Gaussian process kernels for rotations and 6D rigid body motions

Gaussian Processes (GPs) are gaining increasing popularity due to their expressive power for learning the dynamics of non-linear time series data, e.g. for human motion prediction. However, so far they are restricted to Euclidean space: input data such as position and velocity need to be Euclidean. In this paper, we examine GPs over time series of 6D rigid body motions including large rotations. As the use of Euler angles with large rotations results in inaccurate predictions, we present an extension of the valid input data to quaternions H and dual quaternions H_D. The quality of a GP prediction over unit quaternions is compared with GP prediction over Euler angles. The results are evaluated based on experimental data from a quadrotor and in a learning task of a collision free 6D motion trajectory incorporating large rotations based on artificial data from a motion planner.