A Constant-Time Algorithm for Vector Field SLAM using an Exactly Sparse Extended Information Filter

Abstract — Designing a localization system for a low-cost robotic consumer product poses a major challenge. In previous work, we introduced Vector Field SLAM [5], a system for simultaneously estimating robot pose and a vector field induced by stationary signal sources present in the environment. In this paper we show how this method can be realized on a low-cost embedded processing unit by applying the concepts of the Exactly Sparse Extended Information Filter [15]. By restricting the set of active features to the 4 nodes of the current cell, the size of the map becomes linear in the area explored by the robot while the time for updating the state can be held constant under certain approximations. We report results from running our method on an ARM 7 embedded board with 64 kByte RAM controlling a Roomba 510 vacuum cleaner in a standard test environment. NS spot1 X (sensor units) Spot1 X readings Node X1 estimate

Batch Nonlinear Continuous-Time Trajectory Estimation as Exactly Sparse Gaussian Process Regression

In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent variable. Our continuous-time prior can be defined by any nonlinear, time-varying stochastic differential equation driven by white noise; this allows the possibility of smoothing our trajectory estimates using a variety of vehicle dynamics models (e.g., `constant-velocity'). We show that this class of prior results in an inverse kernel matrix (i.e., covariance matrix between all pairs of measurement times) that is exactly sparse (block-tridiagonal) and that this can be exploited to carry out GP regression (and interpolation) very efficiently. When the prior is based on a linear, time-varying stochastic differential equation and the measurement model is also linear, this GP approach is equivalent to classical, discrete-time smoothing (at the measurement times); when a nonlinearity is present, we iterate over the whole trajectory to maximize accuracy. We test the approach experimentally on a simultaneous trajectory estimation and mapping problem using a mobile robot dataset.Comment: Submitted to Autonomous Robots on 20 November 2014, manuscript # AURO-D-14-00185, 16 pages, 7 figure

D-SLAM: A decoupled solution to simultaneous localization and mapping

The main contribution of this paper is the reformulation of the simultaneous localization and mapping (SLAM) problem for mobile robots such that the mapping and localization can be treated as two concurrent yet separated processes: D-SLAM (decoupled SLAM). It is shown that SLAM with a range and bearing sensor in an environment populated with point features can be decoupled into solving a nonlinear static estimation problem for mapping and a low-dimensional dynamic estimation problem for localization. This is achieved by transforming the measurement vector into two parts: one containing information relating features in the map and another with information relating the map and robot. It is shown that the new formulation results in an exactly sparse information matrix for mapping when it is solved using an Extended Information Filter (EIF).Thus a significant saving in the computational effort can be achieved for large-scale problems by exploiting the special properties of sparse matrices. An important feature of D-SLAM is that the correlation among features in the map are still kept and it is demonstrated that the uncertainty of the feature estimates monotonically decreases. The algorithm is illustrated and evaluated through computer simulations and experiments. © 2007 SAGE Publications

Sparse Bayesian information filters for localization and mapping

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2008This thesis formulates an estimation framework for Simultaneous Localization and Mapping (SLAM) that addresses the problem of scalability in large environments. We describe an estimation-theoretic algorithm that achieves significant gains in computational efficiency while maintaining consistent estimates for the vehicle pose and the map of the environment. We specifically address the feature-based SLAM problem in which the robot represents the environment as a collection of landmarks. The thesis takes a Bayesian approach whereby we maintain a joint posterior over the vehicle pose and feature states, conditioned upon measurement data. We model the distribution as Gaussian and parametrize the posterior in the canonical form, in terms of the information (inverse covariance) matrix. When sparse, this representation is amenable to computationally efficient Bayesian SLAM filtering. However, while a large majority of the elements within the normalized information matrix are very small in magnitude, it is fully populated nonetheless. Recent feature-based SLAM filters achieve the scalability benefits of a sparse parametrization by explicitly pruning these weak links in an effort to enforce sparsity. We analyze one such algorithm, the Sparse Extended Information Filter (SEIF), which has laid much of the groundwork concerning the computational benefits of the sparse canonical form. The thesis performs a detailed analysis of the process by which the SEIF approximates the sparsity of the information matrix and reveals key insights into the consequences of different sparsification strategies. We demonstrate that the SEIF yields a sparse approximation to the posterior that is inconsistent, suffering from exaggerated confidence estimates. This overconfidence has detrimental effects on important aspects of the SLAM process and affects the higher level goal of producing accurate maps for subsequent localization and path planning. This thesis proposes an alternative scalable filter that maintains sparsity while preserving the consistency of the distribution. We leverage insights into the natural structure of the feature-based canonical parametrization and derive a method that actively maintains an exactly sparse posterior. Our algorithm exploits the structure of the parametrization to achieve gains in efficiency, with a computational cost that scales linearly with the size of the map. Unlike similar techniques that sacrifice consistency for improved scalability, our algorithm performs inference over a posterior that is conservative relative to the nominal Gaussian distribution. Consequently, we preserve the consistency of the pose and map estimates and avoid the effects of an overconfident posterior. We demonstrate our filter alongside the SEIF and the standard EKF both in simulation as well as on two real-world datasets. While we maintain the computational advantages of an exactly sparse representation, the results show convincingly that our method yields conservative estimates for the robot pose and map that are nearly identical to those of the original Gaussian distribution as produced by the EKF, but at much less computational expense. The thesis concludes with an extension of our SLAM filter to a complex underwater environment. We describe a systems-level framework for localization and mapping relative to a ship hull with an Autonomous Underwater Vehicle (AUV) equipped with a forward-looking sonar. The approach utilizes our filter to fuse measurements of vehicle attitude and motion from onboard sensors with data from sonar images of the hull. We employ the system to perform three-dimensional, 6-DOF SLAM on a ship hull

