  This paper addresses the trajectory-tracking problem under uncertain
road-surface conditions for autonomous vehicles. We propose a stochastic
nonlinear model predictive controller (SNMPC) that learns a tire--road friction
model online using standard automotive-grade sensors. Learning the entire
tire--road friction model in real time requires driving in the nonlinear,
potentially unstable regime of the vehicle dynamics, using a prediction model
that may not have fully converged. To handle this, we formulate the
tire-friction model learning in a Bayesian framework, and propose two
estimators that learn different aspects of the tire--road friction. The
estimators output the estimate of the tire-friction model as well as the
uncertainty of the estimate, which expresses the confidence in the model for
different driving regimes. The SNMPC exploits the uncertainty estimate in its
prediction model to take proper action when the uncertainty is large. We
validate the approach in an extensive Monte-Carlo study using real vehicle
parameters and in CarSim. The results when comparing to various MPC approaches
indicate a substantial reduction in constraint violations, as well as a
reduction in closed-loop cost. We also demonstrate the real-time feasibility in
automotive-grade processors using a dSPACE MicroAutoBox-II rapid prototyping
unit, showing a worst-case computation time of roughly 40ms.
