Density-Based Stochastic Reachability Computation for Occupancy Prediction in Automated Driving

We propose a stochastic reachability computation framework for occupancy prediction in automated driving by directly solving the underlying transport partial differential equation (PDE) governing the advection of the closed-loop joint density functions. The resulting nonparametric gridless computation is based on integration along the characteristic curves, and it allows online computation of the time-varying collision probabilities. We provide numerical simulations for multi-lane highway driving scenarios to highlight the scope of the proposed method.