  We present a simplified model of a vehicle driving on a nonplanar road. A
parametric surface is used to describe the nonplanar road which can describe
any combination of curvature, bank and slope. We show that the proposed
modeling approach generalizes planar vehicle models that reference a
centerline, such as the Frenet model.
  We use the proposed approach for vehicle path planning and following using
model predictive control. We also model and control vehicle contact with the
road surface. We demonstrate that the proposed controller improves speed and
lane following on complex roads compared to planar vehicle controllers, and
mitigates loss of control on complex road surfaces including off-camber turns.
