We address the problem of motion planning for four-way intersection crossings with right-of-ways. Road safety typically assigns liability to the follower in rear-end collisions and to the approaching vehicle required to yield in side crashes. As an alternative to previous models based on heuristic state machines, we propose a planning framework which changes the prediction model of other cars (e.g. their prototypical accelerations and decelerations) depending on the given longitudinal or lateral priority rules. Combined with a state-of-the-art trajectory optimization approach ROPT (Risk Optimization Method) this allows to find ego velocity profiles minimizing risks from curves and all involved vehicles while maximizing utility (needed time to arrive at a goal) and comfort (change and duration of acceleration) under the presence of regulatory conditions. Analytical and statistical evaluations show that our method is able to follow right-of-ways for a wide range of other vehicle behaviors and path geometries. Even when the other cars drive in a non-priority-compliant way, ROPT achieves good risk-comfort tradeoffs.

We consider the problem of correct motion planning for T-intersection merge-ins of arbitrary geometry and vehicle density. A merge-in support system has to estimate the chances that a gap between two consecutive vehicles can be taken successfully. In contrast to previous models based on heuristic gap size rules, we present an approach which optimizes the integral risk of the situation using parametrized velocity ramps. It accounts for the risks from curves and all involved vehicles (front and rear on all paths) with a so-called survival analysis. For comparison, we also introduce a specially designed extension of the Intelligent Driver Model (IDM) for entering intersections. We show in a quantitative statistical evaluation that the survival method provides advantages in terms of lower absolute risk (i.e., no crash happens) and better risk-utility tradeoff (i.e., making better use of appearing gaps). Furthermore, our approach generalizes to more complex situations with additional risk sources.