Damers, Julien

Jaulin, Luc

Rauh, Andreas

Rohou, Simon

Schön, Steffen

English

Institutionelles Repositorium der Leibniz Universität Hannover

Lie symmetries applied to guaranteedintegration: application to mobile roboticslocalisationJulien Damers1, Luc Jaulin 1 and Simon Rohou11 Lab-STICC, ENSTA Bretagne2 rue François Verny, 29200 Brest, Francejulien.damers@ensta-bretagne.orgKeywords: Guaranteed Integration, Lie Symmetries, Localisation, RoboticsIntroductionWhen dealing with mobile robots, localisation is one of the main problemsone will be required to solve. One may use complex and expensive devicesto localise the vehicle. However, with the development of swarms of robots,the need for cheaper units requires finding alternatives to these expensivedevices. Here we will use the dynamical model of the system studied.Guaranteed integration using Lie symmetriesIn [1] and [2], we presented a method to perform guaranteed integrationfor large initial conditions. We recall the principle quickly here. Providedwe have a reference trajectory ( x10(t), black arrow in Fig. 1) computed foran initial condition x10 (the bottom left black car), it is possible, using Liesymmetries of the system (if they are known) to find the solution (top rightgreen car) for another initial condition (bottom right green car).Combining interval analysis tools to solve the localisa-tion problemConsider a robot with a known dynamical model and an unknown initialstate. We want to localise it, using range-only measurements to beacons forwhich we know the exact location as it progresses throughout the mission.Applying both our integration method and contractors related to range mea-surements on tubes [3] used to enclose the robot trajectory, it is possible toestimate the initial condition of the robot with backward constraint prop-agation. Then, propagating the constraints in a forward manner, one canestimate the trajectory of the robot. This is illustrated in a video which canbe found on youtube1.AcknowledgementThis work has been funded by Kopadia, a French company specialized inunderwater systems engineering and operations. It has also been partiallysupported by the French Agence National de la Recherche (ANR) [grantnumber ANR-16-CE33-0024].References[1] J. Damers, L. Jaulin and S. Rohou, Lie symmetries applied tointerval integration, Automatica (accepted), 2022.[2] J. Damers, L. Jaulin and S. Rohou, Guaranteed interval integrationfor large initial boxes SWIM 2019.[3] S. Rohou et al., Reliable Robot Localization: A Constraint-ProgrammingApproach Over Dynamical System, John Wiley & Sons, London, 2019.Figure 1: Guaranteed integration principle using Lie symmetries1State estimation using Lie symmetries by Julien DAMERS

Lie symmetries applied to guaranteed integration: application to mobile robotics localisation

https://www.repo.uni-hannover.de/bitstream/123456789/13317/1/Damers_etal_SWIM22.pdf

Lie symmetries applied to guaranteed integration: application to mobile robotics localisation

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Institutionelles Repositorium der Leibniz Universität Hannover