Anmelden
Literatur vom gleichen Autor/der gleichen Autor*in
plus bei Google Scholar
Bibliografische Daten exportieren		  

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

Titelangaben

Xausa, Ilaria ; Baier, Robert ; Bokanowski, Olivier ; Gerdts, Matthias:
Computation of avoidance 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 , 2019 . - 30 S.

Volltext

Link zum Volltext (externe URL): Volltext

Angaben zu Projekten

Projekttitel:
Offizieller Projekttitel
Projekt-ID
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)
264735-SADCO
Projektfinanzierung: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union

Abstract

We consider the problem of computing safety regions, modelled as backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation of level set functions for obstacle avoidance is given and sufficient conditions for granting the obstacle avoidance on the whole time interval are obtained, even though the conditions are checked only at discrete times. Different scenarios including various road configurations, different geometry of vehicle and obstacles, as well as fixed or moving obstacles, are then studied and computed. Computations involve solving nonlinear partial differential equations of up to five space dimensions plus time with nonsmooth obstacle representations, and an efficient solver is used to this end. A comparison with a direct optimal control approach is also done for one of the examples.

Weitere Angaben

Publikationsform: Preprint, Postprint
Begutachteter Beitrag: Nein
Zusätzliche Informationen: Published in HAL Archive, id: 01123490v3

Contents:
1. Motivation
2. Problem Setting and Modelling
2.1 Presentation of the problem
2.2 The 4-dimensional point mass model
2.3 Level set functions for target and state constraints
3. Hamilton-Jacobi-Bellman Approach
.. Minimal time function and optimal trajectory reconstruction
4. Level Set Functions for Different Problem Data and Collision Avoidance
4.1 Road configurations
4.2 Obstacles and corresponding level set functions
... Circular obstacles
... Rectangular obstacles
... Moving obstacles
... Collision avoidance between time steps
5. Numerical Simulations
5.1 Scenario 1: straight road with a fixed rectangular obstacle
... Convergence test (scenario 1)
... Comparison with a direct method (scenario 1)
5.2 Scenario 2: straight road with varying width
5.3 Scenario 3: curved road with fix or moving obstacles
5.4 Scenario 4: crossing road and moving obstacles
6. Conclusion
Keywords: Collision avoidance; Hamilton-Jacobi-Bellman equations; Backward reachable sets; Level set approach; High dimensional partial differential equations
Fachklassifikationen: Mathematics Subject Classification Code: 93B03 (49K15 49L25 93C10)
Institutionen der Universität: Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Profilfelder
Profilfelder > Advanced Fields
Profilfelder > Advanced Fields > Nichtlineare Dynamik
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 09 Sep 2020 06:24
Letzte Änderung: 09 Sep 2020 06:24
URI: https://eref.uni-bayreuth.de/id/eprint/56853

Zu diesem Eintrag verfügbare Versionen