This paper presents a problem of model learning to navigate a ball to a goal state in a circular maze environment with two degrees of freedom. Motion of the ball in the maze environment is influenced by several non-linear effects such as friction and contacts, which are difficult to model. We propose a hybrid model to estimate the dynamics of the ball in the maze based on Gaussian Process Regression equipped with basis functions obtained from physic first principles. The accuracy of the hybrid model is compared with standard algorithms for model learning to highlight its efficacy. The learned model is then used to design trajectories for the ball using a trajectory optimization algorithm. We also hope that the system presented in the paper can be used as a benchmark problem for reinforcement and robot learning for its interesting and challenging dynamics and its ease of reproducibility.
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