Worst-case Analysis of the Time-To-React Using Reachable Sets

Collision mitigation and collision avoidance systems in intelligent vehicles reduce the severity and number of accidents. To determine the optimal point in time at which such systems should intervene, time-based criticality metrics such as the Time-To-React (TTR) are commonly used. The TTR describes the last point in time along the current trajectory at which an evasive trajectory exists. In this paper, we present a novel approach to determine the point in time after which it is guaranteed that no evasive maneuver exists, i.e., by using reachable sets, we over-approximate the TTR. Our deterministic upper bound of the TTR can be used to trigger a collision mitigation system or to find a feasible emergency maneuver which avoids the collision. We demonstrate the efficient computation of the tight over-approximated TTR in different urban and rural traffic scenarios, and compare our results to an estimated TTR using an optimization-based trajectory planner.