Asymptotic Stability and Vehicle Safety in Dynamic Car-Following Platoon

A vehicle in a platoon sometimes faces the risk of causing a rear-end collision when it is following a vehicle in front. The stability theory of the well-known General Motors car-following models says that the fluctuations of vehicle speeds and headways will increasingly propagate to the rear vehicle in a platoon if the platoon is asymptotically unstable. However, almost no research has been done to validate this phenomenon with the real car-following platoon data. Therefore, the car-following platoon data, including 10 vehicle trajectories, were used to evaluate asymptotic stability in the platoon. The asymptotic stability in vehicle safety is evaluated on the assumption that the vehicle in the rear position is exposed to riskier conditions than the vehicle positioned in front because of the shorter headways created by increased fluctuations of speeds and headways in a platoon if the asymptotic stability is unstable. Three indicators for safety are defined: potential danger time, impact speed, and expected impact speed. The outcomes in these safety indicators did not show that the car-following platoon was in asymptotically unstable conditions. Therefore, two supplemental indicators were defined to closely observe asymptotic stability: maximum speed amplitude and maximum spacing amplitude. These stability indicators were used to explain that the car-following platoon was under asymptotically unstable conditions. As a result, a hidden aspect of the relationship between asymptotic stability and vehicle safety was discovered in the real car-following platoon.