Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/gaussian-process-for-6-dof-rigid-motions-UeaLm0Onvv
References (38)
-
W. Takano, Yoshihiko Nakamura (2007)
Incremental learning of full body motions via adaptive Factorial Hidden Markov Models -
P. Meer, R. Subbarao (2008)
Robust statistics over riemannian manifolds for computer vision -
R. Calandra, Jan Peters, C. Rasmussen, M. Deisenroth (2014)
Manifold Gaussian Processes for regression2016 International Joint Conference on Neural Networks (IJCNN)
-
Erhan Ata, Y. Yaylı (2008)
Dual unitary matrices and unit dual quaternions -
Muriel Lang, S. Hirche (2017)
Computationally Efficient Rigid-Body Gaussian Process for Motion DynamicsIEEE Robotics and Automation Letters, 2
-
S. Roweis, L. Saul (2000)
Nonlinear dimensionality reduction by locally linear embedding.Science, 290 5500
-
N. Sebanz, G. Knoblich (2009)
Prediction in Joint Action: What, When, and WhereTopics in cognitive science, 1 2
-
Jonathan Ko, D. Fox (2008)
GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation modelsAutonomous Robots, 27
-
M. Harandi, M. Salzmann, F. Porikli (2014)
Bregman Divergences for Infinite Dimensional Covariance Matrices2014 IEEE Conference on Computer Vision and Pattern Recognition
-
N. Jarrassé, J. Paik, V. Pasqui, G. Morel (2008)
How can human motion prediction increase transparency?2008 IEEE International Conference on Robotics and Automation
-
Jens Nilsson, Fei Sha, Michael Jordan (2007)
Regression on manifolds using kernel dimension reduction -
F. Thomas (2014)
Approaching Dual Quaternions From Matrix AlgebraIEEE Transactions on Robotics, 30
-
Hyuk-jin Kang, F. Park (2015)
Motion optimization using Gaussian process dynamical modelsMultibody System Dynamics, 34
-
K. Fukumizu, Bharath Sriperumbudur, A. Gretton, B. Scholkopf (2008)
Characteristic Kernels on Groups and Semigroups -
K Fukumizu, A Gretton, B Schölkopf, BK Sriperumbudur (2009)
Adv Neural Inf Process Syst -
(2007)
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE Gaussian Process Dynamical Model -
R. Urtasun, David Fleet, Andreas Geiger, J. Popović, Trevor Darrell, Neil Lawrence (2008)
Topologically-constrained latent variable models -
S. Khansari-Zadeh, A. Billard (2011)
Learning Stable Nonlinear Dynamical Systems With Gaussian Mixture ModelsIEEE Transactions on Robotics, 27
-
M. Belkin, P. Niyogi (2003)
Laplacian Eigenmaps for Dimensionality Reduction and Data RepresentationNeural Computation, 15
-
Radford Neal (2006)
Pattern Recognition and Machine LearningPattern Recognition and Machine Learning
-
Muriel Lang, O. Dunkley, S. Hirche (2014)
Gaussian process kernels for rotations and 6D rigid body motions2014 IEEE International Conference on Robotics and Automation (ICRA)
-
Sadeep Jayasumana, R. Hartley, M. Salzmann, Hongdong Li, M. Harandi (2013)
Kernel Methods on the Riemannian Manifold of Symmetric Positive Definite Matrices2013 IEEE Conference on Computer Vision and Pattern Recognition
-
JM Wang, DJ Fleet, A Hertzmann (2008)
Gaussian process dynamical models for human motionIEEE Transactions on Pattern Analysis and Machine Intelligence, 30
-
Jihun Ham, Daniel Lee, S. Mika, B. Scholkopf (2004)
A kernel view of the dimensionality reduction of manifoldsProceedings of the twenty-first international conference on Machine learning
-
J. Medina, M. Lawitzky, A. Mortl, Dongheui Lee, S. Hirche (2011)
An experience-driven robotic assistant acquiring human knowledge to improve haptic cooperation2011 IEEE/RSJ International Conference on Intelligent Robots and Systems
-
Seungsu Kim, A. Billard (2012)
Estimating the non-linear dynamics of free-flying objectsRobotics Auton. Syst., 60
-
C. Rasmussen, H. Nickisch (2010)
Gaussian Processes for Machine Learning (GPML) ToolboxJ. Mach. Learn. Res., 11
-
S. Vaerenbergh, M. Lázaro-Gredilla, I. Santamaría (2012)
Kernel Recursive Least-Squares Tracker for Time-Varying RegressionIEEE Transactions on Neural Networks and Learning Systems, 23
-
Muriel Lang, W. Feiten (2012)
MPG - Fast Forward Reasoning on 6 DOF Pose Uncertainty -
B. Corteville, E. Aertbeliën, H. Bruyninckx, J. Schutter, H. Brussel (2007)
Human-inspired robot assistant for fast point-to-point movementsProceedings 2007 IEEE International Conference on Robotics and Automation
-
J. Tenenbaum, V. Silva, J. Langford (2000)
A global geometric framework for nonlinear dimensionality reduction.Science, 290 5500
-
S. Miossec, A. Kheddar (2009)
Human motion in cooperative tasks: Moving object case study2008 IEEE International Conference on Robotics and Biomimetics
-
Dell Zhang, X. Chen, Wee Lee (2005)
Text classification with kernels on the multinomial manifold -
Y Matsuoka, H Durrant-Whyte, J Neira (2011)
Robotics: Science and systems VI -
Muriel Lang, M. Kleinsteuber, O. Dunkley, S. Hirche (2015)
Gaussian process dynamical models over dual quaternions2015 European Control Conference (ECC)
-
(2011)
2011).Robotics: Science and systems VI -
Muriel Lang (2017)
Approximation of probability density functions on the Euclidean group parametrized by dual quaternionsarXiv: Machine Learning
-
E. Castillo, B. Colosimo, S. Tajbakhsh (2015)
Geodesic Gaussian Processes for the Parametric Reconstruction of a Free-Form SurfaceTechnometrics, 57
- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Springer Science+Business Media, LLC, part of Springer Nature
- Subject
- Engineering; Robotics and Automation; Artificial Intelligence (incl. Robotics); Computer Imaging, Vision, Pattern Recognition and Graphics; Control, Robotics, Mechatronics
- ISSN
- 0929-5593
- eISSN
- 1573-7527
- DOI
- 10.1007/s10514-017-9683-4
- Publisher site
- See Article on Publisher Site
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.
Journal
Autonomous Robots – Springer Journals
Published: Nov 17, 2017