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We consider the problem of computing safety regions, modeled as nonconvexbackward reachable sets, for a nonlinear car collision avoidance model withtime-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A newformulation of level set functions for obstacle avoidance is given andsufficient conditions for granting the obstacle avoidance on the whole timeinterval are obtained, even though the conditions are checked only at discretetimes. Different scenarios including various road configurations, differentgeometry of vehicle and obstacles, as well as fixed or moving obstacles, arethen studied and computed. Computations involve solving nonlinear partialdifferential equations of up to five space dimensions plus time with nonsmoothobstacle representations, and an efficient solver is used to this end. Acomparison with a direct optimal control approach is also done for one of theexamples.

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