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Dellaert, Frank

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Author: Indelman, Vadim ×

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Distributed Real-time Cooperative Localization and Mapping Using an Uncertainty-Aware Expectation Maximization Approach

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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Planning in the Continuous Domain: a Generalized Belief Space Approach for Autonomous Navigation in Unknown Environments

2015 , Indelman, Vadim , Carlone, Luca , Dellaert, Frank

We investigate 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. Decision making is entrusted to a Model Predictive Control (MPC) scheme. The formulation is valid for general cost functions and does not discretize the state or control space, enabling planning in continuous domain. Moreover, it allows to relax the assumption of maximum likelihood observations: predicted measurements are treated as random variables, and binary random variables are used to model the event that a measurement is actually taken by the robot. We successfully apply our approach to the problem of uncertainty-constrained exploration, in which the robot has to perform tasks in an unknown environment, while maintaining localization uncertainty within given bounds. We present an extensive numerical analysis of the proposed approach and compare it against related work. In practice, our planning approach produces smooth and natural trajectories and is able to impose soft upper bounds on the uncertainty. Finally, we exploit the results of this analysis to identify current limitations and show that the proposed framework can accommodate several desirable extensions.

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An Experimental Study of Robust Distributed Multi-Robot Data Association from Arbitrary Poses

2014-06 , Nelson, Erik , Indelman, Vadim , Michael, Nathan , Dellaert, Frank

In this work, we experimentally investigate the problem of computing the relative transformation between multiple vehicles from corresponding interrobot observations during autonomous operation in a common unknown environment. Building on our prior work, we consider an EM-based methodology which evaluates sensory observations gathered over vehicle trajectories to establish robust relative pose transformations between robots. We focus on experimentally evaluating the performance of the approach as well as its computational complexity and shared data requirements using multiple autonomous vehicles (aerial robots). We describe an observation subsampling technique which utilizes laser scan autocovariance to reduce the total number of observations shared between robots. Employing this technique reduces run time of the algorithm significantly, while only slightly diminishing the accuracies of computed inter-robot transformations. Finally, we provide discussion on data transfer and the feasibility of implementing the approach on a mesh network.

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Eliminating Conditionally Independent Sets in Factor Graphs: A Unifying Perspective based on Smart Factors

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.

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Information-based Reduced Landmark SLAM

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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Incremental Light Bundle Adjustment for Structure From Motion and Robotics

2015 , Indelman, Vadim , Roberts, Richard , Dellaert, Frank

Bundle adjustment (BA) is essential in many robotics and structure-from-motion applications. In robotics, often a bundle adjustment solution is desired to be available incrementally as new poses and 3D points are observed. Similarly in batch structure from motion, cameras are typically added incrementally to allow good initializations. Current incremental BA methods quickly become computationally expensive as more camera poses and 3D points are added into the optimization. In this paper we introduce incremental light bundle adjustment (iLBA), an efficient optimization framework that substantially reduces computational complexity compared to incremental bundle adjustment. First, the number of variables in the optimization is reduced by algebraic elimination of observed 3D points, leading to a structureless BA. The resulting cost function is formulated in terms of three-view constraints instead of re-projection errors and only the camera poses are optimized. Second, the optimization problem is represented using graphical models and incremental inference is applied, updating the solution using adaptive partial calculations each time a new camera is incorporated into the optimization. Typically, only a small fraction of the camera poses are recalculated in each optimization step. The 3D points, although not explicitly optimized, can be reconstructed based on the optimized camera poses at any time. We study probabilistic and computational aspects of iLBA and compare its accuracy against incremental BA and another recent structureless method using real-imagery and synthetic datasets. Results indicate iLBA is 2-10 times faster than incremental BA, depending on number of image observations per frame.

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Planning Under Uncertainty in the Continuous Domain: A Generalized Belief Space Approach

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.

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Distributed Navigation with Unknown Initial Poses and Data Association via Expectation Maximization

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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Incremental Distributed Robust Inference from Arbitrary Robot Poses via EM and Model Selection

2014-07 , 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 perceptual 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 and use the Chinese restaurant process to disambiguate the hypotheses prior probabilities over time.

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Concurrent Filtering and Smoothing: A Parallel Architecture for Real-Time Navigation and Full Smoothing

2014 , Williams, Stephen , Indelman, Vadim , Kaess, Michael , Roberts, Richard , Leonard, John J. , Dellaert, Frank

We present a parallelized navigation architecture that is capable of running in real-time and incorporating long-term loop closure constraints while producing the optimal Bayesian solution. This architecture splits the inference problem into a low-latency update that incorporates new measurements using just the most recent states (filter), and a high-latency update that is capable of closing long loops and smooths using all past states (smoother). This architecture employs the probabilistic graphical models of Factor Graphs, which allows the low-latency inference and high-latency inference to be viewed as sub-operations of a single optimization performed within a single graphical model. A specific factorization of the full joint density is employed that allows the different inference operations to be performed asynchronously while still recovering the optimal solution produced by a full batch optimization. Due to the real-time, asynchronous nature of this algorithm, updates to the state estimates from the high-latency smoother will naturally be delayed until the smoother calculations have completed. This architecture has been tested within a simulated aerial environment and on real data collected from an autonomous ground vehicle. In all cases, the concurrent architecture is shown to recover the full batch solution, even while updated state estimates are produced in real-time.

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