  This paper presents a game-theoretic path-following formulation where the
opponent is an adversary road model. This formulation allows us to compute safe
sets using tools from viability theory, that can be used as terminal
constraints in an optimization-based motion planner. Based on the adversary
road model, we first derive an analytical discriminating domain, which even
allows guaranteeing safety in the case when steering rate constraints are
considered. Second, we compute the discriminating kernel and show that the
output of the gridding based algorithm can be accurately approximated by a
fully connected neural network, which can again be used as a terminal
constraint. Finally, we show that by using our proposed safe sets, an
optimization-based motion planner can successfully drive on city and country
roads with prediction horizons too short for other baselines to complete the
task.
