  This paper presents an adaptive high performance control method for
autonomous miniature race cars. Racing dynamics are notoriously hard to model
from first principles, which is addressed by means of a cautious nonlinear
model predictive control (NMPC) approach that learns to improve its dynamics
model from data and safely increases racing performance. The approach makes use
of a Gaussian Process (GP) and takes residual model uncertainty into account
through a chance constrained formulation. We present a sparse GP approximation
with dynamically adjusting inducing inputs, enabling a real-time implementable
controller. The formulation is demonstrated in simulations, which show
significant improvement with respect to both lap time and constraint
satisfaction compared to an NMPC without model learning.
