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.

翻译：本文提出了一种通用框架，用于高效获取碰撞避免系统恰好避免追尾事故的适当干预时间。该框架融合了驾驶员舒适模型与车辆模型。我们证明了基于加速度和加加速度的驾驶员转向操作与转向角及转向角速率曲线之间存在关联。研究了四种不同车辆模型对避免追尾所需启动转向时间的影响，评估模型包括：动力学自行车模型（DM）、稳态转弯模型（SSCM）、运动学模型（KM）和质点模型（PMM）。研究表明所有模型均可通过参数变化线性系统描述。我们提出了三种基于线性系统的转向算法，可高效计算四种车辆模型的干预时间，其中两种采用后向可达性仿真，一种采用前向仿真。结果表明SSCM、KM和PMM在特定车辆工况下无法准确估计干预时间。由于计算快速性，采用后向可达性算法的DM适用于快速离线安全效益评估，而采用前向仿真算法的DM更适合在线实时应用。