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iSAM: Incremental Smoothing and Mapping
, 2008
"... We present incremental smoothing and mapping (iSAM), a novel approach to the simultaneous localization and mapping problem that is based on fast incremental matrix factorization. iSAM provides an efficient and exact solution by updating a QR factorization of the naturally sparse smoothing informatio ..."
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Cited by 153 (35 self)
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We present incremental smoothing and mapping (iSAM), a novel approach to the simultaneous localization and mapping problem that is based on fast incremental matrix factorization. iSAM provides an efficient and exact solution by updating a QR factorization of the naturally sparse smoothing information matrix, therefore recalculating only the matrix entries that actually change. iSAM is efficient even for robot trajectories with many loops as it avoids unnecessary fillin in the factor matrix by periodic variable reordering. Also, to enable data association in realtime, we provide efficient algorithms to access the estimation uncertainties of interest based on the factored information matrix. We systematically evaluate the different components of iSAM as well as the overall algorithm using various simulated and realworld datasets for both landmark and poseonly settings.
Square Root SAM: Simultaneous localization and mapping via square root information smoothing
 International Journal of Robotics Reasearch
, 2006
"... Solving 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 filterbased solutions to the problem. In particular, we look at approaches that factorize either th ..."
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Cited by 144 (39 self)
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Solving 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 filterbased 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 nonlinear 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 largescale environments that underscore the potential of these methods as an alternative to EKFbased approaches. 1
iSAM2: Incremental Smoothing and Mapping Using the Bayes Tree
"... We 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 probabili ..."
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Cited by 69 (26 self)
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We 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 reordering 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.
Compressive Cooperative Sensing and Mapping in Mobile Networks
"... Abstract—In this paper we consider a mobile cooperative network that is tasked with building a map of the spatial variations of a parameter of interest, such as an obstacle map or an aerial map. We propose a new framework that allows the nodes to build a map of the parameter of interest with a small ..."
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Cited by 17 (2 self)
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Abstract—In this paper we consider a mobile cooperative network that is tasked with building a map of the spatial variations of a parameter of interest, such as an obstacle map or an aerial map. We propose a new framework that allows the nodes to build a map of the parameter of interest with a small number of measurements. By using the recent results in the area of compressive sensing, we show how the nodes can exploit the sparse representation of the parameter of interest in the transform domain in order to build a map with minimal sensing. The proposed work allows the nodes to efficiently map the areas that are not sensed directly. To illustrate the performance of the proposed framework, we show how the nodes can build an aerial map or a map of obstacles with sparse sensing. We furthermore show how our proposed framework enables a novel noninvasive approach to mapping obstacles by using wireless channel measurements. Index Terms—mobile networks, compressive sensing, mapping of obstacles, cooperative mapping I.
1 Subgraphpreconditioned Conjugate Gradients for Large Scale SLAM
"... Figure 1: The main idea in this paper is to combine the advantages of direct and iterative methods: we identify a subgraph that can easily be solved using direct methods, and use that as a preconditioner in conjugate gradients. This is illustrated above with a map of Beijing, where the subgraph is a ..."
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Cited by 16 (6 self)
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Figure 1: The main idea in this paper is to combine the advantages of direct and iterative methods: we identify a subgraph that can easily be solved using direct methods, and use that as a preconditioner in conjugate gradients. This is illustrated above with a map of Beijing, where the subgraph is a spanning tree (in black), and the remaining loopclosing constraints are shown in red. Abstract — In this paper we propose an efficient preconditioned conjugate gradients (PCG) approach to solving largescale SLAM problems. While direct methods, popular in the literature, exhibit quadratic convergence and can be quite efficient for sparse problems, they typically require a lot of storage as well as efficient elimination orderings to be found. In contrast, iterative optimization methods only require access to the gradient and have a small memory footprint, but can suffer from poor convergence. Our new method, subgraph preconditioning, is obtained by reinterpreting the method of conjugate gradients in terms of the graphical model representation of the SLAM problem. The main idea is to combine the advantages of direct and iterative methods, by identifying a subproblem that can be easily solved using direct methods, and solving for the remaining part using PCG. The easy subproblems correspond to a spanning tree, a planar subgraph, or any other substructure that can be efficiently solved. As such, our approach provides new insights into the performance of state of the art iterative SLAM methods based on reparameterized stochastic gradient descent. The efficiency of our new algorithm is illustrated on large datasets, both simulated and real.
