  This paper presents a problem of model learning for the purpose of learning
how to navigate a ball to a goal state in a circular maze environment with two
degrees of freedom. The motion of the ball in the maze environment is
influenced by several non-linear effects such as dry friction and contacts,
which are difficult to model physically. We propose a semiparametric model to
estimate the motion dynamics of the ball based on Gaussian Process Regression
equipped with basis functions obtained from physics first principles. The
accuracy of this semiparametric model is shown not only in estimation but also
in prediction at n-steps ahead and its compared with standard algorithms for
model learning. The learned model is then used in a trajectory optimization
algorithm to compute ball trajectories. We propose the system presented in the
paper as a benchmark problem for reinforcement and robot learning, for its
interesting and challenging dynamics and its relative ease of reproducibility.
