Challenges related to automated driving are no longer focused on just the construction of such automated vehicles (AVs) but also on assuring the safety of operation. Recent advances in Level 3 and Level 4 autonomous driving have motivated more extensive study in safety guarantees of complicated AV maneuvers, which aligns with the goal of ISO 21448 (Safety of the Intended Functions or SOTIF), i.e., minimizing unsafe scenarios both known and unknown, as well as Vision Zero -- eliminating highway fatalities by 2050. A majority of approaches used in providing safety guarantees for AV motion control originate from formal methods, especially reachability analysis (RA), which relies on mathematical models for the dynamic evolution of the system to provide guarantees. However, to the best of the authors' knowledge, there have been no review papers dedicated to describing and interpreting state-of-the-art of formal methods in the context of AVs. In this work, we provide both an overview of the safety verification, validation, and certification process, as well as a review of formal safety techniques that are best suited to AV applications. We also propose a unified scenario coverage framework that can provide either a formal or sample-based estimate of safety verification for full AVs. Finally, challenges and future opportunities beyond the scope of current published research for assured AV safety are presented.

Challenges related to automated driving are no longer focused on just the construction of such automated vehicles (AVs), but in assuring the safety of their operation. Recent advances in Level 3 and Level 4 autonomous driving have motivated more extensive study in safety guarantees of complicated AV maneuvers, which aligns with the goal of ISO 21448 (Safety of the Intended Functions, or SOTIF), i.e. minimizing unsafe scenarios both known and unknown, as well as Vision Zero -- eliminating highway fatalities by 2050. A majority of approaches used in providing safety guarantees for AV motion control originate from formal methods, especially reachability analysis (RA), which relies on mathematical models for the dynamic evolution of the system to provide guarantees. However, to the best of the authors' knowledge, there have been no review papers dedicated to describing and interpreting state-of-the-art of formal methods in the context of AVs. In this work, we provide both an overview of the safety verification, validation and certification process, as well as review formal safety techniques that are best suited to AV applications. We also propose a unified scenario coverage framework that can provide either a formal or sample-based estimate of safety verification for full AVs. Finally, remaining challenges and future opportunities beyond the scope of current published research for assured AV safety are presented.