%0 Journal Article %T Proving the existence of loops in robot trajectories %T Prouver l'existence de boucles dans des trajectoires de robots %+ Lab-STICC_ENSTAB_CID_PRASYS %+ Institute of Science and Technology [Klosterneuburg, Austria] (IST Austria) %+ Institut de Recherche de l'Ecole Navale (IRENAV) %A Rohou, Simon %A Franek, Peter %A Aubry, Clément %A Jaulin, Luc %< avec comité de lecture %@ 0278-3649 %J The International Journal of Robotics Research %I SAGE Publications %V 37 %N 12 %P 1500-1516 %8 2018-10-24 %D 2018 %R 10.1177/0278364918808367 %K mobile robotics %K SLAM %K loop detection %K interval analysis %K topological degree %K tubes %Z Computer Science [cs]/Robotics [cs.RO] %Z Mathematics [math]/Dynamical Systems [math.DS] %Z Mathematics [math]/Numerical Analysis [math.NA] %Z Engineering Sciences [physics]/Automatic %Z Computer Science [cs]/Artificial Intelligence [cs.AI]Journal articles %X 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. %G English %2 https://hal.science/hal-01904112/document %2 https://hal.science/hal-01904112/file/loopproof_paper.pdf %L hal-01904112 %U https://hal.science/hal-01904112 %~ UNIV-BREST %~ INSTITUT-TELECOM %~ ENSTA-BRETAGNE %~ CNRS %~ UNIV-UBS %~ ENSAM %~ ENSTA-BRETAGNE-STIC %~ INSMI %~ ENIB %~ LAB-STICC %~ TDS-MACS %~ I2M-BX %~ INSTITUTS-TELECOM %~ INRAE %~ HESAM %~ HESAM-ENSAM %~ IRENAV %~ LAMPA %~ LCPI %~ LABOMAP %~ LISPEN %~ MSMP