Proving the existence of loops in robot trajectories

TL;DR

This paper introduces a topological degree-based method to reliably verify loop closures in robot trajectories using only proprioceptive data, enhancing SLAM robustness in challenging environments.

Contribution

It presents a novel, generic approach employing topological degree theory to prove robot loops under uncertainty, compatible with existing SLAM algorithms.

Findings

Effective loop verification demonstrated on underwater vehicle datasets

Reduces computational load in SLAM processes

Provides a mathematically rigorous proof of loop existence

Abstract

This paper presents a reliable method to verify the existence of loops along the uncertain trajectory of a robot, based on proprioceptive measurements only, within a bounded-error context. The loop closure detection is one of the key points in SLAM methods, especially in homogeneous environments with difficult scenes recognitions. The proposed approach is generic and could be coupled with conventional SLAM algorithms to reliably reduce their computing burden, thus improving the localization and mapping processes in the most challenging environments such as unexplored underwater extents. To prove that a robot performed a loop whatever the uncertainties in its evolution, we employ the notion of topological degree that originates in the field of differential topology. We show that a verification tool based on the topological degree is an optimal method for proving robot loops. This is demonstrated both on datasets from real missions involving autonomous underwater vehicles, and by a mathematical discussion.