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Gaussian process for 6-DoF rigid motions

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Abstract

Data-driven modeling approaches receive significant attention in robotics as they are capable of representing system behavior to which first-order principles cannot be employed. Modeling of human motions, based on observations is one of the many application areas. So far, however, the available probabilistic approaches cannot handle dynamics evolving in the space of rigid motions, as rotations are not appropriately considered. In this article, we present a mathematical framework for Gaussian process modeling, where the valid input domain is generalized to full rigid motions, namely the special Euclidean group SE(3). The kernel functions inside the Gaussian process are modified to exploit properties of the input data representation by dual quaternions. We further prove that the presented covariance functions maintain the Gaussian process properties. The correctness and accuracy of our approach is validated on simulated and real human motion data. We analyze the estimation performance of the novel Gaussian process framework in comparison to state of the art techniques, and show significantly improved model behavior of rigid motions.

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Acknowledgements

The research leading to these results has received funding from the ERC Starting Grant “Control based on Human Models (con-humo)” under Grant agreement n\(^\circ \) 337654 and from the European Union Seventh Framework Programme FP7/ 2007–2013 under Grant agreement n\(^\circ \) 601165 of the project “WEARHAP—WEARable HAPtics for humans and robots”.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Technical University Munich, 80333, Munich, Germany

    Muriel Lang, Martin Kleinsteuber & Sandra Hirche

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  1. Muriel Lang
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  2. Martin Kleinsteuber
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  3. Sandra Hirche
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Correspondence to Muriel Lang.

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Lang, M., Kleinsteuber, M. & Hirche, S. Gaussian process for 6-DoF rigid motions. Auton Robot 42, 1151–1167 (2018). https://doi.org/10.1007/s10514-017-9683-4

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