A Linear Approximation for Graph-based Simultaneous Localization and Mapping

Abstract

Abstract-This article investigates the problem of SimultaneousLocalization and Mapping (SLAM) from the perspective of linear estimation theory. The problem is first formulated in terms of graph embedding: a graph describing robot poses at subsequent instants of time needs be embedded in a three-dimensional space, assuring that the estimated configuration maximizes measurement likelihood. Combining tools belonging to linear estimation and graph theory, a closed-form approximation to the full SLAM problem is proposed, under the assumption that the relative position and the relative orientation measurements are independent. The approach needs no initial guess for optimization and is formally proven to admit solution under the SLAM setup. The resulting estimate can be used as an approximation of the actual nonlinear solution or can be further refined by using it as an initial guess for nonlinear optimization techniques. Finally, the experimental analysis demonstrates that such refinement is often unnecessary, since the linear estimate is already accurate.

A Sensor Fusion Layer to Cope with Reduced Visibility in SLAM

“…However, a study of the current available algorithms was required in order to investigate which algorithm best fits our needs. Five 2D laser-based SLAM algorithms available in ROS were reviewed and evaluated, namely: HectorSLAM [13], GMapping [10], CoreSLAM [23], LagoSLAM [24] and KartoSLAM [25].…”

“…The basis of graph-based SLAM algorithms is the minimization of a nonlinear non-convex cost function [24]. More precisely, at each iteration, a local convex approximation of the initial problem is solved in order to update the graph configuration.…”

“…However, this optimization process is highly dependent on an initial guess to converge. Carlone et al [24] developed a new approach denoted as LagoSLAM 6 (Linear Approximation for Graph Optimization), in which the optimization process requires no initial guess. In addition, the technique can be used with any standard optimizer.…”

Robust optimization of factor graphs by using condensed measurements

“…Furthermore, they assume that the covariance is roughly spherical and thus have difficulties in optimizing pose-graphs, where some constraints have covariances with null spaces or substantial differences in the eigenvalues. Assuming diagonal covariances Carlone et al [11] recently demonstrated how to obtain a linear approximation independent of the initial guess. However, their method is limited to 2D pose-graphs.…”

Eliminating conditionally independent sets in factor graphs: A unifying perspective based on smart factors

“…These techniques are based on a maximum a posteriori estimation paradigm that computes the optimal state estimate by solving a nonlinear optimization problem. While in specific cases it is possible to exploit problem structure and devise closed-form solutions (or approximations) [5], [6], general techniques are based on iterative nonlinear optimization. The optimal solution of the original nonlinear optimization problem is computed by solving a sequence of linear systems (normal equations).…”