I. Introduction
Guaranteeing safety without sacrificing performance in automated driving, especially in a mixed traffic of autonomous, semi-autonomous, and human-driven vehicles, requires real-time planning and decision-making against time-varying uncertainties. From a decision-making (ego) vehicle’s perspective, these uncertainties stem not only from the environment (states and intents of neighboring traffic, road geometry, weather, and lighting conditions) but also from the intrinsic sources (sensing and localization errors, communication packet drop, computational latency, model mismatch between the planning and control software). Thus, timely and accurate forecasting of the states of the ego vehicle and its environment is critical for provably safe decision-making. At the same time, given the complexity of the dynamics and environment, it is extremely challenging to perform such forecasting computation at a time scale much smaller than the physical dynamics time scale. Therefore, a critical gap exists in real-time forecasting to enable provably safe automation for achieving objectives such as collision avoidance, safe lane change, and separation management. This article presents a framework for automated navigation by designing novel computational tools for stochastic uncertainty propagation enabling fast occupancy prediction in multi-lane driving scenarios.