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Computation of avoidance regions for driver assistance systems by using a Hamilton‐Jacobi approach
Author(s) -
Xausa Ilaria,
Baier Robert,
Bokanowski Olivier,
Gerdts Matthias
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2565
Subject(s) - obstacle avoidance , solver , computation , collision avoidance , obstacle , interval (graph theory) , nonlinear system , computer science , set (abstract data type) , control theory (sociology) , interval arithmetic , mathematical optimization , mathematics , hamilton–jacobi equation , algorithm , collision , control (management) , artificial intelligence , mathematical analysis , mobile robot , robot , computer security , law , quantum mechanics , political science , bounded function , programming language , physics , combinatorics
Summary 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.