Impact of Ordering of Heterogeneous Vehicles on String Stability

Amplification of errors can occur in a string of vehicles equipped with an Adaptive Cruise Control System (ACC) and Cooperative Adaptive Cruise Control System (CACC), which can lead to string instability and rear-end collisions in a platoon. Traditionally, homogeneous vehicle strings have been considered in the literature, wherein every vehicle adopts the same time headway setting. A lower bound on the employable time headway in terms of maximum parasitic lag ensures string stability. Typically, vehicles with ACC and CACC systems are provided with a set of finite and discrete time headway settings choices; this leads to heterogeneity in traffic. In this paper, we address the impact of heterogeneity in time headway among autonomous and connected vehicles on string stability. We provide an analysis of the ordering of vehicles with different time headways and its effects on the spacing error between the lead and last vehicles of the platoon. We pose the problem of minimal spacing error between the lead and last vehicles as a Mixed-Integer Semi-Definite Program (MISDP). Since solving an MISDP is intractable, we propose an exhaustive and a heuristic ordering-enumeration algorithm. In these algorithms, a series of continuous Semi-Definite Programs (SDPs) are solved to determine the “best” and “worst” ordering of vehicles with respect to the minimum spacing error for smaller-scale platoons. We present numerical results for different platoon sizes to corroborate the analysis of the effects of vehicles employing different time headways on string stability.