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Dellaert,
Frank
Dellaert,
Frank
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ItemConcurrent Filtering and Smoothing: A Parallel Architecture for Real-Time Navigation and Full Smoothing(Georgia Institute of Technology, 2014) Williams, Stephen ; Indelman, Vadim ; Kaess, Michael ; Roberts, Richard ; Leonard, John J. ; Dellaert, FrankWe 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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ItemInformation Fusion in Navigation Systems via Factor Graph Based Incremental Smoothing(Georgia Institute of Technology, 2013-08) Indelman, Vadim ; Williams, Stephen ; Kaess, Michael ; Dellaert, FrankThis paper presents a new approach for high-rate information fusion in modern inertial navigation systems, that have a variety of sensors operating at different frequencies. Optimal information fusion corresponds to calculating the maximum a posteriori estimate over the joint probability distribution function (pdf) of all states, a computationally-expensive process in the general case. Our approach consists of two key components, which yields a flexible, high-rate, near-optimal inertial navigation system. First, the joint pdf is represented using a graphical model, the factor graph, that fully exploits the system sparsity and provides a plug and play capability that easily accommodates the addition and removal of measurement sources. Second, an efficient incremental inference algorithm over the factor graph is applied, whose performance approaches the solution that would be obtained by a computationally-expensive batch optimization at a fraction of the computational cost. To further aid high-rate performance, we introduce an equivalent IMU factor based on a recently developed technique for IMU pre-integration, drastically reducing the number of states that must be added to the system. The proposed approach is experimentally validated using real IMU and imagery data that was recorded by a ground vehicle, and a statistical performance study is conducted in a simulated aerial scenario. A comparison to conventional fixed-lag smoothing demonstrates that our method provides a considerably improved trade-off between computational complexity and performance.
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ItemAutonomous Flight in GPS-Denied Environments Using Monocular Vision and Inertial Sensors(Georgia Institute of Technology, 2013-04) Wu, Allen D. ; Johnson, Eric N. ; Kaess, Michael ; Dellaert, Frank ; Chowdhary, GirishA vision-aided inertial navigation system that enables autonomous flight of an aerial vehicle in GPS-denied environments is presented. Particularly, feature point information from a monocular vision sensor are used to bound the drift resulting from integrating accelerations and angular rate measurements from an Inertial Measurement Unit (IMU) forward in time. An Extended Kalman filter framework is proposed for performing the tasks of vision-based mapping and navigation separately. When GPS is available, multiple observations of a single landmark point from the vision sensor are used to estimate the point’s location in inertial space. When GPS is not available, points that have been sufficiently mapped out can be used for estimating vehicle position and attitude. Simulation and flight test results of a vehicle operating autonomously in a simplified loss-of-GPS scenario verify the presented method.
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ItemiSAM2: Incremental Smoothing and Mapping Using the Bayes Tree(Georgia Institute of Technology, 2012-02) Kaess, Michael ; Johannsson, Hordur ; Roberts, Richard ; Ila, Viorela ; Leonard, John ; Dellaert, FrankWe present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root information matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of the matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, named iSAM2, which achieves improvements in efficiency through incremental variable re-ordering and fluid relinearization, eliminating the need for periodic batch steps. We analyze various properties of iSAM2 in detail, and show on a range of real and simulated datasets that our algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.
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ItemSquare Root SAM Simultaneous Localization and Mapping via Square Root Information Smoothing(Georgia Institute of Technology, 2006) Dellaert, Frank ; Kaess, MichaelSolving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filter-based solutions to the problem. In particular, we look at approaches that factorize either the associated information matrix or the measurement Jacobian into square root form. Such techniques have several significant advantages over the EKF: they are faster yet exact, they can be used in either batch or incremental mode, are better equipped to deal with non-linear process and measurement models, and yield the entire robot trajectory, at lower cost for a large class of SLAM problems. In addition, in an indirect but dramatic way, column ordering heuristics automatically exploit the locality inherent in the geographic nature of the SLAM problem. In this paper we present the theory underlying these methods, along with an interpretation of factorization in terms of the graphical model associated with the SLAM problem. We present both simulation results and actual SLAM experiments in large-scale environments that underscore the potential of these methods as an alternative to EKF-based approaches.