Abstract
This paper addresses the safety of two approaches to the collision avoidance of vehicle platoons with adaptive cruise control. It has been shown that $\mathcal{L}_{2}$ string stability, which is often used in the literature to achieve safety in the platoon, is not sufficient for collision avoidance. A stricter local condition, which is external positivity of the controlled vehicles, will be applied to guarantee collision avoidance by preventing overshooting responses of the vehicles. The theoretical results are verified by experiments with a set of mobile robots.
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