Stable Interaction of Autonomous Vehicle Platoons with Human-Driven Vehicles

A necessary prerequisite for the safe interaction of autonomous systems with a human-driven vehicle is for the overall closed-loop system (autonomous systems plus human-driven vehicle) to be stable. This paper studies the safe and stable interaction between a platoon of autonomous vehicles and a set of human-driven vehicles. Considering the longitudinal motion of the vehicles in the platoon, the problem is to ensure a safe emergency braking by the autonomous platoon considering the actions of human-driven vehicles, which may vary based on the driver type. We consider two types of platoon topologies, namely unidirectional and bidirectional. Safe emergency braking is characterized by a specific type of platoon stability, called head-to-tail stability (HTS). We present system-theoretic necessary and sufficient conditions for the combination of the autonomous platoon and human-driven vehicles to be HTS for two platoon control laws, namely the velocity tracking and the platoon formation. Modeling the input-output behavior of each vehicle via a transfer function, the HTS conditions restrict the human-driven vehicles' transfer functions to have H-infinity norms below certain thresholds. A safe interaction algorithm first identifies the transfer functions of the human-driven vehicles. Then, it tunes the platoon control gains such that the overall system meets HTS conditions. Theoretical results are validated with both experimental data with human subject studies and simulation studies.