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Autonomous vehicles' safety in mixed traffic: Accounting for incoming vehicles when overtaking

The author builds on his previous work on formalization the traffic rules, to keep the autonomous vehicles (AV) legally accountable when planning and performing different maneuvers, employing a methodology based on Legal, Logic and Engineering Analyses to assess the safety of overtaking in mixed traffic. As the overtaking models were developed by now only for setups like Operational Designed Domain which is a controlled, known in advance environment, or for simplified scenarios as overtaking on highways with traffic separated by medians, the present paper developed a model able to account for the incoming traffic when overtaking, extending the applicability range from highways to the complex situation of urban streets or rural roads, two-ways and undivided traffic. Aiming to facilitate the translation of formulas expressed in Linear Temporal Logic to High Order Logic Languages, a series of definitions and theorems were developed, variables as time/distance-to-collision and time/distance-for-overtaking calculated, and finally the predicates as safe-distance-incoming, avoid-head-on-collision or safe-lateral-distance were assessed. The model fills another literature gap as well, by introducing variable speeds and acceleration during overtaking. Three control strategies emerged from these model's control functions: Passive, Reactive and Pro-active Control Strategies able, for different condition and extents to safely trade-off with the kinematics' variation detected at incoming vehicles, and to timely trigger the appropriate countermeasure packages of AV.