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## iSAM2: Incremental Smoothing and Mapping Using the Bayes Tree

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8752 |
Probabilistic Reasoning in Intelligence Systems
- Pearl
- 1988
(Show Context)
Citation Context ...phs, elimination is done via a bipartite elimination game, as described by Heggernes and Matstoms (1996). This can be understood as taking apart the factor graph and transforming it into a Bayes net (=-=Pearl, 1988-=-). One proceeds by eliminating one variable at a time, and converting it into a node of the Bayes net, which is gradually built up. AfterM. Kaess, H. Johannsson, R. Roberts, V. Ila, J. Leonard, and F... |

4681 |
Multiple View Geometry in Computer Vision. Cambridge Univ
- Hartley, Zisserman
- 2000
(Show Context)
Citation Context ...tinuable Levenberg-Marquardt algorithm and focuses on a fast setup of the information matrix, often the most costly part in batch factorization. Smoothing is closely related to structure from motion (=-=Hartley and Zisserman, 2000-=-) and bundle adjustment (Triggs et al., 1999) in computer vision. Both bundle adjustment and the smoothing formulation of SLAM keep all poses and landmarks in the estimation problem (pose-graph SLAM i... |

1756 | Factor graphs and the sum-product algorithm
- Kschischang, Frey, et al.
- 2001
(Show Context)
Citation Context ...detailed comparison with other SLAM algorithms in terms of computation and accuracy, using a range of 2D and 3D, simulated and real-world, pose-only and landmark-based datasets. Fig. 2: Factor graph (=-=Kschischang et al., 2001-=-) formulation of the SLAM problem, where variable nodes are shown as large circles, and factor nodes (measurements) as small solid circles. The factors shown are odometry measurements u, a prior p, lo... |

1304 |
Probabilistic Robotics
- Thrun, Burgard, et al.
- 2005
(Show Context)
Citation Context ...t when applied to the inherently nonlinear SLAM problem (Julier and Uhlmann, 2001), i.e., the average taken over a large number of experiments diverges from the true solution. In contrast, full SLAM (=-=Thrun et al., 2005-=-) retains all robot poses and can provide an exact solution, which does not suffer from inconsistency. Folkesson and Christensen (2004) presented Graphical SLAM, a graph-based full SLAM solution that ... |

872 |
Probabilistic Graphical Models: Principles and Techniques
- Koller, Friedman
- 2009
(Show Context)
Citation Context ...l Bayes net can be converted into a treestructured graphical model in which these operations are easy. This data structure is similar to the clique tree (Pothen and Sun, 1992; Blair and Peyton, 1993; =-=Koller and Friedman, 2009-=-), also known as the junction tree in the AI literature (Cowell et al., 1999), which has already been exploited for distributed inference in SLAM (Dellaert et al., 2005; Paskin, 2003). However, the ne... |

770 |
Probabilistic Networks and Expert Systems
- Cowell
- 1999
(Show Context)
Citation Context ...operations are easy. This data structure is similar to the clique tree (Pothen and Sun, 1992; Blair and Peyton, 1993; Koller and Friedman, 2009), also known as the junction tree in the AI literature (=-=Cowell et al., 1999-=-), which has already been exploited for distributed inference in SLAM (Dellaert et al., 2005; Paskin, 2003). However, the new data structure we propose here, the Bayes tree, is directed and correspond... |

553 | Bundle Adjustment - A Modern Synthesis
- Triggs, Mclauchlan, et al.
- 2000
(Show Context)
Citation Context ...n a fast setup of the information matrix, often the most costly part in batch factorization. Smoothing is closely related to structure from motion (Hartley and Zisserman, 2000) and bundle adjustment (=-=Triggs et al., 1999-=-) in computer vision. Both bundle adjustment and the smoothing formulation of SLAM keep all poses and landmarks in the estimation problem (pose-graph SLAM is a special case that omits landmarks). The ... |

525 | Globally consistent range scan alignment for environment mapping - Lu, Milios - 1997 |

