Computation of avoidance regions for driver assistance systems by using a Hamilton-Jacobi approach |
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| Authors: | Ilaria Xausa Robert Baier Olivier Bokanowski Matthias Gerdts |
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| Institution: | 1. Institute of Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Bundeswehr University Munich, Munich, Germany;2. Chair of Applied Mathematics, University of Bayreuth, Bayreuth, Germany;3. Laboratoire Jacques-Louis Lions (LJLL), Université de Paris, Paris, France |
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| Abstract: | We consider the problem of computing safety regions, modeled as nonconvex 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. |
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| Keywords: | backward reachable sets collision avoidance Hamilton-Jacobi-Bellman equations high-dimensional partial differential equations level-set approach |
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