Exactly Sparse Delayed-State Filters for View-Based SLAM

Abstract

Abstract-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.Index Terms-Information filters, Kalman filtering, machine vision, mobile robot motion planning, mobile robots, recursive estimation, robot vision systems, simultaneous localization and mapping (SLAM), underwater vehicles.

Simultaneous Localization and Mapping in Marine Environments

“…One of the downfalls of that approach was that it resulted in overconfident estimates. These issues were addressed in the exactly sparse delayed-state filters (ESDFs) by Eustice et al [14,15] and later with the exactly sparse extended information filter (ESEIF) by Walter et al [78].…”

Vision-based loop closing for delayed state robot mapping

“…These camera pose constraints are used as relative pose measurements in a delayed-state information-form SLAM. A substantial computational complexity advantage of the delayed-state information-form SLAM is that predictions and updates take constant time prior to loop closure given its exact sparseness [2]. Thanks to the features used, the proposed technique is robust enough not only to relate consecutive image pairs during robot motion, but also, to assert loop closure hypotheses.…”

“…Compared to the Extended Kalman Filter (EKF) SLAM which has quadratic time complexity in the number of states, the delayed-state information-form SLAM has been shown to produce exactly sparse information matrices [2]. If consecutive robot poses are added to the state, the result is a tri-block diagonal information matrix, linking consecutive measurements.…”

“…The revision of the entire history of poses, as a result of adding the new information that links the current and predicted poses, can be computed in information form [2] withη…”

“…An exact computation of Σ t+1 and Σ i requires the inverse ofΛ, which can be computed in linear time using conjugate gradient techniques [2]. Motivated by [11], these covariances can be efficiently approximated in constant time from their Markov blankets.…”