A General Relationship between Optimality Criteria and Connectivity Indices for Active Graph-SLAM

TL;DR

This paper establishes a theoretical link between the Fisher information matrix and graph Laplacian in active graph-SLAM, enabling efficient decision-making using connectivity indices with optimality guarantees.

Contribution

It introduces a general relationship between FIM and Laplacian matrices, allowing the use of graph connectivity indices as utility functions in active SLAM.

Findings

Connectivity indices approximate optimality criteria effectively.

Proposed method reduces computational time significantly.

Experimental results confirm decision equivalence with traditional methods.

Abstract

Quantifying uncertainty is a key stage in active simultaneous localization and mapping (SLAM), as it allows to identify the most informative actions to execute. However, dealing with full covariance or even Fisher information matrices (FIMs) is computationally heavy and easily becomes intractable for online systems. In this work, we study the paradigm of active graph-SLAM formulated over \textit{SE(n)}, and propose a general relationship between the FIM of the system and the Laplacian matrix of the underlying pose-graph. This link makes possible to use graph connectivity indices as utility functions with optimality guarantees, since they approximate the well-known optimality criteria that stem from optimal design theory. Experimental validation demonstrates that the proposed method leads to equivalent decisions for active SLAM in a fraction of the time.