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A Novel Measure of Uncertainty for Mobile Robot SLAM with Rao—Blackwellized Particle Filters

Rao—Blackwellized particle filters (RBPFs) are an implementation of sequential Bayesian filtering that has been successfully applied to mobile robot simultaneous localization and mapping (SLAM) and exploration. Measuring the uncertainty of the distribution estimated by a RBPF is required for tasks such as information gain-guided exploration or detecting loop closures in nested loop environments. In this paper we propose a new measure that takes the uncertainty in both the robot path and the map into account. Our approach relies on the entropy of the expected map (EM) of the RBPF, a new variable built by integrating the map hypotheses from all of the particles. Unlike previous works that use the joint entropy of the RBPF for active exploration, our proposal is better suited to detect opportunities to close loops, a key aspect to reduce the robot path uncertainty and consequently to improve the quality of the maps being built. We provide a theoretical discussion and experimental results with real data that support our claims.