Determining the maximum time horizon for vehicles to safely follow a trajectory

Dealing with the unknown future behavior of other traffic participants is one of the main challenges when generating safe trajectories for autonomous vehicles. When the ego vehicle (i.e., the vehicle to be controlled) follows a given trajectory, an emergency maneuver should be kept available for all times in order to avoid collisions. However, generating an emergency maneuver for each time step is computationally expensive and often not required. In this paper, we propose an algorithm for determining the maximum time horizon under which the ego vehicle can safely follow a given trajectory. First, an upper and a lower bound of this time horizon are computed. Then, binary search is used to find the maximum time horizon for which safety is still guaranteed. Our algorithm reduces the frequency of generating emergency maneuvers while still guaranteeing collision-free trajectories. The approach is tested on real traffic data, and it is shown that our algorithm indeed reduces the frequency of generating emergency maneuvers compared to previous work.