488 | A solution to the simultaneous localization and map building (SLAM) problem
- Dissanayake, Newman, et al.
- 2001
(Show Context)
Citation Context ...e environment, new measurements often only affect small parts of the tree, and only those parts are re-calculated. as is standard in the SLAM literature (Smith et al., 1987; Castellanos et al., 1999; =-=Dissanayake et al., 2001-=-), the factored objective function to maximize (2) corresponds to the nonlinear least-squares criterion argmin Θ 1 (−log f (Θ)) = argmin Θ 2 ∑ i ‖hi(Θi) − zi‖ 2 Σi (4) where hi(Θi) is a measurement fu... |

378 | Complexity of finding embeddings in a k-tree
- Arnborg, Corneil, et al.
- 1987
(Show Context)
Citation Context ...slower computations. Fill-in can usually not be completely avoided, unless the original Bayes net already is chordal. While finding the variable ordering that leads to the minimal fill-in is NP-hard (=-=Arnborg et al., 1987-=-) for general problems, one typically uses heuristics such as the column approximate minimum degree (COLAMD) algorithm by Davis et al. (2004), which provide close x1 x2 x3 Fig. 7: For a trajectory wit... |

313 | An approximate minimum degree ordering algorithm
- Amestoy, Davis, et al.
- 1996
(Show Context)
Citation Context ...t steps, we therefore propose an incremental variable ordering strategy that forces the most recently accessed variables to the end of the ordering. We use the constrained COLAMD (CCOLAMD) algorithm (=-=Davis et al., 2004-=-) to both, force the most recently accessed variables to the end and still provide a good overall ordering. Subsequent updates will then only affect a small part of the tree, and can therefore be expe... |

298 | Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs - Tarjan, Yannakakis - 1984 |

204 |
Generalized nested dissection
- Lipton, Rose, et al.
- 1979
(Show Context)
Citation Context ...application of COLAMD. To understand how the local variable ordering affects the cost of subsequent updates, consider a simple loop example in Fig. 7. In the case of a simple loop, nested dissection (=-=Lipton and Tarjan, 1979-=-) provides the optimal ordering. The first cut can either (a) not include the loop closing, or (b) include the loop closing, and both solutions are equivalent in terms of fill-in. However, there is a ... |

158 |
Methods for modifying matrix factorizations
- Gill, Golub, et al.
- 1974
(Show Context)
Citation Context ...hich performs fast incremental updates of the square root information matrix, yet is able to compute the full map and trajectory at any time. New measurements are added using matrix update equations (=-=Gill et al., 1974-=-; Gentleman, 1973; Golub and Loan, 1996), so that previously calculated components of the square root information matrix are reused. However, to remain efficient and consistent, iSAM requires periodic... |

158 | A stochastic map for uncertain spatial relationships
- Smith, Self, et al.
- 1988
(Show Context)
Citation Context ...lution, the Bayes tree. As a robot explores the environment, new measurements often only affect small parts of the tree, and only those parts are re-calculated. as is standard in the SLAM literature (=-=Smith et al., 1987-=-; Castellanos et al., 1999; Dissanayake et al., 2001), the factored objective function to maximize (2) corresponds to the nonlinear least-squares criterion argmin Θ 1 (−log f (Θ)) = argmin Θ 2 ∑ i ‖hi... |

151 | The SPmap: A probabilistic framework for simultaneous localization and map building
- Castellanos, Montiel, et al.
- 1999
(Show Context)
Citation Context ...ee. As a robot explores the environment, new measurements often only affect small parts of the tree, and only those parts are re-calculated. as is standard in the SLAM literature (Smith et al., 1987; =-=Castellanos et al., 1999-=-; Dissanayake et al., 2001), the factored objective function to maximize (2) corresponds to the nonlinear least-squares criterion argmin Θ 1 (−log f (Θ)) = argmin Θ 2 ∑ i ‖hi(Θi) − zi‖ 2 Σi (4) where ... |

151 | iSAM: Incremental smoothing and mapping
- Kaess, Ranganathan, et al.
- 2008
(Show Context)
Citation Context .... 1 shows a summary of the necessary steps to solve the smoothing formulation of the SLAM problem with direct methods. Incremental and online smoothing can be achieved by our original iSAM algorithm (=-=Kaess et al., 2008-=-), but relinearization is only performed during periodic batch reordering steps. A batch solution, as proposed above, performs unnecessary calculations, because it solves the complete problem at every... |

