Autonomous Robots

, Volume 42, Issue 6, pp 1151–1167 | Cite as

Gaussian process for 6-DoF rigid motions

  • Muriel Lang
  • Martin Kleinsteuber
  • Sandra Hirche


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.


Gaussian process Data-driven modelling Nonlinear dynamics Dual quaternions Covariance function Special Euclidean group Rigid motion dynamics Manifold modelling 



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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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringTechnical University MunichMunichGermany

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