeneous problems, ranging from structureless bundle adjustment to robust estimation in SLAM. Moreover, it enables to exploit the underlying structure of the optimization problem and the treatment of degenerate instances, enhancing both computational efficiency and robustness.
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ItemConstrained Optimal Selection for Multi-Sensor Robot Navigation Using Plug-and-Play Factor Graphs(Georgia Institute of Technology, 2014) Chiu, Han-Pang ; Zhou, Xun S. ; Carlone, Luca ; Dellaert, Frank ; Samarasekera, Supun ; Kumar, RakeshThis paper proposes a real-time navigation approach that is able to integrate many sensor types while fulfilling performance needs and system constraints. Our approach uses a plug-and-play factor graph framework, which extends factor graph formulation to encode sensor measurements with different frequencies, latencies, and noise distributions. It provides a flexible foundation for plug-and-play sensing, and can incorporate new evolving sensors. A novel constrained optimal selection mechanism is presented to identify the optimal subset of active sensors to use, during initialization and when any sensor condition changes. This mechanism constructs candidate subsets of sensors based on heuristic rules and a ternary tree expansion algorithm. It quickly decides the optimal subset among candidates by maximizing observability coverage on state variables, while satisfying resource constraints and accuracy demands. Experimental results demonstrate that our approach selects subsets of sensors to provide satisfactory navigation solutions under various conditions, on large-scale real data sets using many sensors.