149 | An introduction to chordal graphs and clique trees
- Blair, Peyton
- 1993
(Show Context)
Citation Context ...well known that a chordal Bayes net can be converted into a treestructured graphical model in which these operations are easy. This data structure is similar to the clique tree (Pothen and Sun, 1992; =-=Blair and Peyton, 1993-=-; Koller and Friedman, 2009), also known as the junction tree in the AI literature (Cowell et al., 1999), which has already been exploited for distributed inference in SLAM (Dellaert et al., 2005; Pas... |

145 | FrameSLAM: from bundle adjustment to real-time visual mapping
- Agrawal, Konolige
- 2008
(Show Context)
Citation Context ...e” to run indefinitely remains open. Note that the number of landmarks per frame is typically much lower for laser range-based applications than for visual SLAM applications (Eade and Drummond, 2007; =-=Konolige and Agrawal, 2008-=-; Paz et al., 2008; Strasdat et al., 2010). However, smoothing has recently also been shown to be the method of choice for visual SLAM in many situations (Strasdat et al., 2010). In an incremental set... |

141 | Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing,” Intl
- Dellaert, Kaess
- 2006
(Show Context)
Citation Context ...opy SAM (Ranganathan et al., 2007) applies loopy belief propagation directly to the SLAM graph. The sparse linear algebra perspective has been explored in Smoothing and Mapping (SAM) (Dellaert, 2005; =-=Dellaert and Kaess, 2006-=-; Kaess et al., 2007, 2008). The matrices associated with smoothing are typically very sparse, and one can do much better than the cubic complexity associated with factorizing a dense matrix (Krauthau... |

135 | Practical parameterization of rotations using the exponential map
- Grassia
- 1998
(Show Context)
Citation Context ...(Hall, 2000). Our original SAM work (Dellaert and Kaess, 2006) used local updates of Euler angles for visual SLAM. Here, as representation, we use rotation matrices in iSAM2 and Quaternions in iSAM1 (=-=Grassia, 1998-=-). We have found that, depending on the application, each representation has its own advantages. Comparing the computational cost of different algorithms is not a simple task. Tight complexity bounds ... |

132 |
Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
- Hall
- 2004
(Show Context)
Citation Context ...n graphical models. The association of cliques and their conditional densities with rows in the R factor is indicated by color. tions in computer vision, an exponential map based on Lie group theory (=-=Hall, 2000-=-) is used instead. The matrix A above is a sparse block-matrix, and its graphical model counterpart is a Gaussian factor graph (i.e. the original factor graph linearized at Θ) with exactly the same st... |

126 | Thin junction tree filters for simultaneous localization and mapping
- Paskin
- 2002
(Show Context)
Citation Context ...orithms. Taking a graphical model perspective to probabilistic inference in SLAM has a rich history (Brooks, 1985) and has especially led to several novel and exciting developments in the last years (=-=Paskin, 2003-=-; Folkesson and Christensen, 2004; Frese et al., 2005; Frese, 2006; Folkesson and Christensen, Draft manuscript, April 6, 2011. Submitted to IJRR. M. Kaess, H. Johannsson, and J. Leonard are with the ... |

108 | A multilevel relaxation algorithm for simultaneous localisation and mapping
- Frese, Larsson, et al.
- 2005
(Show Context)
Citation Context ...o probabilistic inference in SLAM has a rich history (Brooks, 1985) and has especially led to several novel and exciting developments in the last years (Paskin, 2003; Folkesson and Christensen, 2004; =-=Frese et al., 2005-=-; Frese, 2006; Folkesson and Christensen, Draft manuscript, April 6, 2011. Submitted to IJRR. M. Kaess, H. Johannsson, and J. Leonard are with the Computer Science and Artificial Intelligence Laborato... |

107 | RAJAMANICKAM S.: Algorithm 887: Cholmod, supernodal sparse cholesky factorization and update/downdate
- CHEN, DAVIS, et al.
(Show Context)
Citation Context ..., which becomes evident in the per iteration time plots for City20000 and W10000 in Fig. 14ab. That difference can partially be explained by the fact that SPA uses the well optimized CHOLMOD library (=-=Chen et al., 2008-=-) for batch Cholesky factorization, while for the algorithms underlying iSAM2 no such library is available yet and we are using our own research implementation. Fig. 15 shows how time is spent in iSAM... |

