This paper addresses the problem of following a vehicle with varying acceleration in a comfortable and safe manner. Our architecture consists of a nominal controller (here: model predictive control) and a safety controller. Although model predictive control attempts to keep a safe distance, it cannot formally guarantee it, due to the assumptions on the behavior of the leading vehicle. We address this problem by holding a formally verified safety controller available. Our novel mechanism gradually engages the safety maneuver since most critical situations resolve quickly. The overall approach is evaluated against real traffic data. The results show good position and velocity tracking performance, while safety and comfort are guaranteed.
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