Computation of avoidance 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 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 , 2017 . - 30 S.

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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.