Multilevel submap based slam using nested dissection
 in IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems (IROS
, 2010
"... Fig. 1. Our algorithm recursively partitions the SLAM graph into a submap tree, and the optimization runs from the leaves to the root. Following the treemap visualization [1], each rectangle represents a submap, and the subrectangles represent the submaps in the child level. The red and green dots ..."
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Cited by 12 (8 self)
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Fig. 1. Our algorithm recursively partitions the SLAM graph into a submap tree, and the optimization runs from the leaves to the root. Following the treemap visualization [1], each rectangle represents a submap, and the subrectangles represent the submaps in the child level. The red and green dots are robot poses and landmarks respectively. From left to right: 1). the finest level of submaps; 2). the coarsest level of submaps; 3). the optimized full map. Abstract — We propose a novel batch algorithm for SLAM problems that distributes the workload in a hierarchical way. We show that the original SLAM graph can be recursively partitioned into multiplelevel submaps using the nested dissection algorithm, which leads to the cluster tree, a powerful graph representation. By employing the nested dissection algorithm, our algorithm greatly minimizes the dependencies between two subtrees, and the optimization of the original SLAM graph can be done using a bottomup inference along the corresponding cluster tree. To speed up the computation, we also introduce a base node for each submap and use it to represent the rigid transformation of the submap in the global coordinate frame. As a result, the optimization moves the base nodes rather than the actual submap variables. We demonstrate that our algorithm is not only exact but also much faster than alternative approaches in both simulations and realworld experiments. I.
Probabilistic Structure Matching for Visual SLAM with a MultiCamera Rig
"... We propose to use a multicamera rig for simultaneous localization and mapping (SLAM), providing flexibility in sensor placement on mobile robot platforms while exploiting the stronger localization constraints provided by omnidirectional sensors. In this context, we present a novel probabilistic ap ..."
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Cited by 4 (0 self)
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We propose to use a multicamera rig for simultaneous localization and mapping (SLAM), providing flexibility in sensor placement on mobile robot platforms while exploiting the stronger localization constraints provided by omnidirectional sensors. In this context, we present a novel probabilistic approach to data association, that takes into account that features can also move between cameras under robot motion. Our approach circumvents the combinatorial data association problem by using an incremental expectation maximization algorithm. In the expectation step we determine a distribution over correspondences by sampling. In the maximization step, we find optimal parameters of a density over the robot motion and environment structure. By summarizing the sampling results in socalled virtual measurements, the resulting optimization simplifies to the equivalent optimization problem for known correspondences. We present results for simulated data, as well as for data obtained by a mobile robot equipped with a multicamera rig. Key words: localization, mapping, mobile robot, multicamera rig, omnidirectional, SFM
Evaluating the Performance of Map Optimization Algorithms
"... Abstract — Localization and mapping are essential capabilities of virtually all mobile robots. These topics have been the focus of a great deal of research, but it is not always easy to tell which methods are best. This paper discusses performance evaluation for an important subproblem of robot map ..."
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Cited by 4 (0 self)
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Abstract — Localization and mapping are essential capabilities of virtually all mobile robots. These topics have been the focus of a great deal of research, but it is not always easy to tell which methods are best. This paper discusses performance evaluation for an important subproblem of robot mapping, map optimization. We explore aspects underlying the evaluation of map optimization such as the quality of the result and computational complexity. For each aspect we discuss evaluation metrics and provide specific recommendations. I.
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