Critical Zones for Comfortable Collision Avoidance with a Leading Vehicle

This paper provides a general framework for efficiently obtaining the appropriate intervention time for collision avoidance systems to just avoid a rear-end crash. The proposed framework incorporates a driver comfort model and a vehicle model. We show that there is a relationship between driver steering manoeuvres based on acceleration and jerk, and steering angle and steering angle rate profiles. We investigate how four different vehicle models influence the time when steering needs to be initiated to avoid a rear-end collision. The models assessed were: a dynamic bicycle model (DM), a steady-state cornering model (SSCM), a kinematic model (KM) and a point mass model (PMM). We show that all models can be described by a parameter-varying linear system. We provide three algorithms for steering that use a linear system to compute the intervention time efficiently for all four vehicle models. Two of the algorithms use backward reachability simulation and one uses forward simulation. Results show that the SSCM, KM and PMM do not accurately estimate the intervention time for a certain set of vehicle conditions. Due to its fast computation time, DM with a backward reachability algorithm can be used for rapid offline safety benefit assessment, while DM with a forward simulation algorithm is better suited for online real-time usage.