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We propose a stochastic prediction-control framework to promote safety inautomated driving by directly controlling the joint state probability densityfunctions (PDFs) subject to the vehicle dynamics via trajectory-level statefeedback. To illustrate the main ideas, we focus on a multi-lane highwaydriving scenario although the proposed framework can be adapted to othercontexts. The computational pipeline consists of a PDF prediction layer,followed by a PDF control layer. The prediction layer performs moving horizonnonparametric forecasts for the ego and the non-ego vehicles' stochasticstates, and thereby derives safe target PDF for the ego. The latter is based onthe forecasted collision probabilities, and promotes the probabilistic safetyfor the ego. The PDF control layer designs a feedback that optimally steers thejoint state PDF subject to the controlled ego dynamics while satisfying theendpoint PDF constraints. Our computation for the PDF prediction layerleverages the structure of the controlled Liouville PDE to evolve the joint PDFvalues, as opposed to empirically approximating the PDFs. Our computation forthe PDF control layer leverages the differential flatness structure in vehicledynamics. We harness recent theoretical and algorithmic advances in optimalmass transport, and the Schr\"{o}dinger bridge. The numerical simulationsillustrate the efficacy of the proposed framework.

Prediction and Optimal Feedback Steering of Probability Density Functions for Safe Automated Driving