A Spectral Learning Approach to Range-Only SLAM

We present a novel spectral learning algorithm for simultaneous localization and mapping (SLAM) from range data with known correspondences. This algorithm is an instance of a general spectral system identification framework, from which it inherits several desirable properties, including statistical consistency and no local optima. Compared with popular batch optimization or multiple-hypothesis tracking (MHT) methods for range-only SLAM, our spectral approach offers guaranteed low computational requirements and good tracking performance. Compared with popular extended Kalman filter (EKF) or extended information filter (EIF) approaches, and many MHT ones, our approach does not need to linearize a transition or measurement model; such linearizations can cause severe errors in EKFs and EIFs, and to a lesser extent MHT, particularly for the highly non-Gaussian posteriors encountered in range-only SLAM. We provide a theoretical analysis of our method, including finite-sample error bounds. Finally, we demonstrate on a real-world robotic SLAM problem that our algorithm is not only theoretically justified, but works well in practice: in a comparison of multiple methods, the lowest errors come from a combination of our algorithm with batch optimization, but our method alone produces nearly as good a result at far lower computational cost

D-SLAM: Decoupled localization and mapping for autonomous robots

The main contribution of this paper is the reformulation of the simultaneous localization and mapping (SLAM) problem for mobile robots such that the mapping and localization can be treated as two concurrent yet separated processes: D-SLAM (decoupled SLAM). It is shown that SLAM can be decoupled into solving a non-linear static estimation problem for mapping and a low-dimensional dynamic estimation problem for localization. The mapping problem can be solved using an Extended Information Filter where the information matrix is shown to be exactly sparse. A significant saving in the computational effort can be achieved for large scale problems by exploiting the special properties of sparse matrices. An important feature of D-SLAM is that the correlation among landmarks are still kept and it is demonstrated that the uncertainty of the map landmarks monotonically decrease. The algorithm is illustrated through computer simulations and experiments

Exact state and covariance sub-matrix recovery for submap based sparse EIF SLAM algorithm

This paper provides a novel state vector and covariance sub-matrix recovery algorithm for a recently developed submap based exactly sparse Extended Information Filter (EIF) SLAM algorithm - Sparse Local Submap Joining Filter (SLSJF). The algorithm achieves exact recovery instead of approximate recovery. The recovery algorithm is very efficient because of an incremental Cholesky factorization approach and a natural reordering of the global state vector. Simulation results show that the computation cost of the SLSJF is much lower as compared with the sequential map joining algorithm using Extended Kalman Filter (EKF). The SLSJF with the proposed recovery algorithm is also successfully applied to the Victoria Park data set. ©2008 IEEE

Exactly Sparse Delayed-State Filters for View-Based SLAM

This paper reports the novel insight that the simultaneous localization and mapping (SLAM) information matrix is exactly sparse in a delayed-state framework. Such a framework is used in view-based representations of the environment that rely upon scan-matching raw sensor data to obtain virtual observations of robot motion with respect to a place it has previously been. The exact sparseness of the delayed-state information matrix is in contrast to other recent feature-based SLAM information algorithms, such as sparse extended information filter or thin junction-tree filter, since these methods have to make approximations in order to force the feature-based SLAM information matrix to be sparse. The benefit of the exact sparsity of the delayed-state framework is that it allows one to take advantage of the information space parameterization without incurring any sparse approximation error. Therefore, it can produce equivalent results to the full-covariance solution. The approach is validated experimentally using monocular imagery for two datasets: a test-tank experiment with ground truth, and a remotely operated vehicle survey of the RMS Titanic.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86062/1/reustice-25.pd

Exactly Sparse Extended Information Filters for Feature-Based SLAM

Recent research concerning the Gaussian canonical form for Simultaneous Localization and Mapping (SLAM) has given rise to a handful of algorithms that attempt to solve the SLAM scalability problem for arbitrarily large environments. One such estimator that has received due attention is the Sparse Extended Information Filter (SEIF) proposed by Thrun et al., which is reported to be nearly constant time, irrespective of the size of the map. The key to the SEIF's scalability is to prune weak links in what is a dense information (inverse covariance) matrix to achieve a sparse approximation that allows for efficient, scalable SLAM. We demonstrate that the SEIF sparsification strategy yields error estimates that are overconfident when expressed in the global reference frame, while empirical results show that relative map consistency is maintained. In this paper, we propose an alternative scalable estimator based on an information form that maintains sparsity while preserving consistency. The paper describes a method for controlling the population of the information matrix, whereby we track a modified version of the SLAM posterior, essentially by ignoring a small fraction of temporal measurements. In this manner, the Exactly Sparse Extended Information Filter (ESEIF) performs inference over a model that is conservative relative to the standard Gaussian distribution. We compare our algorithm to the SEIF and standard EKF both in simulation as well as on two nonlinear datasets. The results convincingly show that our method yields conservative estimates for the robot pose and map that are nearly identical to those of the EKF.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86031/1/mwalter-22.pd