Title: Proving the existence of loops in robot trajectories,
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.