Gaussian Mixture Model for 3-DoF orientations

This paper presents learning and generalization algorithms for Gaussian Mixture Model (GMM) in order to accurately encode 3-DoF orientations and Euclidean variables in a common model. We employ correct displacement, integration and weighted averaging arithmetics for unit quaternions to adapt the learning and generalization methods of standard GMMs.We validate the proposed method in three different applications, learning a 3-dimensional rotation matrix, learning reachable space of a robot, and learning the motion model from demonstrations. We show good experimental results compared to the state-of-the-art method.

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