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

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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 S.

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Abstract

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.