Dellaert, Frank

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Now showing 1 - 10 of 103
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    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.
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    Monocular Image Space Tracking on a Computationally Limited MAV
    (Georgia Institute of Technology, 2015-05) Ok, Kyel ; Gamage, Dinesh ; Drummond, Tom ; Dellaert, Frank ; Roy, Nicholas
    We propose a method of monocular camera-inertial based navigation for computationally limited micro air vehicles (MAVs). Our approach is derived from the recent development of parallel tracking and mapping algorithms, but unlike previous results, we show how the tracking and mapping processes operate using different representations.The separation of representations allows us not only to move the computational load of full map inference to a ground station, but to further reduce the computational cost of on-board tracking for pose estimation. Our primary contribution is to show how the cost of tracking the vehicle pose on-board can be substantially reduced by estimating the camera motion directly in the image frame, rather than in the world co-ordinate frame. We demonstrate our method on an Ascending Technologies Pelican quad-rotor, and show that we can track the vehicle pose with reduced on-board computation but without compromised navigation accuracy.
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    Differential Dynamic Programming for Optimal Estimation
    (Georgia Institute of Technology, 2015-05) Kobilarov, Marin ; Ta, Duy-Nguyen ; Dellaert, Frank
    This paper studies an optimization-based approach for solving optimal estimation and optimal control problems through a unified computational formulation. The goal is to perform trajectory estimation over extended past horizons and model-predictive control over future horizons by enforcing the same dynamics, control, and sensing constraints in both problems, and thus solving both problems with identical computational tools. Through such systematic estimation-control formulation we aim to improve the performance of autonomous systems such as agile robotic vehicles. This work focuses on sequential sweep trajectory optimization methods, and more specifically extends the method known as differential dynamic programming to the parameter-dependent setting in order to enable the solutions to general estimation and control problems.
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    Distributed Real-time Cooperative Localization and Mapping Using an Uncertainty-Aware Expectation Maximization Approach
    (Georgia Institute of Technology, 2015-05) Dong, Jing ; Nelson, Erik ; Indelman, Vadim ; Michael, Nathan ; Dellaert, Frank
    We demonstrate distributed, online, and real-time cooperative localization and mapping between multiple robots operating throughout an unknown environment sing indirect measurements. We present a novel Expectation Maximization (EM) based approach to efficiently identify inlier multi-robot loop closures by incorporating robot pose uncertainty, which significantly improves the trajectory accuracy over long-term navigation. An EM and hypothesis based method is used to determine a common reference frame. We detail a 2D laser scan correspondence method to form robust correspondences between laser scans shared amongst robots. The implementation is experimentally validated using teams of aerial vehicles, and analyzed to determine its accuracy, computational efficiency, scalability to many robots, and robustness to varying environments. We demonstrate through multiple experiments that our method can efficiently build maps of large indoor and outdoor environments in a distributed, online, and real-time setting.
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    Information-based Reduced Landmark SLAM
    (Georgia Institute of Technology, 2015-05) Choudhary, Siddharth ; Indelman, Vadim ; Christensen, Henrik I. ; Dellaert, Frank
    In this paper, we present an information-based approach to select a reduced number of landmarks and poses for a robot to localize itself and simultaneously build an accurate map. We develop an information theoretic algorithm to efficiently reduce the number of landmarks and poses in a SLAM estimate without compromising the accuracy of the estimated trajectory. We also propose an incremental version of the reduction algorithm which can be used in SLAM framework resulting in information based reduced landmark SLAM. The results of reduced landmark based SLAM algorithm are shown on Victoria park dataset and a Synthetic dataset and are compared with standard graph SLAM (SAM [6]) algorithm. We demonstrate a reduction of 40-50% in the number of landmarks and around 55% in the number of poses with minimal estimation error as compared to standard SLAM algorithm.
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    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.
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    Distributed Navigation with Unknown Initial Poses and Data Association via Expectation Maximization
    (Georgia Institute of Technology, 2015-02) Indelman, Vadim ; Michael, Nathan ; Dellaert, Frank
    We present a novel approach for multi-robot distributed and incremental inference over variables of interest, such as robot trajectories, considering the initial relative poses between the robots and multi-robot data association are both unknown. Assuming robots share with each other informative observations, this inference problem is formulated within an Expectation-Maximization (EM) optimization, performed by each robot separately, alternating between inference over variables of interest and multi-robot data association. To facilitate this process, a common reference frame between the robots should first be established. We show the latter is coupled with determining multi-robot data association, and therefore concurrently infer both using a separate EM optimization. This optimization is performed by each robot starting from several promising initial solutions, converging to locally-optimal hypotheses regarding data association and reference frame transformation. Choosing the best hypothesis in an incremental problem setting is in particular challenging due to high sensitivity to measurement aliasing and possibly insufficient amount of data. Selecting an incorrect hypothesis introduces outliers and can lead to catastrophic results. To address these challenges we develop a model-selection based approach to choose the most probable hypothesis, while resorting to Chinese Restaurant Process to represent statistical knowledge regarding hypothesis prior probabilities. We evaluate our approach in real-data experiments.
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    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].
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    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.
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    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.