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

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