104 | A Counter Example to the Theory of Simultaneous Localization and Map Building 2001
- Julier, Uhlmann, et al.
(Show Context)
Citation Context ...TF), which provides an incremental solution directly based on graphical models. However, filtering is applied, which is known to be inconsistent when applied to the inherently nonlinear SLAM problem (=-=Julier and Uhlmann, 2001-=-), i.e., the average taken over a large number of experiments diverges from the true solution. In contrast, full SLAM (Thrun et al., 2005) retains all robot poses and can provide an exact solution, wh... |

88 |
Large-scale map-making
- Konolige
- 2004
(Show Context)
Citation Context ...wn iterative techniques such as relaxation (Duckett et al., 2002; Bosse et al., 2004; Thrun et al., 2005), gradient descent (Folkesson and Christensen, 2004, 2007), preconditioned conjugate gradient (=-=Konolige, 2004-=-; Dellaert et al., 2010), multi-level relaxation (Frese et al., 2005), and belief propagation (Ranganathan et al., 2007). Direct methods, such as QR and Cholesky matrix factorization, provide the adva... |

80 | A tree parameterization for efficiently computing maximum likelihood maps using gradient descent - Grisetti, Stachniss, et al. - 2007 |

80 | Fast iterative alignment of pose graphs with poor initial estimates
- Olson, Leonard, et al.
- 2006
(Show Context)
Citation Context ... proposed constrained ordering strategy in Fig. 8, by comparing it to the naive way of simply applying COLAMD. The top row of Fig. 8 shows a color coded trajectory of the Manhattan simulated dataset (=-=Olson et al., 2006-=-). The robot starts in the center, traverses the loop counter clockwise, and finally ends at the bottom left. The number of affected variables significantly drops from the naive approach (left) to the... |

78 |
Simultaneous localization and map building in large-scale cyclic environments using the Atlas framework
- Bosse, Newman, et al.
(Show Context)
Citation Context ...on (Gutmann and Nebel, 1997). A number of improved and numerically more stable algorithms have since been developed, based on well known iterative techniques such as relaxation (Duckett et al., 2002; =-=Bosse et al., 2004-=-; Thrun et al., 2005), gradient descent (Folkesson and Christensen, 2004, 2007), preconditioned conjugate gradient (Konolige, 2004; Dellaert et al., 2010), multi-level relaxation (Frese et al., 2005),... |

67 |
Visual map making for a mobile robot
- Brooks
- 1985
(Show Context)
Citation Context ...ssential for most real applications, therefore our work focuses on efficient incremental online algorithms. Taking a graphical model perspective to probabilistic inference in SLAM has a rich history (=-=Brooks, 1985-=-) and has especially led to several novel and exciting developments in the last years (Paskin, 2003; Folkesson and Christensen, 2004; Frese et al., 2005; Frese, 2006; Folkesson and Christensen, Draft ... |

66 |
1809) Theoria motus corporum coelestium in sectionibus conicis solem ambientium. Hamburg: Perthes et Besser. English translation by C.H. Davis, reprinted by
- Gauss
- 1963
(Show Context)
Citation Context ...orithm. Variable elimination (Blair and Peyton, 1993; Cowell et al., 1999) originated in order to solve systems of linear equations, and was first applied in modern times by Gauss in the early 1800s (=-=Gauss, 1809-=-). In factor graphs, elimination is done via a bipartite elimination game, as described by Heggernes and Matstoms (1996). This can be understood as taking apart the factor graph and transforming it in... |

66 | Real-time monocular SLAM: Why filter
- Strasdat, Montiel, et al.
- 2010
(Show Context)
Citation Context ...oposed by Dellaert (2005), but is now widely used (Dellaert and Kaess, 2006; Frese, 2006; Folkesson et al., 2007; Kaess et al., 2008; Mahon et al., 2008; Grisetti et al., 2010; Konolige et al., 2010; =-=Strasdat et al., 2010-=-). Square Root SAM (Dellaert, 2005; Dellaert and Kaess, 2006) performs smoothing by Cholesky factorization of the complete, naturally sparse information matrix in every step using the Levenberg-Marqua... |

