Thesis
Grant : DGA + ARED (région)
Start: October 2021.
Supervisors: Luc Jaulin and Christophe Viel
Title: Guaranteed ellipsoidal numerical method for the stability analysis of the formation control of a group of underwater robots
Jury
- Michel Kieffer (rapporteur),Full Professor, Centrale-Supélec
- Nacim Ramdani (rapporteur), Full Professor, Université of Orléans and IUT de Bourges
- Helène Piet-Lahanier (examiner), Scientific deputy, DTIS, ONERA
- Olivier Kermorgant (examiner), Associate Professor, Centrale Nantes
- Andreas Rauh (examiner), Full Professor, Oldenburg University
- Nicolas Marchand (examiner, president of jury), Directeur de Recherche CNRS, CNRS
- Luc Jaulin (PhD director), Full Professor, ENSTA Bretagne
- Christophe Viel (supervisor), Chargé de recherche, CNRS
Manuscript Paper version / Numerical version
Defence
2024 November 5th, 10am, Brest, ENSTA-Bretagne, room F231.
Experiments
Abstract
In the development of human marine activity, groups of underwater robots can automate certain tasks. Since these robots are difficult to localise because of the underwater constraints, they must move in formation to be reliable. While various theoretical controllers have been proposed to challenge these constraints, they still need to consider more complex constraints and to be tested on real systems. As for every autonomous system, the stability of the formation must be verified by a mathematical proof. However, the complexity of these nonlinear systems makes the conventional Lyapunov method difficult to use. Thus, this thesis’ main objective is to develop guaranteed numerical methods, based on interval arithmetic, that can assist the stability proof.
Based on ellipsoidal guaranteed propagation, a first method is designed for discrete-time systems to compute an ellipsoidal domain of attraction. This method is then extended to continuous-time systems and then to synchronous hybrid systems which are more realistic modellings. In addition, the ellipsoidal propagation is extended to consider singular mappings and degenerate ellipsoids. Finally, some real-world underwater formation control was achieved to illustrate the stability.
Publications of Morgan Louedec
Morgan Louedec, Christophe Viel, Luc Jaulin – Computational tractable guaranteed numerical method to study the stability of n-dimensional time-independent
nonlinear systems with bounded perturbation – Automatica, July 2023, volume 153
IFAC ACNDC June 2024 (London) – Morgan Louedec, Christophe Viel, Luc Jaulin – Outer Enclosures of Nonlinear Mapping with Degenerate Ellipsoids
Morgan Louedec, Christophe Viel, Luc Jaulin – A guaranteed numerical method to prove the exponential stability of nonlinear discrete-time systems – IEEE
Transaction on Automatic Control 2024 (under review)
M. Louédec, L. Jaulin and C. Viel, A guaranteed numerical method to find ellipsoidal domain of attraction for n-dimensional nonlinear synchronous hybrid
systems, Systems & Control Letters 2024 (Under Review)
Satellite Seminars
Michel KIEFFER – Target Search and Tracking in an Unknown Environment by a Fleet of UAVs using a Set-Membership Approach
This presentation addresses the problem of search and tracking an unknown number of mobile ground targets within an uncharted Region of Interest (RoI) using a fleet of cooperating Unmanned Aerial Vehicles (UAVs). Each UAV embeds a Computer Vision System providing images with labeled pixels, depth maps, and bounding boxes around identified targets. This information is used by a set-membership estimator to characterize sets guaranteed to contain the locations of already identified targets and a set containing the locations of all targets remaining to detect. A map of the unknown environment is constructed during search to favor exploration of areas previously occluded by obstacles.
at 3pm in the room F207