Person:

Dellaert, Frank

Permanent Link

https://hdl.handle.net/1853/71202

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Organizational Unit

School of Interactive Computing

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Now showing 1 - 10 of 18

Supplementary Material to: IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation

(Georgia Institute of Technology, 2015-05-30) Forster, Christian ; Carlone, Luca ; Dellaert, Frank ; Scaramuzza, Davide
Rapid Loop Updates

(Georgia Institute of Technology, 2012-09-11) Indelman, Vadim ; Dellaert, Frank
Factor Graphs and GTSAM: A Hands-on Introduction

(Georgia Institute of Technology, 2012-09) Dellaert, Frank

In this document I provide a hands-on introduction to both factor graphs and GTSAM. Factor graphs are graphical models (Koller and Friedman, 2009) that are well suited to modeling complex estimation problems, such as Simultaneous Localization and Mapping (SLAM) or Structure from Motion (SFM). You might be familiar with another often used graphical model, Bayes networks, which are directed acyclic graphs. A factor graph, however, is a bipartite graph consisting of factors connected to variables. The variables represent the unknown random variables in the estimation problem, whereas the factors represent probabilistic information on those variables, derived from measurements or prior knowledge. In the following sections I will show many examples from both robotics and vision. The GTSAM toolbox (GTSAM stands for “Georgia Tech Smoothing and Mapping”) toolbox is a BSD-licensed C++ library based on factor graphs, developed at the Georgia Institute of Technology by myself, many of my students, and collaborators. It provides state of the art solutions to the SLAM and SFM problems, but can also be used to model and solve both simpler and more complex estimation problems. It also provides a MATLAB interface which allows for rapid prototype development, visualization, and user interaction. GTSAM exploits sparsity to be computationally efficient. Typically measurements only provide information on the relationship between a handful of variables, and hence the resulting factor graph will be sparsely connected. This is exploited by the algorithms implemented in GTSAM to reduce computational complexity. Even when graphs are too dense to be handled efficiently by direct methods, GTSAM provides iterative methods that are quite efficient regardless. You can download the latest version of GTSAM at http://tinyurl.com/gtsam.
The Bayes Tree: Enabling Incremental Reordering and Fluid Relinearization for Online Mapping

(Georgia Institute of Technology, 2010-01-29) Kaess, Michael ; Ila, Viorela ; Roberts, Richard ; Dellaert, Frank

In this paper we present a novel data structure, the Bayes tree, which exploits the connections between graphical model inference and sparse linear algebra. The proposed data structure provides a new perspective on an entire class of simultaneous localization and mapping (SLAM) algorithms. Similar to a junction tree, a Bayes tree encodes a factored probability density, but unlike the junction tree it is directed and maps more naturally to the square root information matrix of the SLAM problem. This makes it eminently suited to encode the sparse nature of the problem, especially in a smoothing and mapping (SAM) context. The inherent sparsity of SAM has already been exploited in the literature to produce efficient solutions in both batch and online mapping. The graphical model perspective allows us to develop a novel incremental algorithm that seamlessly incorporates reordering and relinearization. This obviates the need for expensive periodic batch operations from previous approaches, which negatively affect the performance and detract from the intended online nature of the algorithm. The new method is evaluated using simulated and real-world datasets in both landmark and pose SLAM settings.
Automatic Landmark Detection for Topological Mapping Using Bayesian Surprise

(Georgia Institute of Technology, 2008) Ranganathan, Ananth ; Dellaert, Frank

Topological maps are graphical representations of the environment consisting of nodes that denote landmarks, and edges that represent the connectivity between the landmarks. Automatic detection of landmarks, usually special places in the environment such as gateways, in a general, sensor-independent manner has proven to be a difficult task. We present a landmark detection scheme based on the notion of “surprise” that addresses these issues. The surprise associated with a measurement is defined as the change in the current model upon updating it using the measurement. We demonstrate that surprise is large when sudden changes in the environment occur, and hence, is a good indicator of landmarks. We evaluate our landmark detector using appearance and laser measurements both qualitatively and quantitatively. Part of this evaluation is performed in the context of a topological mapping algorithm, thus demonstrating the practical applicability of the detector.
Probabilistic Topological Mapping for Mobile Robots using Urn Models

