Avoiding critical situations is a prerequisite for Advanced Driver Assistant Systems and Autonomous Driving to decrease the number of total hazards and fatal collisions. As a guide for safe motion behavior and for avoiding critical situations in complex scenarios with several interacting traffic participants, an appropriate risk measurement is necessary. It should incorporate system-inherent uncertainties like present in environment recognition, behavior predictions and physical model assumptions. In this paper, we introduce a time-course-aware incremental risk model for motion planning which predicts state distributions along forecasted trajectories and regards their magnitude evolution by the Survival Theory and their shape adaptation by removing collided distribution parts while preserving statistical moments. Our approach is able to reproduce motion risk probability costs as found by particle-based Monte-Carlo (MC) simulations in a range of scenarios, at much lower computational costs.

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