Computationally Efficient Rigid-Body Gaussian Process for Motion Dynamics

In this letter, we address the modeling and learning of complex nonlinear rigid-body motions employing Gaussian processes. As the common procedure of using Euler angles in the Gaussian process results in inaccurate predictions for large rotations, we represent the input data by axis-angle pseudovectors for rotations and Euclidean vectors for translation. Our decision in favor of this representation of the special Euclidean group SE(3) is due to its computational efficiency. To allow Gaussian process estimation on a non-Euclidean input domain, such as the space of rigid motions, we generalize the model by introducing novel mean and covariance functions on SE(3). We prove that those functions fulfill the requirements of Gaussian processes. The proposed approach is validated on simulated and on real human motion data. Our results demonstrate significant benefits of the proposed rigid-body Gaussian process with respect to alternative variants in terms of regression performance and computational efficiency.