  Autonomous racing creates challenging control problems, but Model Predictive
Control (MPC) has made promising steps toward solving both the minimum lap-time
problem and head-to-head racing. Yet, accurate models of the system are
necessary for model-based control, including models of vehicle dynamics and
opponent behavior. Both dynamics model error and opponent behavior can be
modeled with Gaussian Process (GP) regression. GP models can be updated
iteratively from data collected using the controller, but the strength of the
GP model depends on the diversity of the training data. We propose a novel
active exploration mechanism for iterative GP regression that purposefully
collects additional data at regions of higher uncertainty in the GP model. In
the exploration, a MPC collects diverse data by balancing the racing objectives
and the exploration criterion; then the GP is re-trained. The process is
repeated iteratively; in later iterations, the exploration is deactivated, and
only the racing objectives are optimized. Thus, the MPC can achieve better
performance by leveraging the improved GP model. We validate our approach in
the highly realistic racing simulation platform Gran Turismo Sport of Sony
Interactive Entertainment Inc for a minimum lap time challenge, and in
numerical simulation of head-to-head. Our active exploration mechanism yields a
significant improvement in the GP prediction accuracy compared to previous
approaches and, thus, an improved racing performance.
