%0 Journal Article %T Lie symmetries applied to interval integration %+ École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne) %+ Equipe ROBotics for EXploration (Lab-STICC_ROBEX) %A DAMERS, Julien %A Jaulin, Luc %A Rohou, Simon %< avec comité de lecture %@ 0005-1098 %J Automatica %I Elsevier %V 144 %P 110502 %8 2022 %D 2022 %R 10.1016/j.automatica.2022.110502 %K Interval analysis %K guaranteed integration %K IVP %K Lie groups %K symmetries %K tubes %Z Engineering Sciences [physics]/AutomaticJournal articles %X In this paper, we propose a new approach for improving significantly existing guaranteed integration methods for state equations with uncertain initial conditions. We first find a tube that encloses the solution of the differential equation assuming that the initial state is known. Then, using Lie symmetries, we inflate the tube in order to contain the uncertainty associated with the initial state. The method is shown to be efficient on examples coming from reachability analysis and robotics. %G English %2 https://hal.science/hal-03749780/document %2 https://hal.science/hal-03749780/file/article-automatica_preprint_gratuit.pdf %L hal-03749780 %U https://hal.science/hal-03749780 %~ UNIV-BREST %~ INSTITUT-TELECOM %~ ENSTA-BRETAGNE %~ CNRS %~ UNIV-UBS %~ ENSTA-BRETAGNE-STIC %~ ENIB %~ LAB-STICC %~ TDS-MACS %~ INSTITUTS-TELECOM %~ ANR %~ LAB-STICC_ROBEX