  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.