60 | Graphical SLAM - a selfcorrecting map
- Folkesson, Christensen
- 2004
(Show Context)
Citation Context ...g a graphical model perspective to probabilistic inference in SLAM has a rich history (Brooks, 1985) and has especially led to several novel and exciting developments in the last years (Paskin, 2003; =-=Folkesson and Christensen, 2004-=-; Frese et al., 2005; Frese, 2006; Folkesson and Christensen, Draft manuscript, April 6, 2011. Submitted to IJRR. M. Kaess, H. Johannsson, and J. Leonard are with the Computer Science and Artificial I... |

58 | Multi-robot mapping using manifold representations - Howard - 2004 |

57 |
Square Root SAM: simultaneous location and mapping via square root information smoothing
- Dellaert
- 2005
(Show Context)
Citation Context ...es of a tree. Loopy SAM (Ranganathan et al., 2007) applies loopy belief propagation directly to the SLAM graph. The sparse linear algebra perspective has been explored in Smoothing and Mapping (SAM) (=-=Dellaert, 2005-=-; Dellaert and Kaess, 2006; Kaess et al., 2007, 2008). The matrices associated with smoothing are typically very sparse, and one can do much better than the cubic complexity associated with factorizin... |

57 |
Least squares computations by Givens transformations without square roots
- Gentleman
- 1973
(Show Context)
Citation Context ...incremental updates of the square root information matrix, yet is able to compute the full map and trajectory at any time. New measurements are added using matrix update equations (Gill et al., 1974; =-=Gentleman, 1973-=-; Golub and Loan, 1996), so that previously calculated components of the square root information matrix are reused. However, to remain efficient and consistent, iSAM requires periodic batch steps to a... |

43 | Hierarchical optimization on manifolds for online 2d and 3d mapping
- Grisetti, Kümmerle, et al.
- 2010
(Show Context)
Citation Context ...refactorized in each step, as we show below. 5 Comparison to Other Methods We compare iSAM2 to other state-of-the-art SLAM algorithms, in particular the iSAM1 algorithm (Kaess et al., 2008), HOG-Man (=-=Grisetti et al., 2010-=-) and SPA (Konolige et al.,12 iSAM2: Incremental Smoothing and Mapping Using the Bayes Tree (a) City20000 (b) W10000 (c) Intel (d) Killian Court Fig. 11: 2D pose-graph datasets, including simulated d... |

37 | Adaptive relative bundle adjustment - Sibley, Mei, et al. - 2009 |

34 | Monocular SLAM as a graph of coalesced observations
- Eade, Drummond
- 2007
(Show Context)
Citation Context ...g a “perpetual SLAM engine” to run indefinitely remains open. Note that the number of landmarks per frame is typically much lower for laser range-based applications than for visual SLAM applications (=-=Eade and Drummond, 2007-=-; Konolige and Agrawal, 2008; Paz et al., 2008; Strasdat et al., 2010). However, smoothing has recently also been shown to be the method of choice for visual SLAM in many situations (Strasdat et al., ... |

29 | Covariance recovery from a square root information matrix for data association
- Kaess, Dellaert
- 2009
(Show Context)
Citation Context ... insights into the recovery of marginal covariances, as we believe that simple recursive algorithms in terms of the Bayes tree are formally equivalent to the dynamic programming methods described in (=-=Kaess and Dellaert, 2009-=-). The graph based structure is also suitable for exploiting parallelization that is becoming available in newer processors. Acknowledgments M. Kaess, H. Johannsson and J. Leonard were partially suppo... |

29 |
Efficient view-based SLAM using visual loop closures
- Mahon, Williams, et al.
- 2008
(Show Context)
Citation Context ...sive. An efficient sparse factorization for SLAM has first been proposed by Dellaert (2005), but is now widely used (Dellaert and Kaess, 2006; Frese, 2006; Folkesson et al., 2007; Kaess et al., 2008; =-=Mahon et al., 2008-=-; Grisetti et al., 2010; Konolige et al., 2010; Strasdat et al., 2010). Square Root SAM (Dellaert, 2005; Dellaert and Kaess, 2006) performs smoothing by Cholesky factorization of the complete, natural... |

