  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.
