Person:

Dellaert, Frank

Permanent Link

https://hdl.handle.net/1853/71202

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Organizational Unit

School of Interactive Computing

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Now showing 1 - 10 of 11

Duality-based Verification Techniques for 2D SLAM

(Georgia Institute of Technology, 2015-05) Carlone, Luca ; Dellaert, Frank

While iterative optimization techniques for Simultaneous Localization and Mapping (SLAM) are now very efficient and widely used, none of them can guarantee global convergence to the maximum likelihood estimate. Local convergence usually implies artifacts in map reconstruction and large localization errors, hence it is very undesirable for applications in which accuracy and safety are of paramount importance. We provide a technique to verify if a given 2D SLAM solution is globally optimal. The insight is that, while computing the optimal solution is hard in general, duality theory provides tools to compute tight bounds on the optimal cost, via convex programming. These bounds can be used to evaluate the quality of a SLAM solution, hence providing a “sanity check” for state-of-the-art incremental and batch solvers. Experimental results show that our technique successfully identifies wrong estimates (i.e., local minima) in large-scale SLAM scenarios. This work, together with [1], represents a step towards the objective of having SLAM techniques with guaranteed performance, that can be used in safety-critical applications.
Initialization Techniques for 3D SLAM: A Survey on Rotation Estimation and its Use in Pose Graph Optimization

(Georgia Institute of Technology, 2015-05) Carlone, Luca ; Tron, Roberto ; Daniilidis, Kostas ; Dellaert, Frank

Pose graph optimization is the non-convex optimization problem underlying pose-based Simultaneous Localization and Mapping (SLAM). If robot orientations were known, pose graph optimization would be a linear least-squares problem, whose solution can be computed efficiently and reliably. Since rotations are the actual reason why SLAM is a difficult problem, in this work we survey techniques for 3D rotation estimation. Rotation estimation has a rich history in three scientific communities: robotics, computer vision, and control theory. We review relevant contributions across these communities, assess their practical use in the SLAM domain, and benchmark their performance on representative SLAM problems (Fig. 1). We show that the use of rotation estimation to bootstrap iterative pose graph solvers entails significant boost in convergence speed and robustness.
IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation

(Georgia Institute of Technology, 2015) Forster, Christian ; Carlone, Luca ; Dellaert, Frank ; Scaramuzza, Davide

Recent results in monocular visual-inertial navigation (VIN) have shown that optimization-based approaches outperform filtering methods in terms of accuracy due to their capability to relinearize past states. However, the improvement comes at the cost of increased computational complexity. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes. The preintegration allows us to accurately summarize hundreds of inertial measurements into a single relative motion constraint. Our first contribution is a preintegration theory that properly addresses the manifold structure of the rotation group and carefully deals with uncertainty propagation. The measurements are integrated in a local frame, which eliminates the need to repeat the integration when the linearization point changes while leaving the opportunity for belated bias corrections. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated in a visual-inertial pipeline under the unifying framework of factor graphs. This enables the use of a structureless model for visual measurements, further accelerating the computation. The third contribution is an extensive evaluation of our monocular VIN pipeline: experimental results confirm that our system is very fast and demonstrates superior accuracy with respect to competitive state-of-the-art filtering and optimization algorithms, including off-the-shelf systems such as Google Tango [1].
Rigid Components Identification and Rigidity Enforcement in Bearing-Only Localization using the Graph Cycle Basis

(Georgia Institute of Technology, 2015) Tron, Roberto ; Carlone, Luca ; Dellaert, Frank ; Daniilidis, Kostas

Bearing-only localization can be formulated in terms of optimal graph embedding: one has to assign a 2-D or 3-D position to each node in a graph while satisfying as close as possible all the bearing-only constraints on the edges. If the graph is parallel rigid, this can be done via spectral methods. When the graph is not rigid the reconstruction is ambiguous, as different subsets of vertices can be scaled differently. It is therefore important to first identify a partition of the problem into maximal rigid components. In this paper we show that the cycle basis matrix of the graph not only translates into an algorithm to identify all rigid sub-graphs, but also provides a more intuitive way to look at graph rigidity, showing, for instance, why triangulated graphs are rigid and why graphs with long cycles may loose this property. Furthermore, it provides practical tools to enforce rigidity by adding a minimal number of measurements.
Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions

(Georgia Institute of Technology, 2015) Carlone, Luca ; Rosen, David W. ; Calafiore, Giuseppe ; Leonard, John J. ; Dellaert, Frank

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide guarantees on the quality of the estimate. This paper shows that Lagrangian duality is a powerful tool to assess the quality of a given candidate solution. Our contribution is threefold. First, we discuss a revised formulation of the SLAM inference problem. We show that this formulation is probabilistically grounded and has the advantage of leading to an optimization problem with quadratic objective. The second contribution is the derivation of the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex) semidefinite program, which can be solved reliably and globally by off-the-shelf solvers. The third contribution is to discuss the relation between the original SLAM problem and its dual. We show that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality. Moreover, when the duality gap is zero, one can compute a guaranteed optimal SLAM solution from the dual problem, circumventing non-convex optimization. We present extensive (real and simulated) experiments supporting our claims and discuss practical relevance and open problems.
Selecting Good Measurements via ℓ₁ Relaxation: A Convex Approach for Robust Estimation Over Graphs

(Georgia Institute of Technology, 2014-09) Carlone, Luca ; Censi, Andrea ; Dellaert, Frank

Pose 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).
Mining Structure Fragments for Smart Bundle Adjustment

(Georgia Institute of Technology, 2014-09) Carlone, Luca ; Alcantarilla, Pablo Fernandez ; Chiu, Han-Pang ; Kira, Zsolt ; Dellaert, Frank

Bundle 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]).
Planning Under Uncertainty in the Continuous Domain: A Generalized Belief Space Approach

(Georgia Institute of Technology, 2014) Indelman, Vadim ; Carlone, Luca ; Dellaert, Frank

This 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.
Eliminating 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, Frank

Factor 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.
Constrained 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, Rakesh

This 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.