27 | Multiple relative pose graphs for robust cooperative mapping
- Kim, Kaess, et al.
- 2010
(Show Context)
Citation Context ...bability distributions or cost functions of any number of variables, allowing the inclusion of calibration parameters or spatial separators as used in T-SAM (Ni et al., 2007) and cooperative mapping (=-=Kim et al., 2010-=-). Gaussian Case When assuming Gaussian measurement models ( fi(Θi) ∝ exp − 1 2 ‖hi(Θi) − zi‖ 2 ) Σi (3)M. Kaess, H. Johannsson, R. Roberts, V. Ila, J. Leonard, and F. Dellaert 3 x398,x399,x400 x396,... |

26 | Tectonic SAM: Exact; out-ofcore; submap-based SLAM
- Ni, Steedly, et al.
- 2007
(Show Context)
Citation Context ...ion allows our work to support general probability distributions or cost functions of any number of variables, allowing the inclusion of calibration parameters or spatial separators as used in T-SAM (=-=Ni et al., 2007-=-) and cooperative mapping (Kim et al., 2010). Gaussian Case When assuming Gaussian measurement models ( fi(Θi) ∝ exp − 1 2 ‖hi(Θi) − zi‖ 2 ) Σi (3)M. Kaess, H. Johannsson, R. Roberts, V. Ila, J. Leon... |

24 |
Navigation mobiler roboter mit laserscans
- Gutmann, Nebel
- 1997
(Show Context)
Citation Context ...M problem was presented by Lu and Milios (1997), where the estimation problem is formulated as a network of constraints between robot poses. The first solution was implemented using matrix inversion (=-=Gutmann and Nebel, 1997-=-). A number of improved and numerically more stable algorithms have since been developed, based on well known iterative techniques such as relaxation (Duckett et al., 2002; Bosse et al., 2004; Thrun e... |

22 | The Bayes tree: An algorithmic foundation for probabilistic robot mapping - Kaess, Ila, et al. - 2010 |

19 | A multifrontal QR factorization approach to distributed inference applied to multi-robot localization and mapping
- Dellaert, Kipp, et al.
- 2005
(Show Context)
Citation Context ...92; Blair and Peyton, 1993; Koller and Friedman, 2009), also known as the junction tree in the AI literature (Cowell et al., 1999), which has already been exploited for distributed inference in SLAM (=-=Dellaert et al., 2005-=-; Paskin, 2003). However, the new data structure we propose here, the Bayes tree, is directed and corresponds more naturally to the result of the QR factorization in linear algebra, allowing us to ana... |

19 |
Distributed multifrontal factorization using clique trees
- Pothen, Sun
- 1991
(Show Context)
Citation Context ...is chordal, and it is well known that a chordal Bayes net can be converted into a treestructured graphical model in which these operations are easy. This data structure is similar to the clique tree (=-=Pothen and Sun, 1992-=-; Blair and Peyton, 1993; Koller and Friedman, 2009), also known as the junction tree in the AI literature (Cowell et al., 1999), which has already been exploited for distributed inference in SLAM (De... |

18 | Fast incremental square root information smoothing
- Kaess, Ranganathan, et al.
- 2007
(Show Context)
Citation Context ...., 2007) applies loopy belief propagation directly to the SLAM graph. The sparse linear algebra perspective has been explored in Smoothing and Mapping (SAM) (Dellaert, 2005; Dellaert and Kaess, 2006; =-=Kaess et al., 2007-=-, 2008). The matrices associated with smoothing are typically very sparse, and one can do much better than the cubic complexity associated with factorizing a dense matrix (Krauthausen et al., 2006). K... |

18 | Large scale 6DOF SLAM with stereo-in-hand
- Paz, Pinies, et al.
(Show Context)
Citation Context ...ns open. Note that the number of landmarks per frame is typically much lower for laser range-based applications than for visual SLAM applications (Eade and Drummond, 2007; Konolige and Agrawal, 2008; =-=Paz et al., 2008-=-; Strasdat et al., 2010). However, smoothing has recently also been shown to be the method of choice for visual SLAM in many situations (Strasdat et al., 2010). In an incremental setting, the cost of ... |

17 | Finding good column orderings for sparse QR factorization - Heggernes, Matstoms - 1996 |

