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Quantifying uncertainty is a key stage in active simultaneous localizationand mapping (SLAM), as it allows to identify the most informative actions toexecute. However, dealing with full covariance or even Fisher informationmatrices (FIMs) is computationally heavy and easily becomes intractable foronline systems. In this work, we study the paradigm of active graph-SLAMformulated over \textit{SE(n)}, and propose a general relationship between theFIM of the system and the Laplacian matrix of the underlying pose-graph. Thislink makes possible to use graph connectivity indices as utility functions withoptimality guarantees, since they approximate the well-known optimalitycriteria that stem from optimal design theory. Experimental validationdemonstrates that the proposed method leads to equivalent decisions for activeSLAM in a fraction of the time.

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