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This paper presents a problem of model learning for the purpose of learninghow to navigate a ball to a goal state in a circular maze environment with twodegrees of freedom. The motion of the ball in the maze environment isinfluenced by several non-linear effects such as dry friction and contacts,which are difficult to model physically. We propose a semiparametric model toestimate the motion dynamics of the ball based on Gaussian Process Regressionequipped with basis functions obtained from physics first principles. Theaccuracy of this semiparametric model is shown not only in estimation but alsoin prediction at n-steps ahead and its compared with standard algorithms formodel learning. The learned model is then used in a trajectory optimizationalgorithm to compute ball trajectories. We propose the system presented in thepaper as a benchmark problem for reinforcement and robot learning, for itsinteresting and challenging dynamics and its relative ease of reproducibility.

Semiparametrical Gaussian Processes Learning of Forward Dynamical Models for Navigating in a Circular Maze