(Georgia Institute of Technology, 2007) Ranganathan, Ananth ; Dellaert, Frank

We present an application of Bayesian modeling and inference to topological mapping in robotics. This is a potentially difficult problem due to (a) the combinatorial nature of the state space, and (b) perceptual aliasing by which two different landmarks in the environment can appear similar to the robot's sensors. Hence, this presents a challenging approximate inference problem, complicated by the fact that the form of the prior on topologies is far from obvious. We deal with the latter problem by introducing the use of urn models, which very naturally encode prior assumptions in the domain of topological mapping. Secondly, we advance simulated tempering as the basis of two rapidly mixing approximate inference algorithms, based on Markov chain Monte Carlo (MCMC) and Sequential Importance Sampling (SIS), respectively. These algorithms converge quickly even though the posterior being estimated is highly peaked and multimodal. Experiments on real robots and in simulation demonstrate the efficiency and robustness of our technique.
Visual SLAM with a Multi-Camera Rig

(Georgia Institute of Technology, 2006) Kaess, Michael ; Dellaert, Frank

Camera-based simultaneous localization and mapping or visual SLAM has received much attention recently. Typically single cameras, multiple cameras in a stereo setup or omni-directional cameras are used. We propose a different approach, where multiple cameras can be mounted on a robot in an arbitrary configuration. Allowing the cameras to face in different directions yields better constraints than single cameras or stereo setups can provide, simplifying the reconstruction of large-scale environments. And in contrast to omni-directional sensors, the available resolution can be focused on areas of interest depending on the application. We describe a sparse SLAM approach that is suitable for real-time reconstruction from such multi-camera configurations. We have implemented the system and show experimental results in a large-scale environment, using a custom made eight-camera rig.
Learning and Inferring Motion Patterns using Parametric Segmental Switching Linear Dynamic Systems

(Georgia Institute of Technology, 2006) Oh, Sang Min ; Rehg, James M. ; Balch, Tucker ; Dellaert, Frank

Switching Linear Dynamic System (SLDS) models are a popular technique for modeling complex nonlinear dynamic systems. An SLDS has significantly more descriptive power than an HMM by using continuous hidden states. However, the use of SLDS models in practical applications is challenging for several reasons. First, exact inference in SLDS models is computationally intractable. Second, the geometric duration model induced in standard SLDSs limits their representational power. Third, standard SLDSs do not provide a systematic way to robustly interpret systematic variations governed by higher order parameters. The contributions in this paper address all three challenges above. First, we present a data-driven MCMC sampling method for SLDSs as a robust and efficient approximate inference method. Second, we present segmental switching linear dynamic systems (S-SLDS), where the geometric distributions are replaced with arbitrary duration models. Third, we extend the standard model with a parametric model that can capture systematic temporal and spatial variations. The resulting parametric SLDS model (P-SLDS) uses EM to robustly interpret parametrized motions by incorporating additional global parameters that underly systematic variations of the overall motion. The overall development of the proposed inference methods and extensions for SLDSs provide a robust framework to interpret complex motions. The framework is applied to the honey bee dance interpretation task in the context of the ongoing BioTracking project at Georgia Institute of Technology. The experimental results suggest that the enhanced models provide an effective framework for a wide range of motion analysis applications.
A Partially Fixed Linearization Approach for Submap-Parametrized Smoothing and Mapping

(Georgia Institute of Technology, 2005) Kipp, Alexander ; Krauthausen, Peter ; Dellaert, Frank

We present an extension of a smoothing approach to Simultaneous Localization and Mapping (SLAM). We have previously introduced Square-Root SAM, a Smoothing and Mapping approach to SLAM based on Levenberg-Marquardt (LM) optimization. It iteratively finds the optimal nonlinear least squares solution (ML), where one iteration comprises of a linearization step, a matrix factorization, and a back-substitution step. We introduce a submap parametrization which enables a rigid transformation of parts relative to each other during the optimization process. This parameterization is used in a multifrontal QR factorization approach, in which we partially fix the linearization point for a subset of the unknowns corresponding to sub-maps. This greatly accelerates the optimization of an entire SAM graph yet yields an exact solution.
Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing

(Georgia Institute of Technology, 2005) Dellaert, Frank

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 filter-based solutions to the problem. In particular, we look at approaches that factorize either the associated information matrix or the measurement matrix 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. 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, an interpretation of factorization in terms of the graphical model associated with the SLAM problem, and simulation results that underscore the potential of these methods for use in practice.