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Computation of safety regions for driver assistance systems by using a Hamilton-Jacobi approach

Title data

Xausa, Ilaria ; Baier, Robert ; Bokanowski, Olivier ; Gerdts, Matthias:
Computation of safety regions for driver assistance systems by using a Hamilton-Jacobi approach.
Volkswagen AG; Department of Mathematics, University of Bayreuth; LJLL - Laboratoire Jacques-Louis Lions, Université Paris-Diderot (Paris 7); Groupe "Optimisation et commande" (OC), L'Unité de Mathématiques Appliquées (UMA), ENSTA ParisTech; Institut für Mathematik und Rechneranwendung, Bundeswehruniversität München
Paris, France , 2014 . - 22 p.

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO

Abstract in another language

We consider the problem of computing safety regions, modelled as backward reachable sets, for a car collision avoidance model with time-dependant obstacles. The Hamilton-Jacobi-Bellman framework is used, following the approach of Bokanowski and Zidani (Proceeding IFAC 2011, Vol. 18, Part 1, pp. 2589–2593). Furthermore several practical issues for specific obstacle avoidance problems are answered in this work. Different scenarios are then studied and computed. Comparison with a more direct optimal control approach is also done in the case of fixed obstacles. Computations involve solving nonlinear Partial Differential Equations up to five space dimensions plus time and for nonsmooth data, and an efficient solver is used to this end.

Further data

Item Type: Preprint, postprint, working paper, discussion paper
Refereed: No
Additional notes: published in HAL archive, id: 01123490
Keywords: safety avoidance; collision avoidance; Hamilton-Jacobi equations; backward reachable sets; level set approach; partial differential equations; high dimension
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 01 Apr 2015 06:37
Last Modified: 13 Mar 2019 12:22
URI: https://eref.uni-bayreuth.de/id/eprint/9576