  We propose a stochastic prediction-control framework to promote safety in
automated driving by directly controlling the joint state probability density
functions (PDFs) subject to the vehicle dynamics via trajectory-level state
feedback. To illustrate the main ideas, we focus on a multi-lane highway
driving scenario although the proposed framework can be adapted to other
contexts. The computational pipeline consists of a PDF prediction layer,
followed by a PDF control layer. The prediction layer performs moving horizon
nonparametric forecasts for the ego and the non-ego vehicles' stochastic
states, and thereby derives safe target PDF for the ego. The latter is based on
the forecasted collision probabilities, and promotes the probabilistic safety
for the ego. The PDF control layer designs a feedback that optimally steers the
joint state PDF subject to the controlled ego dynamics while satisfying the
endpoint PDF constraints. Our computation for the PDF prediction layer
leverages the structure of the controlled Liouville PDE to evolve the joint PDF
values, as opposed to empirically approximating the PDFs. Our computation for
the PDF control layer leverages the differential flatness structure in vehicle
dynamics. We harness recent theoretical and algorithmic advances in optimal
mass transport, and the Schr\"{o}dinger bridge. The numerical simulations
illustrate the efficacy of the proposed framework.