16 | Subgraphpreconditioned conjugate gradients for large scale slam
- Dellaert, Carlson, et al.
- 2010
(Show Context)
Citation Context ...hniques such as relaxation (Duckett et al., 2002; Bosse et al., 2004; Thrun et al., 2005), gradient descent (Folkesson and Christensen, 2004, 2007), preconditioned conjugate gradient (Konolige, 2004; =-=Dellaert et al., 2010-=-), multi-level relaxation (Frese et al., 2005), and belief propagation (Ranganathan et al., 2007). Direct methods, such as QR and Cholesky matrix factorization, provide the advantage of faster converg... |

15 | Closing the loop with graphical SLAM - Folkesson, Christensen - 2007 |

14 |
Treemap: An o(logn) algorithm for indoor simultaneous localization and mapping
- Frese
(Show Context)
Citation Context ...rence in SLAM has a rich history (Brooks, 1985) and has especially led to several novel and exciting developments in the last years (Paskin, 2003; Folkesson and Christensen, 2004; Frese et al., 2005; =-=Frese, 2006-=-; Folkesson and Christensen, Draft manuscript, April 6, 2011. Submitted to IJRR. M. Kaess, H. Johannsson, and J. Leonard are with the Computer Science and Artificial Intelligence Laboratory (CSAIL), M... |

14 | Exploiting locality by nested dissection for square root smoothing and mapping
- Krauthausen, Dellaert, et al.
- 2006
(Show Context)
Citation Context ...ss, 2006; Kaess et al., 2007, 2008). The matrices associated with smoothing are typically very sparse, and one can do much better than the cubic complexity associated with factorizing a dense matrix (=-=Krauthausen et al., 2006-=-). Kaess et al. (2008) proposed incremental smoothing and mapping (iSAM), which performs fast incremental updates of the square root information matrix, yet is able to compute the full map and traject... |

13 |
Sparse pose adjustment for 2d mapping
- Konolige, Grisetti, et al.
- 2010
(Show Context)
Citation Context ... SLAM has first been proposed by Dellaert (2005), but is now widely used (Dellaert and Kaess, 2006; Frese, 2006; Folkesson et al., 2007; Kaess et al., 2008; Mahon et al., 2008; Grisetti et al., 2010; =-=Konolige et al., 2010-=-; Strasdat et al., 2010). Square Root SAM (Dellaert, 2005; Dellaert and Kaess, 2006) performs smoothing by Cholesky factorization of the complete, naturally sparse information matrix in every step usi... |

12 | Multi-level submap based SLAM using nested dissection
- Ni, Dellaert
- 2010
(Show Context)
Citation Context ...ematic for 3D applications. Relative formulations have also been used on a different level, to split the problem into submaps, for example Atlas (Bosse et al., 2004) or Tectonic SAM (Ni et al., 2007; =-=Ni and Dellaert, 2010-=-). In some way, iSAM2 provides a separation into submaps represented by different sub-trees, even though they are not completely separated in a way, as new measurements can change that topology at any... |

8 | Fast, on-line learning of globally consistent maps
- Duckett, Marsland, et al.
- 2002
(Show Context)
Citation Context ...d using matrix inversion (Gutmann and Nebel, 1997). A number of improved and numerically more stable algorithms have since been developed, based on well known iterative techniques such as relaxation (=-=Duckett et al., 2002-=-; Bosse et al., 2004; Thrun et al., 2005), gradient descent (Folkesson and Christensen, 2004, 2007), preconditioned conjugate gradient (Konolige, 2004; Dellaert et al., 2010), multi-level relaxation (... |

6 | Feature tracking for underwater navigation using sonar
- Folkesson, Leonard, et al.
- 2007
(Show Context)
Citation Context ...se a naive dense implementation is too expensive. An efficient sparse factorization for SLAM has first been proposed by Dellaert (2005), but is now widely used (Dellaert and Kaess, 2006; Frese, 2006; =-=Folkesson et al., 2007-=-; Kaess et al., 2008; Mahon et al., 2008; Grisetti et al., 2010; Konolige et al., 2010; Strasdat et al., 2010). Square Root SAM (Dellaert, 2005; Dellaert and Kaess, 2006) performs smoothing by Cholesk... |